//! fixed reference date, fixed market data
public CapFloorTermVolCurve(Date settlementDate,
Calendar calendar,
BusinessDayConvention bdc,
List <Period> optionTenors,
List <double> vols,
DayCounter dc = null) // Actual365Fixed()
: base(settlementDate, calendar, bdc, dc ?? new Actual365Fixed())
{
nOptionTenors_ = optionTenors.Count;
optionTenors_ = optionTenors;
optionDates_ = new InitializedList <Date>(nOptionTenors_);
optionTimes_ = new InitializedList <double>(nOptionTenors_);
volHandles_ = new InitializedList <Handle <Quote> >(vols.Count);
vols_ = vols; // do not initialize with nOptionTenors_
checkInputs();
initializeOptionDatesAndTimes();
// fill dummy handles to allow generic handle-based computations later
for (int i = 0; i < nOptionTenors_; ++i)
{
volHandles_[i] = new Handle <Quote>(new SimpleQuote(vols_[i]));
}
interpolate();
}
public MersenneTwisterUniformRng(List <ulong> seeds)
{
mt = new InitializedList <ulong>(N);
seedInitialization(19650218UL);
int i = 1, j = 0, k = (N > seeds.Count ? N : seeds.Count);
for (; k != 0; k--)
{
mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >> 30)) * 1664525UL)) + seeds[j] + (ulong)j; /* non linear */
mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
i++; j++;
if (i >= N)
{
mt[0] = mt[N - 1];
i = 1;
}
if (j >= seeds.Count)
{
j = 0;
}
}
for (k = N - 1; k != 0; k--)
{
mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >> 30)) * 1566083941UL)) - (ulong)i; /* non linear */
mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
i++;
if (i >= N)
{
mt[0] = mt[N - 1];
i = 1;
}
}
mt[0] = 0x80000000UL; /*MSB is 1; assuring non-zero initial array*/
}
public Fj_Helper(Handle <PiecewiseTimeDependentHestonModel> model, double term, double strike, int j)
{
j_ = j;
term_ = term;
v0_ = model.link.v0();
x_ = Math.Log(model.link.s0());
sx_ = Math.Log(strike);
r_ = new InitializedList <double>(model.link.timeGrid().size() - 1);
q_ = new InitializedList <double>(model.link.timeGrid().size() - 1);
model_ = model;
timeGrid_ = model.link.timeGrid();
for (int i = 0; i < timeGrid_.size() - 1; ++i)
{
double begin = Math.Min(term_, timeGrid_[i]);
double end = Math.Min(term_, timeGrid_[i + 1]);
r_[i] = model.link.riskFreeRate().link.forwardRate(begin, end,
Compounding.Continuous, Frequency.NoFrequency).rate();
q_[i] = model.link.dividendYield().link.forwardRate(begin, end,
Compounding.Continuous, Frequency.NoFrequency).rate();
}
Utils.QL_REQUIRE(term_ < model_.link.timeGrid().Last(), () => "maturity is too large");
}
public override List <SparseMatrix> toMatrixDecomp()
{
List <SparseMatrix> retVal = new InitializedList <SparseMatrix>(1, mapT_.toMatrix());
return(retVal);
}
public static List <Func <Vector, double> > multiPathBasisSystem(int dim, int order, PolynomType polynomType)
{
List <Func <double, double> > b = pathBasisSystem(order, polynomType);
List <Func <Vector, double> > ret = new List <Func <Vector, double> >();
ret.Add((xx) => 1.0);
for (int i = 1; i <= order; ++i)
{
List <Func <Vector, double> > a = w(dim, i, polynomType, b);
foreach (var iter in a)
{
ret.Add(iter);
}
}
// remove-o-zap: now remove redundant functions.
// usually we do have a lot of them due to the construction schema.
// We use a more "hands on" method here.
List <bool> rm = new InitializedList <bool>(ret.Count, true);
Vector x = new Vector(dim), v = new Vector(ret.Count);
MersenneTwisterUniformRng rng = new MersenneTwisterUniformRng(1234UL);
for (int i = 0; i < 10; ++i)
{
int k;
// calculate random x vector
for (k = 0; k < dim; ++k)
{
x[k] = rng.next().value;
}
// get return values for all basis functions
for (k = 0; k < ret.Count; ++k)
{
v[k] = ret[k](x);
}
// find duplicates
for (k = 0; k < ret.Count; ++k)
{
if (v.First(xx => (Math.Abs(v[k] - xx) <= 10 * v[k] * Const.QL_EPSILON)).IsEqual(v.First() + k))
{
// don't remove this item, it's unique!
rm[k] = false;
}
}
}
int iter2 = 0;
for (int i = 0; i < rm.Count; ++i)
{
if (rm[i])
{
ret.RemoveAt(iter2);
}
else
{
++iter2;
}
}
return(ret);
}
public AmericanExercise(Date latest, bool payoffAtExpiry = false) : base(Type.American, payoffAtExpiry)
{
dates_ = new InitializedList <Date>(2);
dates_[0] = Date.minDate();
dates_[1] = latest;
}
protected void calculateNextGeneration(List <Candidate> population,
CostFunction costFunction)
{
List <Candidate> mirrorPopulation = null;
List <Candidate> oldPopulation = (List <Candidate>)population.Clone();
switch (configuration().strategy)
{
case Strategy.Rand1Standard:
{
population.Shuffle();
List <Candidate> shuffledPop1 = (List <Candidate>)population.Clone();
population.Shuffle();
List <Candidate> shuffledPop2 = (List <Candidate>)population.Clone();
population.Shuffle();
mirrorPopulation = (List <Candidate>)shuffledPop1.Clone();
for (int popIter = 0; popIter < population.Count; popIter++)
{
population[popIter].values = population[popIter].values
+ configuration().stepsizeWeight
*(shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
}
break;
case Strategy.BestMemberWithJitter:
{
population.Shuffle();
List <Candidate> shuffledPop1 = (List <Candidate>)population.Clone();
population.Shuffle();
Vector jitter = new Vector(population[0].values.size(), 0.0);
for (int popIter = 0; popIter < population.Count; popIter++)
{
for (int jitterIter = 0; jitterIter < jitter.Count; jitterIter++)
{
jitter[jitterIter] = rng_.nextReal();
}
population[popIter].values = bestMemberEver_.values
+ Vector.DirectMultiply(
shuffledPop1[popIter].values - population[popIter].values
, 0.0001 * jitter + configuration().stepsizeWeight);
}
mirrorPopulation = new InitializedList <Candidate>(population.Count);
mirrorPopulation.ForEach((ii, vv) => mirrorPopulation[ii] = (Candidate)bestMemberEver_.Clone());
}
break;
case Strategy.CurrentToBest2Diffs:
{
population.Shuffle();
List <Candidate> shuffledPop1 = (List <Candidate>)population.Clone();
population.Shuffle();
for (int popIter = 0; popIter < population.Count; popIter++)
{
population[popIter].values = oldPopulation[popIter].values
+ configuration().stepsizeWeight
*(bestMemberEver_.values - oldPopulation[popIter].values)
+ configuration().stepsizeWeight
*(population[popIter].values - shuffledPop1[popIter].values);
}
mirrorPopulation = (List <Candidate>)shuffledPop1.Clone();
}
break;
case Strategy.Rand1DiffWithPerVectorDither:
{
population.Shuffle();
List <Candidate> shuffledPop1 = (List <Candidate>)population.Clone();
population.Shuffle();
List <Candidate> shuffledPop2 = (List <Candidate>)population.Clone();
population.Shuffle();
mirrorPopulation = (List <Candidate>)shuffledPop1.Clone();
Vector FWeight = new Vector(population.First().values.size(), 0.0);
for (int fwIter = 0; fwIter < FWeight.Count; fwIter++)
{
FWeight[fwIter] = (1.0 - configuration().stepsizeWeight)
* rng_.nextReal() + configuration().stepsizeWeight;
}
for (int popIter = 0; popIter < population.Count; popIter++)
{
population[popIter].values = population[popIter].values
+ Vector.DirectMultiply(FWeight,
shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
}
break;
case Strategy.Rand1DiffWithDither:
{
population.Shuffle();
List <Candidate> shuffledPop1 = (List <Candidate>)population.Clone();
population.Shuffle();
List <Candidate> shuffledPop2 = (List <Candidate>)population.Clone();
population.Shuffle();
mirrorPopulation = (List <Candidate>)shuffledPop1.Clone();
double FWeight = (1.0 - configuration().stepsizeWeight) * rng_.nextReal()
+ configuration().stepsizeWeight;
for (int popIter = 0; popIter < population.Count; popIter++)
{
population[popIter].values = population[popIter].values
+ FWeight * (shuffledPop1[popIter].values -
shuffledPop2[popIter].values);
}
}
break;
case Strategy.EitherOrWithOptimalRecombination:
{
population.Shuffle();
List <Candidate> shuffledPop1 = (List <Candidate>)population.Clone();
population.Shuffle();
List <Candidate> shuffledPop2 = (List <Candidate>)population.Clone();
population.Shuffle();
mirrorPopulation = (List <Candidate>)shuffledPop1.Clone();
double probFWeight = 0.5;
if (rng_.nextReal() < probFWeight)
{
for (int popIter = 0; popIter < population.Count; popIter++)
{
population[popIter].values = oldPopulation[popIter].values
+ configuration().stepsizeWeight
*(shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
}
else
{
double K = 0.5 * (configuration().stepsizeWeight + 1); // invariant with respect to probFWeight used
for (int popIter = 0; popIter < population.Count; popIter++)
{
population[popIter].values = oldPopulation[popIter].values
+ K
* (shuffledPop1[popIter].values - shuffledPop2[popIter].values
- 2.0 * population[popIter].values);
}
}
}
break;
case Strategy.Rand1SelfadaptiveWithRotation:
{
population.Shuffle();
List <Candidate> shuffledPop1 = (List <Candidate>)population.Clone();
population.Shuffle();
List <Candidate> shuffledPop2 = (List <Candidate>)population.Clone();
population.Shuffle();
mirrorPopulation = (List <Candidate>)shuffledPop1.Clone();
adaptSizeWeights();
for (int popIter = 0; popIter < population.Count; popIter++)
{
if (rng_.nextReal() < 0.1)
{
population[popIter].values = rotateArray(bestMemberEver_.values);
}
else
{
population[popIter].values = bestMemberEver_.values
+ currGenSizeWeights_[popIter]
* (shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
}
}
break;
default:
Utils.QL_FAIL("Unknown strategy ("
+ Convert.ToInt32(configuration().strategy) + ")");
break;
}
// in order to avoid unnecessary copying we use the same population object for mutants
crossover(oldPopulation, population, population, mirrorPopulation,
costFunction);
}
public override void calculate()
{
// copy black version then adapt to others
double value = 0.0;
int optionlets = arguments_.startDates.Count;
List <double> values = new InitializedList <double>(optionlets, 0.0);
List <double> stdDevs = new InitializedList <double>(optionlets, 0.0);
List <double> forwards = new InitializedList <double> (optionlets, 0.0);
CapFloorType type = arguments_.type;
Handle <YoYInflationTermStructure> yoyTS
= index().yoyInflationTermStructure();
Handle <YieldTermStructure> nominalTS
= yoyTS.link.nominalTermStructure();
Date settlement = nominalTS.link.referenceDate();
for (int i = 0; i < optionlets; ++i)
{
Date paymentDate = arguments_.payDates[i];
if (paymentDate > settlement)
{
// discard expired caplets
double d = arguments_.nominals[i] *
arguments_.gearings[i] *
nominalTS.link.discount(paymentDate) *
arguments_.accrualTimes[i];
// We explicitly have the index and assume that
// the fixing is natural, i.e. no convexity adjustment.
// If that was required then we would also need
// nominal vols in the pricing engine, i.e. a different engine.
// This also means that we do not need the coupon to have
// a pricing engine to return the swaplet rate and then
// the adjusted fixing in the instrument.
forwards[i] = yoyTS.link.yoyRate(arguments_.fixingDates[i], new Period(0, TimeUnit.Days));
double forward = forwards[i];
Date fixingDate = arguments_.fixingDates[i];
double sqrtTime = 0.0;
if (fixingDate > volatility_.link.baseDate())
{
sqrtTime = Math.Sqrt(volatility_.link.timeFromBase(fixingDate));
}
if (type == CapFloorType.Cap || type == CapFloorType.Collar)
{
double strike = arguments_.capRates[i].Value;
if (sqrtTime > 0.0)
{
stdDevs[i] = Math.Sqrt(volatility_.link.totalVariance(fixingDate, strike, new Period(0, TimeUnit.Days)));
}
// sttDev=0 for already-fixed dates so everything on forward
values[i] = optionletImpl(Option.Type.Call, strike, forward, stdDevs[i], d);
}
if (type == CapFloorType.Floor || type == CapFloorType.Collar)
{
double strike = arguments_.floorRates[i].Value;
if (sqrtTime > 0.0)
{
stdDevs[i] = Math.Sqrt(volatility_.link.totalVariance(fixingDate, strike, new Period(0, TimeUnit.Days)));
}
double floorlet = optionletImpl(Option.Type.Put, strike, forward, stdDevs[i], d);
if (type == CapFloorType.Floor)
{
values[i] = floorlet;
}
else
{
// a collar is long a cap and short a floor
values[i] -= floorlet;
}
}
value += values[i];
}
}
results_.value = value;
results_.additionalResults["optionletsPrice"] = values;
results_.additionalResults["optionletsAtmForward"] = forwards;
if (type != CapFloorType.Collar)
{
results_.additionalResults["optionletsStdDev"] = stdDevs;
}
}
public override void calculate()
{
Utils.QL_REQUIRE(arguments_.settlementMethod != Settlement.Method.ParYieldCurve, () =>
"cash-settled (ParYieldCurve) swaptions not priced with tree engine");
Utils.QL_REQUIRE(model_ != null, () => "no model specified");
Date referenceDate;
DayCounter dayCounter;
ITermStructureConsistentModel tsmodel =
(ITermStructureConsistentModel)base.model_.link;
try
{
if (tsmodel != null)
{
referenceDate = tsmodel.termStructure().link.referenceDate();
dayCounter = tsmodel.termStructure().link.dayCounter();
}
else
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
}
catch
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
DiscretizedSwaption swaption = new DiscretizedSwaption(arguments_, referenceDate, dayCounter);
Lattice lattice;
if (lattice_ != null)
{
lattice = lattice_;
}
else
{
List <double> times = swaption.mandatoryTimes();
TimeGrid timeGrid = new TimeGrid(times, times.Count, timeSteps_);
lattice = model_.link.tree(timeGrid);
}
List <double> stoppingTimes = new InitializedList <double>(arguments_.exercise.dates().Count);
for (int i = 0; i < stoppingTimes.Count; ++i)
{
stoppingTimes[i] =
dayCounter.yearFraction(referenceDate,
arguments_.exercise.date(i));
}
swaption.initialize(lattice, stoppingTimes.Last());
double nextExercise;
List <double> listExercise = new List <double>();
listExercise.AddRange(stoppingTimes.FindAll(x => x >= 0));
nextExercise = listExercise[0];
swaption.rollback(nextExercise);
results_.value = swaption.presentValue();
}
private void initialize()
{
sqrtdt_[0] = Math.Sqrt(t_[0]);
for (int i = 1; i < size_; ++i)
{
sqrtdt_[i] = Math.Sqrt(t_[i] - t_[i - 1]);
}
// map is used to indicate which points are already constructed.
// If map[i] is zero, path point i is yet unconstructed.
// map[i]-1 is the index of the variate that constructs
// the path point # i.
List <int> map = new InitializedList <int>(size_);
// The first point in the construction is the global step.
map[size_ - 1] = 1;
// The global step is constructed from the first variate.
bridgeIndex_[0] = size_ - 1;
// The variance of the global step
stdDev_[0] = Math.Sqrt(t_[size_ - 1]);
// The global step to the last point in time is special.
leftWeight_[0] = rightWeight_[0] = 0.0;
for (int j = 0, i = 1; i < size_; ++i)
{
// Find the next unpopulated entry in the map.
while (map[j] != 0)
{
++j;
}
int k = j;
// Find the next populated entry in the map from there.
while (map[k] == 0)
{
++k;
}
// l-1 is now the index of the point to be constructed next.
int l = j + ((k - 1 - j) >> 1);
map[l] = i;
// The i-th Gaussian variate will be used to set point l-1.
bridgeIndex_[i] = l;
leftIndex_[i] = j;
rightIndex_[i] = k;
if (j != 0)
{
leftWeight_[i] = (t_[k] - t_[l]) / (t_[k] - t_[j - 1]);
rightWeight_[i] = (t_[l] - t_[j - 1]) / (t_[k] - t_[j - 1]);
stdDev_[i] =
Math.Sqrt(((t_[l] - t_[j - 1]) * (t_[k] - t_[l]))
/ (t_[k] - t_[j - 1]));
}
else
{
leftWeight_[i] = (t_[k] - t_[l]) / t_[k];
rightWeight_[i] = t_[l] / t_[k];
stdDev_[i] = Math.Sqrt(t_[l] * (t_[k] - t_[l]) / t_[k]);
}
j = k + 1;
if (j >= size_)
{
j = 0; // wrap around
}
}
}
public void calculate()
{
// we might have to call initialize even if the curve is initialized
// and not moving, just because helpers might be date relative and change
// with evaluation date change.
// anyway it makes little sense to use date relative helpers with a
// non-moving curve if the evaluation date changes
if (!initialized_ || ts_.moving_)
{
initialize();
}
// setup helpers
for (int j = firstAliveHelper_; j < n_; ++j)
{
BootstrapHelper <U> helper = ts_.instruments_[j];
// check for valid quote
Utils.QL_REQUIRE(helper.quote().link.isValid(), () =>
(j + 1) + " instrument (maturity: " +
helper.pillarDate() + ") has an invalid quote");
// don't try this at home!
// This call creates helpers, and removes "const".
// There is a significant interaction with observability.
ts_.setTermStructure(ts_.instruments_[j]);
}
List <double> times = ts_.times_;
List <double> data = ts_.data_;
double accuracy = accuracy_ != null ? accuracy_.Value : ts_.accuracy_;
int maxIterations = ts_.maxIterations() - 1;
// there might be a valid curve state to use as guess
bool validData = validCurve_;
for (int iteration = 0; ; ++iteration)
{
previousData_ = new List <double>(ts_.data_);
List <double?> minValues = new InitializedList <double?>(alive_ + 1, null);
List <double?> maxValues = new InitializedList <double?>(alive_ + 1, null);
List <int> attempts = new InitializedList <int>(alive_ + 1, 1);
for (int i = 1; i <= alive_; ++i)
{
// shorter aliases for readability and to avoid duplication
double?min = minValues[i];
double?max = maxValues[i];
// bracket root and calculate guess
if (min == null)
{
min = (minValue_ != null ? minValue_ :
ts_.minValueAfter(i, ts_, validData, firstAliveHelper_));
max = (maxValue_ != null ? maxValue_ :
ts_.maxValueAfter(i, ts_, validData, firstAliveHelper_));
}
else
{
min = (min.Value < 0.0 ? min.Value * minFactor_ : min.Value / minFactor_);
max = (max.Value > 0.0 ? max.Value * maxFactor_ : max.Value / maxFactor_);
}
double guess = ts_.guess(i, ts_, validData, firstAliveHelper_);
// adjust guess if needed
if (guess >= max.Value)
{
guess = max.Value - (max.Value - min.Value) / 5.0;
}
else if (guess <= min.Value)
{
guess = min.Value + (max.Value - min.Value) / 5.0;
}
// extend interpolation if needed
if (!validData)
{
try
{
// extend interpolation a point at a time
// including the pillar to be boostrapped
ts_.interpolation_ = ts_.interpolator_.interpolate(ts_.times_, i + 1, ts_.data_);
}
catch (Exception)
{
if (!ts_.interpolator_.global)
{
throw; // no chance to fix it in a later iteration
}
// otherwise use Linear while the target
// interpolation is not usable yet
ts_.interpolation_ = new Linear().interpolate(ts_.times_, i + 1, ts_.data_);
}
ts_.interpolation_.update();
}
try
{
var error = new BootstrapError <T, U>(ts_, ts_.instruments_[i - 1], i);
if (validData)
{
ts_.data_[i] = solver_.solve(error, accuracy, guess, min.Value, max.Value);
}
else
{
ts_.data_[i] = firstSolver_.solve(error, accuracy, guess, min.Value, max.Value);
}
}
catch (Exception e)
{
if (validCurve_)
{
// the previous curve state might have been a
// bad guess, so we retry without using it.
// This would be tricky to do here (we're
// inside multiple nested for loops, we need
// to re-initialize...), so we invalidate the
// curve, make a recursive call and then exit.
validCurve_ = initialized_ = false;
calculate();
return;
}
// If we have more attempts left on this iteration, try again. Note that the max and min
// bounds will be widened on the retry.
if (attempts[i] < maxAttempts_)
{
attempts[i]++;
i--;
continue;
}
if (dontThrow_)
{
// Use the fallback value
var error = new BootstrapError <T, U>(ts_, ts_.instruments_[i - 1], i);
ts_.data_[i] = dontThrowFallback(error, min.Value, max.Value, dontThrowSteps_);
// Remember to update the interpolation. If we don't and we are on the last "i", we will still
// have the last attempted value in the solver being used in ts_->interpolation_.
ts_.interpolation_.update();
}
else
{
Utils.QL_FAIL((iteration + 1) + " iteration: failed " +
"at " + (i) + " alive instrument, " +
"pillar " + ts_.instruments_[i - 1].pillarDate() + ", " +
"maturity " + ts_.instruments_[i - 1].maturityDate() +
", reference date " + ts_.dates_[0] +
": " + e.Message);
}
}
}
if (!loopRequired_)
{
break; // no need for convergence loop
}
// exit condition
double change = Math.Abs(data[1] - previousData_[1]);
for (int i = 2; i <= alive_; ++i)
{
change = Math.Max(change, Math.Abs(data[i] - previousData_[i]));
}
if (change <= accuracy) // convergence reached
{
break;
}
Utils.QL_REQUIRE(iteration < maxIterations, () =>
"convergence not reached after " + iteration +
" iterations; last improvement " + change +
", required accuracy " + accuracy);
validData = true;
}
validCurve_ = true;
}
public DiscretizedConvertible(ConvertibleBond.option.Arguments args,
GeneralizedBlackScholesProcess process, TimeGrid grid)
{
arguments_ = args;
process_ = process;
dividendValues_ = new Vector(arguments_.dividends.Count, 0.0);
Date settlementDate = process.riskFreeRate().link.referenceDate();
for (int i = 0; i < arguments_.dividends.Count; i++)
{
if (arguments_.dividends[i].date() >= settlementDate)
{
dividendValues_[i] = arguments_.dividends[i].amount() *
process.riskFreeRate().link.discount(arguments_.dividends[i].date());
}
}
DayCounter dayCounter = process.riskFreeRate().currentLink().dayCounter();
Date bondSettlement = arguments_.settlementDate;
stoppingTimes_ = new InitializedList <double>(arguments_.exercise.dates().Count, 0.0);
for (var i = 0; i < stoppingTimes_.Count; i++)
{
stoppingTimes_[i] = dayCounter.yearFraction(bondSettlement, arguments_.exercise.date(i));
}
callabilityTimes_ = new InitializedList <double>(arguments_.callabilityDates.Count, 0.0);
for (var i = 0; i < callabilityTimes_.Count; i++)
{
callabilityTimes_[i] = dayCounter.yearFraction(bondSettlement, arguments_.callabilityDates[i]);
}
couponTimes_ = new InitializedList <double>(arguments_.couponDates.Count, 0.0);
for (var i = 0; i < couponTimes_.Count; i++)
{
couponTimes_[i] = dayCounter.yearFraction(bondSettlement, arguments_.couponDates[i]);
}
dividendTimes_ = new InitializedList <double>(arguments_.dividendDates.Count, 0.0);
for (var i = 0; i < dividendTimes_.Count; i++)
{
dividendTimes_[i] = dayCounter.yearFraction(bondSettlement, arguments_.dividendDates[i]);
}
if (!grid.empty())
{
// adjust times to grid
for (var i = 0; i < stoppingTimes_.Count; i++)
{
stoppingTimes_[i] = grid.closestTime(stoppingTimes_[i]);
}
for (var i = 0; i < couponTimes_.Count; i++)
{
couponTimes_[i] = grid.closestTime(couponTimes_[i]);
}
for (var i = 0; i < dividendTimes_.Count; i++)
{
dividendTimes_[i] = grid.closestTime(dividendTimes_[i]);
}
for (var i = 0; i < callabilityTimes_.Count; i++)
{
callabilityTimes_[i] = grid.closestTime(callabilityTimes_[i]);
}
}
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
int stationaryStateIterations_ = 0;
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x = P.currentValue();
iteration_ = 0;
n_ = x.size();
ptry_ = new Vector(n_, 0.0);
// build vertices
vertices_ = new InitializedList <Vector>(n_ + 1, x);
for (i_ = 0; i_ < n_; i_++)
{
Vector direction = new Vector(n_, 0.0);
direction[i_] = 1.0;
Vector tmp = vertices_[i_ + 1];
P.constraint().update(ref tmp, direction, lambda_);
vertices_[i_ + 1] = tmp;
}
values_ = new Vector(n_ + 1, 0.0);
for (i_ = 0; i_ <= n_; i_++)
{
if (!P.constraint().test(vertices_[i_]))
{
values_[i_] = Double.MaxValue;
}
else
{
values_[i_] = P.value(vertices_[i_]);
}
if (Double.IsNaN(ytry_))
{
// handle NAN
values_[i_] = Double.MaxValue;
}
}
// minimize
T_ = T0_;
yb_ = Double.MaxValue;
pb_ = new Vector(n_, 0.0);
do
{
iterationT_ = iteration_;
do
{
sum_ = new Vector(n_, 0.0);
for (i_ = 0; i_ <= n_; i_++)
{
sum_ += vertices_[i_];
}
tt_ = -T_;
ilo_ = 0;
ihi_ = 1;
ynhi_ = values_[0] + tt_ * Math.Log(rng_.next().value);
ylo_ = ynhi_;
yhi_ = values_[1] + tt_ * Math.Log(rng_.next().value);
if (ylo_ > yhi_)
{
ihi_ = 0;
ilo_ = 1;
ynhi_ = yhi_;
yhi_ = ylo_;
ylo_ = ynhi_;
}
for (i_ = 2; i_ < n_ + 1; i_++)
{
yt_ = values_[i_] + tt_ * Math.Log(rng_.next().value);
if (yt_ <= ylo_)
{
ilo_ = i_;
ylo_ = yt_;
}
if (yt_ > yhi_)
{
ynhi_ = yhi_;
ihi_ = i_;
yhi_ = yt_;
}
else
{
if (yt_ > ynhi_)
{
ynhi_ = yt_;
}
}
}
// GSL end criterion in x (cf. above)
if (endCriteria.checkStationaryPoint(simplexSize(), 0.0,
ref stationaryStateIterations_,
ref ecType) ||
endCriteria.checkMaxIterations(iteration_, ref ecType))
{
// no matter what, we return the best ever point !
P.setCurrentValue(pb_);
P.setFunctionValue(yb_);
return(ecType);
}
iteration_ += 2;
amotsa(P, -1.0);
if (ytry_ <= ylo_)
{
amotsa(P, 2.0);
}
else
{
if (ytry_ >= ynhi_)
{
ysave_ = yhi_;
amotsa(P, 0.5);
if (ytry_ >= ysave_)
{
for (i_ = 0; i_ < n_ + 1; i_++)
{
if (i_ != ilo_)
{
for (j_ = 0; j_ < n_; j_++)
{
sum_[j_] = 0.5 * (vertices_[i_][j_] +
vertices_[ilo_][j_]);
vertices_[i_][j_] = sum_[j_];
}
values_[i_] = P.value(sum_);
}
}
iteration_ += n_;
for (i_ = 0; i_ < n_; i_++)
{
sum_[i_] = 0.0;
}
for (i_ = 0; i_ <= n_; i_++)
{
sum_ += vertices_[i_];
}
}
}
else
{
iteration_ += 1;
}
}
}while (iteration_ <
iterationT_ + (scheme_ == Scheme.ConstantFactor ? m_ : 1));
switch (scheme_)
{
case Scheme.ConstantFactor:
T_ *= (1.0 - epsilon_);
break;
case Scheme.ConstantBudget:
if (iteration_ <= K_)
{
T_ = T0_ *
Math.Pow(1.0 - Convert.ToDouble(iteration_) / Convert.ToDouble(K_), alpha_);
}
else
{
T_ = 0.0;
}
break;
}
}while (true);
}
public override void calculate()
{
Utils.QL_REQUIRE(arguments_.settlementMethod != Settlement.Method.ParYieldCurve, () =>
"cash-settled (ParYieldCurve) swaptions not priced by Jamshidian engine");
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European, () =>
"cannot use the Jamshidian decomposition on exotic swaptions");
Utils.QL_REQUIRE(arguments_.swap.spread.IsEqual(0.0), () =>
"non zero spread (" + arguments_.swap.spread + ") not allowed");
Date referenceDate;
DayCounter dayCounter;
ITermStructureConsistentModel tsmodel = (ITermStructureConsistentModel)base.model_.link;
try
{
if (tsmodel != null)
{
referenceDate = tsmodel.termStructure().link.referenceDate();
dayCounter = tsmodel.termStructure().link.dayCounter();
}
else
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
}
catch
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
List <double> amounts = new InitializedList <double>(arguments_.fixedCoupons.Count);
for (int i = 0; i < amounts.Count; i++)
{
amounts[i] = arguments_.fixedCoupons[i];
}
amounts[amounts.Count - 1] = amounts.Last() + arguments_.nominal;
double maturity = dayCounter.yearFraction(referenceDate,
arguments_.exercise.date(0));
List <double> fixedPayTimes = new InitializedList <double>(arguments_.fixedPayDates.Count);
for (int i = 0; i < fixedPayTimes.Count; i++)
{
fixedPayTimes[i] =
dayCounter.yearFraction(referenceDate,
arguments_.fixedPayDates[i]);
}
rStarFinder finder = new rStarFinder(model_, arguments_.nominal, maturity,
fixedPayTimes, amounts);
Brent s1d = new Brent();
double minStrike = -10.0;
double maxStrike = 10.0;
s1d.setMaxEvaluations(10000);
s1d.setLowerBound(minStrike);
s1d.setUpperBound(maxStrike);
double rStar = s1d.solve(finder, 1e-8, 0.05, minStrike, maxStrike);
Option.Type w = arguments_.type == VanillaSwap.Type.Payer ?
Option.Type.Put : Option.Type.Call;
int size = arguments_.fixedCoupons.Count;
double value = 0.0;
for (int i = 0; i < size; i++)
{
double fixedPayTime =
dayCounter.yearFraction(referenceDate,
arguments_.fixedPayDates[i]);
double strike = model_.link.discountBond(maturity,
fixedPayTime,
rStar);
double dboValue = model_.link.discountBondOption(
w, strike, maturity,
fixedPayTime);
value += amounts[i] * dboValue;
}
results_.value = value;
}
protected LmCorrelationModel(int size, int nArguments)
{
size_ = size;
arguments_ = new InitializedList <Parameter>(nArguments);
}
public List <double> value(double x, List <double> y)
{
List <double> res = new InitializedList <double>(1, ode1d_(x, y[0]));
return(res);
}
public FdmLinearOpIterator(List <int> dim)
{
index_ = 0;
dim_ = dim;
coordinates_ = new InitializedList <int>(dim.Count, 0);
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// set up of the problem
//double ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
double xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
// Initialize vertices of the simplex
bool end = false;
int n = x_.Count;
vertices_ = new InitializedList <Vector>(n + 1, x_);
for (int i = 0; i < n; i++)
{
Vector direction = new Vector(n, 0.0);
Vector vertice = vertices_[i + 1];
direction[i] = 1.0;
P.constraint().update(ref vertice, direction, lambda_);
vertices_[i + 1] = vertice;
}
// Initialize function values at the vertices of the simplex
values_ = new Vector(n + 1, 0.0);
for (int i = 0; i <= n; i++)
{
values_[i] = P.value(vertices_[i]);
}
// Loop looking for minimum
do
{
sum_ = new Vector(n, 0.0);
for (int i = 0; i <= n; i++)
{
sum_ += vertices_[i];
}
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
int iLowest = 0;
int iHighest;
int iNextHighest;
if (values_[0] < values_[1])
{
iHighest = 1;
iNextHighest = 0;
}
else
{
iHighest = 0;
iNextHighest = 1;
}
for (int i = 1; i <= n; i++)
{
if (values_[i] > values_[iHighest])
{
iNextHighest = iHighest;
iHighest = i;
}
else
{
if ((values_[i] > values_[iNextHighest]) && i != iHighest)
{
iNextHighest = i;
}
}
if (values_[i] < values_[iLowest])
{
iLowest = i;
}
}
// Now compute accuracy, update iteration number and check end criteria
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
double simplexSize = Utils.computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryPoint(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(ecType);
}
// If end criteria is not met, continue
double factor = -1.0;
double vTry = extrapolate(ref P, iHighest, ref factor);
if ((vTry <= values_[iLowest]) && (factor.IsEqual(-1.0)))
{
factor = 2.0;
extrapolate(ref P, iHighest, ref factor);
}
else if (Math.Abs(factor) > Const.QL_EPSILON)
{
if (vTry >= values_[iNextHighest])
{
double vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(ref P, iHighest, ref factor);
if (vTry >= vSave && Math.Abs(factor) > Const.QL_EPSILON)
{
for (int i = 0; i <= n; i++)
{
if (i != iLowest)
{
#if QL_ARRAY_EXPRESSIONS
vertices_[i] = 0.5 * (vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (Math.Abs(factor) <= Const.QL_EPSILON)
{
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(EndCriteria.Type.StationaryFunctionValue);
}
}while (end == false);
Utils.QL_FAIL("optimization failed: unexpected behaviour");
return(0);
}
public SobolRsg(int dimensionality, ulong seed, DirectionIntegers directionIntegers)
{
dimensionality_ = dimensionality;
sequenceCounter_ = 0;
firstDraw_ = true;
sequence_ = new Sample <List <double> >(new InitializedList <double>(dimensionality), 1.0);
integerSequence_ = new InitializedList <ulong>(dimensionality);
directionIntegers_ = new InitializedList <List <ulong> >(dimensionality);
for (int i = 0; i < dimensionality; i++)
{
directionIntegers_[i] = new InitializedList <ulong>(bits_);
}
Utils.QL_REQUIRE(dimensionality > 0, () => "dimensionality must be greater than 0");
Utils.QL_REQUIRE(dimensionality <= PPMT_MAX_DIM, () =>
"dimensionality " + dimensionality + " exceeds the number of available " +
"primitive polynomials modulo two (" + PPMT_MAX_DIM + ")");
// initializes coefficient array of the k-th primitive polynomial
// and degree of the k-th primitive polynomial
List <uint> degree = new InitializedList <uint>(dimensionality_);
List <long> ppmt = new InitializedList <long>(dimensionality_);
bool useAltPolynomials = false;
if (directionIntegers == DirectionIntegers.Kuo || directionIntegers == DirectionIntegers.Kuo2 ||
directionIntegers == DirectionIntegers.Kuo3 || directionIntegers == DirectionIntegers.SobolLevitan ||
directionIntegers == DirectionIntegers.SobolLevitanLemieux)
{
useAltPolynomials = true;
}
// degree 0 is not used
ppmt[0] = 0;
degree[0] = 0;
int k, index;
uint currentDegree = 1;
k = 1;
index = 0;
uint altDegree = useAltPolynomials ? maxAltDegree : 0;
for (; k < Math.Min(dimensionality_, altDegree); k++, index++)
{
ppmt[k] = AltPrimitivePolynomials[currentDegree - 1][index];
if (ppmt[k] == -1)
{
++currentDegree;
index = 0;
ppmt[k] = AltPrimitivePolynomials[currentDegree - 1][index];
}
degree[k] = currentDegree;
}
for (; k < dimensionality_; k++, index++)
{
ppmt[k] = PrimitivePolynomials[currentDegree - 1][index];
if (ppmt[k] == -1)
{
++currentDegree;
index = 0;
ppmt[k] = PrimitivePolynomials[currentDegree - 1][index];
}
degree[k] = currentDegree;
}
// initializes bits_ direction integers for each dimension
// and store them into directionIntegers_[dimensionality_][bits_]
//
// In each dimension k with its associated primitive polynomial,
// the first degree_[k] direction integers can be chosen freely
// provided that only the l leftmost bits can be non-zero, and
// that the l-th leftmost bit must be set
// degenerate (no free direction integers) first dimension
int j;
for (j = 0; j < bits_; j++)
{
directionIntegers_[0][j] = (1UL << (bits_ - j - 1));
}
int maxTabulated = 0;
// dimensions from 2 (k=1) to maxTabulated (k=maxTabulated-1) included
// are initialized from tabulated coefficients
switch (directionIntegers)
{
case DirectionIntegers.Unit:
maxTabulated = dimensionality_;
for (k = 1; k < maxTabulated; k++)
{
for (int l = 1; l <= degree[k]; l++)
{
directionIntegers_[k][l - 1] = 1UL;
directionIntegers_[k][l - 1] <<= (bits_ - l);
}
}
break;
case DirectionIntegers.Jaeckel:
// maxTabulated=32
maxTabulated = initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.SobolLevitan:
// maxTabulated=40
maxTabulated = SLinitializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (SLinitializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = SLinitializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.SobolLevitanLemieux:
// maxTabulated=360
maxTabulated = Linitializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (Linitializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = Linitializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.JoeKuoD5:
// maxTabulated=1898
maxTabulated = JoeKuoD5initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (JoeKuoD5initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = JoeKuoD5initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.JoeKuoD6:
// maxTabulated=1799
maxTabulated = JoeKuoD6initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (JoeKuoD6initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = JoeKuoD6initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.JoeKuoD7:
// maxTabulated=1898
maxTabulated = JoeKuoD7initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (JoeKuoD7initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = JoeKuoD7initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.Kuo:
// maxTabulated=4925
maxTabulated = Kuoinitializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (Kuoinitializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = Kuoinitializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.Kuo2:
// maxTabulated=3946
maxTabulated = Kuo2initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (Kuo2initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = Kuo2initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.Kuo3:
// maxTabulated=4585
maxTabulated = Kuo3initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (Kuo3initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = Kuo3initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
default:
break;
}
// random initialization for higher dimensions
if (dimensionality_ > maxTabulated)
{
MersenneTwisterUniformRng uniformRng = new MersenneTwisterUniformRng(seed);
for (k = maxTabulated; k < dimensionality_; k++)
{
for (int l = 1; l <= degree[k]; l++)
{
do
{
// u is in (0,1)
double u = uniformRng.next().value;
// the direction integer has at most the
// rightmost l bits non-zero
directionIntegers_[k][l - 1] = (ulong)(u * (1UL << l));
}while ((directionIntegers_[k][l - 1] & 1UL) == 0);
// iterate until the direction integer is odd
// that is it has the rightmost bit set
// shifting bits_-l bits to the left
// we are guaranteed that the l-th leftmost bit
// is set, and only the first l leftmost bit
// can be non-zero
directionIntegers_[k][l - 1] <<= (bits_ - l);
}
}
}
// computation of directionIntegers_[k][l] for l>=degree_[k]
// by recurrence relation
for (k = 1; k < dimensionality_; k++)
{
uint gk = degree[k];
for (int l = (int)gk; l < bits_; l++)
{
// eq. 8.19 "Monte Carlo Methods in Finance" by P. Jдckel
ulong n = (directionIntegers_[k][(int)(l - gk)] >> (int)gk);
// a[k][j] are the coefficients of the monomials in ppmt[k]
// The highest order coefficient a[k][0] is not actually
// used in the recurrence relation, and the lowest order
// coefficient a[k][gk] is always set: this is the reason
// why the highest and lowest coefficient of
// the polynomial ppmt[k] are not included in its encoding,
// provided that its degree is known.
// That is: a[k][j] = ppmt[k] >> (gk-j-1)
for (uint z = 1; z < gk; z++)
{
// XORed with a selection of (unshifted) direction
// integers controlled by which of the a[k][j] are set
if ((((ulong)ppmt[k] >> (int)(gk - z - 1)) & 1UL) != 0)
{
n ^= directionIntegers_[k][(int)(l - z)];
}
}
// a[k][gk] is always set, so directionIntegers_[k][l-gk]
// will always enter
n ^= directionIntegers_[k][(int)(l - gk)];
directionIntegers_[k][l] = n;
}
}
// initialize the Sobol integer/double vectors
// first draw
for (k = 0; k < dimensionality_; k++)
{
integerSequence_[k] = directionIntegers_[k][0];
}
}
protected GMRESResult solveImpl(Vector b, Vector x0)
{
double bn = Vector.Norm2(b);
GMRESResult result;
if (bn.IsEqual(0.0))
{
result = new GMRESResult(new InitializedList <double>(1, 0.0), b);
return(result);
}
Vector x = !x0.empty() ? x0 : new Vector(b.size(), 0.0);
Vector r = b - A_(x);
double g = Vector.Norm2(r);
if (g / bn < relTol_)
{
result = new GMRESResult(new InitializedList <double>(1, g / bn), x);
return(result);
}
List <Vector> v = new InitializedList <Vector>(1, r / g);
List <Vector> h = new InitializedList <Vector>(1, new Vector(maxIter_, 0.0));
List <double> c = new List <double>(maxIter_ + 1),
s = new List <double>(maxIter_ + 1),
z = new List <double>(maxIter_ + 1);
z[0] = g;
List <double> errors = new InitializedList <double>(1, g / bn);
for (int j = 0; j < maxIter_ && errors.Last() >= relTol_; ++j)
{
h.Add(new Vector(maxIter_, 0.0));
Vector w = A_((M_ != null) ? M_(v[j]) : v[j]);
for (int i = 0; i <= j; ++i)
{
h[i][j] = Vector.DotProduct(w, v[i]);
w -= h[i][j] * v[i];
}
h[j + 1][j] = Vector.Norm2(w);
if (h[j + 1][j] < Const.QL_EPSILON * Const.QL_EPSILON)
{
break;
}
v.Add(w / h[j + 1][j]);
for (int i = 0; i < j; ++i)
{
double h0 = c[i] * h[i][j] + s[i] * h[i + 1][j];
double h1 = -s[i] * h[i][j] + c[i] * h[i + 1][j];
h[i][j] = h0;
h[i + 1][j] = h1;
}
double nu = Math.Sqrt((h[j][j]) * (h[j][j])
+ (h[j + 1][j]) * (h[j + 1][j]));
c[j] = h[j][j] / nu;
s[j] = h[j + 1][j] / nu;
h[j][j] = nu;
h[j + 1][j] = 0.0;
z[j + 1] = -s[j] * z[j];
z[j] = c[j] * z[j];
errors.Add(Math.Abs(z[j + 1] / bn));
}
int k = v.Count - 1;
Vector y = new Vector(k, 0.0);
y[k - 1] = z[k - 1] / h[k - 1][k - 1];
for (int i = k - 2; i >= 0; --i)
{
y[i] = (z[i] - h[i].inner_product(
i + 1, k, i + 1, y, 0.0)) / h[i][i];
}
Vector xm = new Vector(x.Count, 0.0);
for (int i = 0; i < x.Count; i++)
{
xm[i] = v[i].inner_product(0, k, 0, y, 0.0);
}
xm = x + ((M_ != null) ? M_(xm) : xm);
result = new GMRESResult(errors, xm);
return(result);
}
public override void update()
{
Vector tmp = new Vector(size_);
List <double> dx = new InitializedList <double>(size_ - 1),
S = new InitializedList <double>(size_ - 1);
for (int i = 0; i < size_ - 1; ++i)
{
dx[i] = xBegin_[i + 1] - xBegin_[i];
S[i] = (yBegin_[i + 1] - yBegin_[i]) / dx[i];
}
// first derivative approximation
if (da_ == CubicInterpolation.DerivativeApprox.Spline)
{
TridiagonalOperator L = new TridiagonalOperator(size_);
for (int i = 1; i < size_ - 1; ++i)
{
L.setMidRow(i, dx[i], 2.0 * (dx[i] + dx[i - 1]), dx[i - 1]);
tmp[i] = 3.0 * (dx[i] * S[i - 1] + dx[i - 1] * S[i]);
}
// left boundary condition
switch (leftType_)
{
case CubicInterpolation.BoundaryCondition.NotAKnot:
// ignoring end condition value
L.setFirstRow(dx[1] * (dx[1] + dx[0]), (dx[0] + dx[1]) * (dx[0] + dx[1]));
tmp[0] = S[0] * dx[1] * (2.0 * dx[1] + 3.0 * dx[0]) + S[1] * dx[0] * dx[0];
break;
case CubicInterpolation.BoundaryCondition.FirstDerivative:
L.setFirstRow(1.0, 0.0);
tmp[0] = leftValue_;
break;
case CubicInterpolation.BoundaryCondition.SecondDerivative:
L.setFirstRow(2.0, 1.0);
tmp[0] = 3.0 * S[0] - leftValue_ * dx[0] / 2.0;
break;
case CubicInterpolation.BoundaryCondition.Periodic:
// ignoring end condition value
throw new NotImplementedException("this end condition is not implemented yet");
case CubicInterpolation.BoundaryCondition.Lagrange:
L.setFirstRow(1.0, 0.0);
tmp[0] = cubicInterpolatingPolynomialDerivative(
this.xBegin_[0], this.xBegin_[1],
this.xBegin_[2], this.xBegin_[3],
this.yBegin_[0], this.yBegin_[1],
this.yBegin_[2], this.yBegin_[3],
this.xBegin_[0]);
break;
default:
throw new ArgumentException("unknown end condition");
}
// right boundary condition
switch (rightType_)
{
case CubicInterpolation.BoundaryCondition.NotAKnot:
// ignoring end condition value
L.setLastRow(-(dx[size_ - 2] + dx[size_ - 3]) * (dx[size_ - 2] + dx[size_ - 3]),
-dx[size_ - 3] * (dx[size_ - 3] + dx[size_ - 2]));
tmp[size_ - 1] = -S[size_ - 3] * dx[size_ - 2] * dx[size_ - 2] -
S[size_ - 2] * dx[size_ - 3] * (3.0 * dx[size_ - 2] + 2.0 * dx[size_ - 3]);
break;
case CubicInterpolation.BoundaryCondition.FirstDerivative:
L.setLastRow(0.0, 1.0);
tmp[size_ - 1] = rightValue_;
break;
case CubicInterpolation.BoundaryCondition.SecondDerivative:
L.setLastRow(1.0, 2.0);
tmp[size_ - 1] = 3.0 * S[size_ - 2] + rightValue_ * dx[size_ - 2] / 2.0;
break;
case CubicInterpolation.BoundaryCondition.Periodic:
// ignoring end condition value
throw new NotImplementedException("this end condition is not implemented yet");
case CubicInterpolation.BoundaryCondition.Lagrange:
L.setLastRow(0.0, 1.0);
tmp[size_ - 1] = cubicInterpolatingPolynomialDerivative(
this.xBegin_[size_ - 4], this.xBegin_[size_ - 3],
this.xBegin_[size_ - 2], this.xBegin_[size_ - 1],
this.yBegin_[size_ - 4], this.yBegin_[size_ - 3],
this.yBegin_[size_ - 2], this.yBegin_[size_ - 1],
this.xBegin_[size_ - 1]);
break;
default:
throw new ArgumentException("unknown end condition");
}
// solve the system
tmp = L.solveFor(tmp);
}
else if (da_ == CubicInterpolation.DerivativeApprox.SplineOM1)
{
Matrix T_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
T_[i, i] = dx[i] / 6.0;
T_[i, i + 1] = (dx[i + 1] + dx[i]) / 3.0;
T_[i, i + 2] = dx[i + 1] / 6.0;
}
Matrix S_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
S_[i, i] = 1.0 / dx[i];
S_[i, i + 1] = -(1.0 / dx[i + 1] + 1.0 / dx[i]);
S_[i, i + 2] = 1.0 / dx[i + 1];
}
Matrix Up_ = new Matrix(size_, 2, 0.0);
Up_[0, 0] = 1;
Up_[size_ - 1, 1] = 1;
Matrix Us_ = new Matrix(size_, size_ - 2, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
Us_[i + 1, i] = 1;
}
Matrix Z_ = Us_ * Matrix.inverse(T_ * Us_);
Matrix I_ = new Matrix(size_, size_, 0.0);
for (int i = 0; i < size_; ++i)
{
I_[i, i] = 1;
}
Matrix V_ = (I_ - Z_ * T_) * Up_;
Matrix W_ = Z_ * S_;
Matrix Q_ = new Matrix(size_, size_, 0.0);
Q_[0, 0] = 1.0 / (size_ - 1) * dx[0] * dx[0] * dx[0];
Q_[0, 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[0] * dx[0] * dx[0];
for (int i = 1; i < size_ - 1; ++i)
{
Q_[i, i - 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[i - 1] * dx[i - 1] * dx[i - 1];
Q_[i, i] = 1.0 / (size_ - 1) * dx[i] * dx[i] * dx[i] + 1.0 / (size_ - 1) * dx[i - 1] * dx[i - 1] * dx[i - 1];
Q_[i, i + 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[i] * dx[i] * dx[i];
}
Q_[size_ - 1, size_ - 2] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[size_ - 2] * dx[size_ - 2] * dx[size_ - 2];
Q_[size_ - 1, size_ - 1] = 1.0 / (size_ - 1) * dx[size_ - 2] * dx[size_ - 2] * dx[size_ - 2];
Matrix J_ = (I_ - V_ * Matrix.inverse(Matrix.transpose(V_) * Q_ * V_) * Matrix.transpose(V_) * Q_) * W_;
Vector Y_ = new Vector(size_);
for (int i = 0; i < size_; ++i)
{
Y_[i] = this.yBegin_[i];
}
Vector D_ = J_ * Y_;
for (int i = 0; i < size_ - 1; ++i)
{
tmp[i] = (Y_[i + 1] - Y_[i]) / dx[i] - (2.0 * D_[i] + D_[i + 1]) * dx[i] / 6.0;
}
tmp[size_ - 1] = tmp[size_ - 2] + D_[size_ - 2] * dx[size_ - 2] + (D_[size_ - 1] - D_[size_ - 2]) * dx[size_ - 2] / 2.0;
}
else if (da_ == CubicInterpolation.DerivativeApprox.SplineOM2)
{
Matrix T_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
T_[i, i] = dx[i] / 6.0;
T_[i, i + 1] = (dx[i] + dx[i + 1]) / 3.0;
T_[i, i + 2] = dx[i + 1] / 6.0;
}
Matrix S_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
S_[i, i] = 1.0 / dx[i];
S_[i, i + 1] = -(1.0 / dx[i + 1] + 1.0 / dx[i]);
S_[i, i + 2] = 1.0 / dx[i + 1];
}
Matrix Up_ = new Matrix(size_, 2, 0.0);
Up_[0, 0] = 1;
Up_[size_ - 1, 1] = 1;
Matrix Us_ = new Matrix(size_, size_ - 2, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
Us_[i + 1, i] = 1;
}
Matrix Z_ = Us_ * Matrix.inverse(T_ * Us_);
Matrix I_ = new Matrix(size_, size_, 0.0);
for (int i = 0; i < size_; ++i)
{
I_[i, i] = 1;
}
Matrix V_ = (I_ - Z_ * T_) * Up_;
Matrix W_ = Z_ * S_;
Matrix Q_ = new Matrix(size_, size_, 0.0);
Q_[0, 0] = 1.0 / (size_ - 1) * dx[0];
Q_[0, 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[0];
for (int i = 1; i < size_ - 1; ++i)
{
Q_[i, i - 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[i - 1];
Q_[i, i] = 1.0 / (size_ - 1) * dx[i] + 1.0 / (size_ - 1) * dx[i - 1];
Q_[i, i + 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[i];
}
Q_[size_ - 1, size_ - 2] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[size_ - 2];
Q_[size_ - 1, size_ - 1] = 1.0 / (size_ - 1) * dx[size_ - 2];
Matrix J_ = (I_ - V_ * Matrix.inverse(Matrix.transpose(V_) * Q_ * V_) * Matrix.transpose(V_) * Q_) * W_;
Vector Y_ = new Vector(size_);
for (int i = 0; i < size_; ++i)
{
Y_[i] = this.yBegin_[i];
}
Vector D_ = J_ * Y_;
for (int i = 0; i < size_ - 1; ++i)
{
tmp[i] = (Y_[i + 1] - Y_[i]) / dx[i] - (2.0 * D_[i] + D_[i + 1]) * dx[i] / 6.0;
}
tmp[size_ - 1] = tmp[size_ - 2] + D_[size_ - 2] * dx[size_ - 2] + (D_[size_ - 1] - D_[size_ - 2]) * dx[size_ - 2] / 2.0;
}
else
{
// local schemes
if (size_ == 2)
{
tmp[0] = tmp[1] = S[0];
}
else
{
switch (da_)
{
case CubicInterpolation.DerivativeApprox.FourthOrder:
throw new NotImplementedException("FourthOrder not implemented yet");
case CubicInterpolation.DerivativeApprox.Parabolic:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
tmp[i] = (dx[i - 1] * S[i] + dx[i] * S[i - 1]) / (dx[i] + dx[i - 1]);
}
// end points
tmp[0] = ((2.0 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[0] + dx[1]);
tmp[size_ - 1] = ((2.0 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] -
dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 2] + dx[size_ - 3]);
break;
case CubicInterpolation.DerivativeApprox.FritschButland:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
double Smin = Math.Min(S[i - 1], S[i]);
double Smax = Math.Max(S[i - 1], S[i]);
tmp[i] = 3.0 * Smin * Smax / (Smax + 2.0 * Smin);
}
// end points
tmp[0] = ((2.0 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[0] + dx[1]);
tmp[size_ - 1] = ((2.0 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] -
dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 2] + dx[size_ - 3]);
break;
case CubicInterpolation.DerivativeApprox.Akima:
tmp[0] = (Math.Abs(S[1] - S[0]) * 2 * S[0] * S[1] +
Math.Abs(2 * S[0] * S[1] - 4 * S[0] * S[0] * S[1]) * S[0]) /
(Math.Abs(S[1] - S[0]) + Math.Abs(2 * S[0] * S[1] - 4 * S[0] * S[0] * S[1]));
tmp[1] = (Math.Abs(S[2] - S[1]) * S[0] + Math.Abs(S[0] - 2 * S[0] * S[1]) * S[1]) /
(Math.Abs(S[2] - S[1]) + Math.Abs(S[0] - 2 * S[0] * S[1]));
for (int i = 2; i < size_ - 2; ++i)
{
if ((S[i - 2].IsEqual(S[i - 1])) && (S[i].IsNotEqual(S[i + 1])))
{
tmp[i] = S[i - 1];
}
else if ((S[i - 2].IsNotEqual(S[i - 1])) && (S[i].IsEqual(S[i + 1])))
{
tmp[i] = S[i];
}
else if (S[i].IsEqual(S[i - 1]))
{
tmp[i] = S[i];
}
else if ((S[i - 2].IsEqual(S[i - 1])) && (S[i - 1].IsNotEqual(S[i])) && (S[i].IsEqual(S[i + 1])))
{
tmp[i] = (S[i - 1] + S[i]) / 2.0;
}
else
{
tmp[i] = (Math.Abs(S[i + 1] - S[i]) * S[i - 1] + Math.Abs(S[i - 1] - S[i - 2]) * S[i]) /
(Math.Abs(S[i + 1] - S[i]) + Math.Abs(S[i - 1] - S[i - 2]));
}
}
tmp[size_ - 2] = (Math.Abs(2 * S[size_ - 2] * S[size_ - 3] - S[size_ - 2]) * S[size_ - 3] +
Math.Abs(S[size_ - 3] - S[size_ - 4]) * S[size_ - 2]) /
(Math.Abs(2 * S[size_ - 2] * S[size_ - 3] - S[size_ - 2]) +
Math.Abs(S[size_ - 3] - S[size_ - 4]));
tmp[size_ - 1] =
(Math.Abs(4 * S[size_ - 2] * S[size_ - 2] * S[size_ - 3] - 2 * S[size_ - 2] * S[size_ - 3]) *
S[size_ - 2] + Math.Abs(S[size_ - 2] - S[size_ - 3]) * 2 * S[size_ - 2] * S[size_ - 3]) /
(Math.Abs(4 * S[size_ - 2] * S[size_ - 2] * S[size_ - 3] - 2 * S[size_ - 2] * S[size_ - 3]) +
Math.Abs(S[size_ - 2] - S[size_ - 3]));
break;
case CubicInterpolation.DerivativeApprox.Kruger:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
if (S[i - 1] * S[i] < 0.0)
{
// slope changes sign at point
tmp[i] = 0.0;
}
else
{
// slope will be between the slopes of the adjacent
// straight lines and should approach zero if the
// slope of either line approaches zero
tmp[i] = 2.0 / (1.0 / S[i - 1] + 1.0 / S[i]);
}
}
// end points
tmp[0] = (3.0 * S[0] - tmp[1]) / 2.0;
tmp[size_ - 1] = (3.0 * S[size_ - 2] - tmp[size_ - 2]) / 2.0;
break;
case CubicInterpolation.DerivativeApprox.Harmonic:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
double w1 = 2 * dx[i] + dx[i - 1];
double w2 = dx[i] + 2 * dx[i - 1];
if (S[i - 1] * S[i] <= 0.0)
{
// slope changes sign at point
tmp[i] = 0.0;
}
else
{
// weighted harmonic mean of S[i] and S[i-1] if they
// have the same sign; otherwise 0
tmp[i] = (w1 + w2) / (w1 / S[i - 1] + w2 / S[i]);
}
}
// end points [0]
tmp[0] = ((2 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[1] + dx[0]);
if (tmp[0] * S[0] < 0.0)
{
tmp[0] = 0;
}
else if (S[0] * S[1] < 0)
{
if (Math.Abs(tmp[0]) > Math.Abs(3 * S[0]))
{
tmp[0] = 3 * S[0];
}
}
// end points [n-1]
tmp[size_ - 1] = ((2 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] - dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 3] + dx[size_ - 2]);
if (tmp[size_ - 1] * S[size_ - 2] < 0.0)
{
tmp[size_ - 1] = 0;
}
else if (S[size_ - 2] * S[size_ - 3] < 0)
{
if (Math.Abs(tmp[size_ - 1]) > Math.Abs(3 * S[size_ - 2]))
{
tmp[size_ - 1] = 3 * S[size_ - 2];
}
}
break;
default:
throw new ArgumentException("unknown scheme");
}
}
}
monotonicityAdjustments_.Erase();
// Hyman monotonicity constrained filter
if (monotonic_)
{
double correction;
double pm, pu, pd, M;
for (int i = 0; i < size_; ++i)
{
if (i == 0)
{
if (tmp[i] * S[0] > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]),
Math.Abs(3.0 * S[0]));
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
else if (i == size_ - 1)
{
if (tmp[i] * S[size_ - 2] > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]), Math.Abs(3.0 * S[size_ - 2]));
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
else
{
pm = (S[i - 1] * dx[i] + S[i] * dx[i - 1]) /
(dx[i - 1] + dx[i]);
M = 3.0 * Math.Min(Math.Min(Math.Abs(S[i - 1]), Math.Abs(S[i])),
Math.Abs(pm));
if (i > 1)
{
if ((S[i - 1] - S[i - 2]) * (S[i] - S[i - 1]) > 0.0)
{
pd = (S[i - 1] * (2.0 * dx[i - 1] + dx[i - 2])
- S[i - 2] * dx[i - 1]) /
(dx[i - 2] + dx[i - 1]);
if (pm * pd > 0.0 && pm * (S[i - 1] - S[i - 2]) > 0.0)
{
M = Math.Max(M, 1.5 * Math.Min(
Math.Abs(pm), Math.Abs(pd)));
}
}
}
if (i < size_ - 2)
{
if ((S[i] - S[i - 1]) * (S[i + 1] - S[i]) > 0.0)
{
pu = (S[i] * (2.0 * dx[i] + dx[i + 1]) - S[i + 1] * dx[i]) /
(dx[i] + dx[i + 1]);
if (pm * pu > 0.0 && -pm * (S[i] - S[i - 1]) > 0.0)
{
M = Math.Max(M, 1.5 * Math.Min(
Math.Abs(pm), Math.Abs(pu)));
}
}
}
if (tmp[i] * pm > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]), M);
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
}
}
// cubic coefficients
for (int i = 0; i < size_ - 1; ++i)
{
a_[i] = tmp[i];
b_[i] = (3.0 * S[i] - tmp[i + 1] - 2.0 * tmp[i]) / dx[i];
c_[i] = (tmp[i + 1] + tmp[i] - 2.0 * S[i]) / (dx[i] * dx[i]);
}
primitiveConst_[0] = 0.0;
for (int i = 1; i < size_ - 1; ++i)
{
primitiveConst_[i] = primitiveConst_[i - 1]
+ dx[i - 1] *
(yBegin_[i - 1] + dx[i - 1] *
(a_[i - 1] / 2.0 + dx[i - 1] *
(b_[i - 1] / 3.0 + dx[i - 1] * c_[i - 1] / 4.0)));
}
}
public void sabrCalibrationSection(Cube marketVolCube, Cube parametersCube, Period swapTenor)
{
List <double> optionTimes = marketVolCube.optionTimes();
List <double> swapLengths = marketVolCube.swapLengths();
List <Date> optionDates = marketVolCube.optionDates();
List <Period> swapTenors = marketVolCube.swapTenors();
int k = swapTenors.IndexOf(swapTenors.First(x => x == swapTenor));
Utils.QL_REQUIRE(k != swapTenors.Count, () => "swap tenor not found");
List <double> calibrationResult = new InitializedList <double>(8, 0.0);
List <Matrix> tmpMarketVolCube = marketVolCube.points();
List <double> strikes = new List <double>(strikeSpreads_.Count);
List <double> volatilities = new List <double>(strikeSpreads_.Count);
for (int j = 0; j < optionTimes.Count; j++)
{
double atmForward = atmStrike(optionDates[j], swapTenors[k]);
double shiftTmp = atmVol_.link.shift(optionTimes[j], swapLengths[k]);
strikes.Clear();
volatilities.Clear();
for (int i = 0; i < nStrikes_; i++)
{
double strike = atmForward + strikeSpreads_[i];
if (strike + shiftTmp >= cutoffStrike_)
{
strikes.Add(strike);
volatilities.Add(tmpMarketVolCube[i][j, k]);
}
}
List <double> guess = parametersGuess_.value(optionTimes[j], swapLengths[k]);
var sabrInterpolation = new SABRInterpolation(strikes,
strikes.Count,
volatilities,
optionTimes[j], atmForward,
guess[0], guess[1],
guess[2], guess[3],
isParameterFixed_[0],
isParameterFixed_[1],
isParameterFixed_[2],
isParameterFixed_[3],
vegaWeightedSmileFit_,
endCriteria_,
optMethod_,
errorAccept_,
useMaxError_,
maxGuesses_,
shiftTmp,
volatilityType());//shiftTmp
sabrInterpolation.update();
double interpolationError = sabrInterpolation.rmsError();
calibrationResult[0] = sabrInterpolation.alpha();
calibrationResult[1] = sabrInterpolation.beta();
calibrationResult[2] = sabrInterpolation.nu();
calibrationResult[3] = sabrInterpolation.rho();
calibrationResult[4] = atmForward;
calibrationResult[5] = interpolationError;
calibrationResult[6] = sabrInterpolation.maxError();
calibrationResult[7] = (double)sabrInterpolation.endCriteria();
Utils.QL_REQUIRE(calibrationResult[7].IsNotEqual((double)EndCriteria.Type.MaxIterations), () =>
"section calibration failed: " +
"option tenor " + optionDates[j] +
", swap tenor " + swapTenors[k] +
": max iteration (" +
endCriteria_.maxIterations() + ")" +
", alpha " + calibrationResult[0] +
", beta " + calibrationResult[1] +
", nu " + calibrationResult[2] +
", rho " + calibrationResult[3] +
", max error " + calibrationResult[6] +
", error " + calibrationResult[5]
);
Utils.QL_REQUIRE(useMaxError_ ? calibrationResult[6] > 0 : calibrationResult[5] < maxErrorTolerance_, () =>
"section calibration failed: " +
"option tenor " + optionDates[j] +
", swap tenor " + swapTenors[k] +
(useMaxError_ ? ": max error " : ": error ") +
(useMaxError_ ? calibrationResult[6] : calibrationResult[5]) +
", alpha " + calibrationResult[0] +
", beta " + calibrationResult[1] +
", nu " + calibrationResult[2] +
", rho " + calibrationResult[3] +
(useMaxError_ ? ": error" : ": max error ") +
(useMaxError_ ? calibrationResult[5] : calibrationResult[6])
);
parametersCube.setPoint(optionDates[j], swapTenors[k], optionTimes[j], swapLengths[k], calibrationResult);
parametersCube.updateInterpolators();
}
}
protected void crossover(List <Candidate> oldPopulation,
List <Candidate> population,
List <Candidate> mutantPopulation,
List <Candidate> mirrorPopulation,
CostFunction costFunction)
{
if (configuration().crossoverIsAdaptive)
{
adaptCrossover();
}
Vector mutationProbabilities = getMutationProbabilities(population);
List <Vector> crossoverMask = new InitializedList <Vector>(population.Count);
crossoverMask.ForEach((ii, vv) => crossoverMask[ii] = new Vector(population.First().values.size(), 1.0));
List <Vector> invCrossoverMask = new InitializedList <Vector>(population.Count);
invCrossoverMask.ForEach((ii, vv) => invCrossoverMask[ii] = new Vector(population.First().values.size(), 1.0));
getCrossoverMask(crossoverMask, invCrossoverMask, mutationProbabilities);
// crossover of the old and mutant population
for (int popIter = 0; popIter < population.Count; popIter++)
{
population[popIter].values = Vector.DirectMultiply(oldPopulation[popIter].values, invCrossoverMask[popIter])
+ Vector.DirectMultiply(mutantPopulation[popIter].values,
crossoverMask[popIter]);
// immediately apply bounds if specified
if (configuration().applyBounds)
{
for (int memIter = 0; memIter < population[popIter].values.size(); memIter++)
{
if (population[popIter].values[memIter] > upperBound_[memIter])
{
population[popIter].values[memIter] = upperBound_[memIter]
+ rng_.nextReal()
* (mirrorPopulation[popIter].values[memIter]
- upperBound_[memIter]);
}
if (population[popIter].values[memIter] < lowerBound_[memIter])
{
population[popIter].values[memIter] = lowerBound_[memIter]
+ rng_.nextReal()
* (mirrorPopulation[popIter].values[memIter]
- lowerBound_[memIter]);
}
}
}
// evaluate objective function as soon as possible to avoid unnecessary loops
try
{
population[popIter].cost = costFunction.value(population[popIter].values);
if (Double.IsNaN(population[popIter].cost))
{
population[popIter].cost = Double.MaxValue;
}
}
catch
{
population[popIter].cost = Double.MaxValue;
}
}
}
public void recalibration(double beta, Period swapTenor)
{
List <double> betaVector = new InitializedList <double>(nOptionTenors_, beta);
recalibration(betaVector, swapTenor);
}
public EuropeanExercise(Date date) : base(Type.European)
{
dates_ = new InitializedList <Date>(1, date);
}
protected Cube sabrCalibration(Cube marketVolCube)
{
List <double> optionTimes = marketVolCube.optionTimes();
List <double> swapLengths = marketVolCube.swapLengths();
List <Date> optionDates = marketVolCube.optionDates();
List <Period> swapTenors = marketVolCube.swapTenors();
Matrix alphas = new Matrix(optionTimes.Count, swapLengths.Count, 0.0);
Matrix betas = new Matrix(alphas);
Matrix nus = new Matrix(alphas);
Matrix rhos = new Matrix(alphas);
Matrix forwards = new Matrix(alphas);
Matrix errors = new Matrix(alphas);
Matrix maxErrors = new Matrix(alphas);
Matrix endCriteria = new Matrix(alphas);
List <Matrix> tmpMarketVolCube = marketVolCube.points();
List <double> strikes = new InitializedList <double>(strikeSpreads_.Count);
List <double> volatilities = new InitializedList <double>(strikeSpreads_.Count);
for (int j = 0; j < optionTimes.Count; j++)
{
for (int k = 0; k < swapLengths.Count; k++)
{
double atmForward = atmStrike(optionDates[j], swapTenors[k]);
double shiftTmp = atmVol_.link.shift(optionTimes[j], swapLengths[k]);
strikes.Clear();
volatilities.Clear();
for (int i = 0; i < nStrikes_; i++)
{
double strike = atmForward + strikeSpreads_[i];
if (strike + shiftTmp >= cutoffStrike_)
{
strikes.Add(strike);
Matrix matrix = tmpMarketVolCube[i];
volatilities.Add(matrix[j, k]);
}
}
List <double> guess = parametersGuess_.value(optionTimes[j], swapLengths[k]);
SABRInterpolation sabrInterpolation = new SABRInterpolation(strikes, strikes.Count,
volatilities,
optionTimes[j], atmForward,
guess[0], guess[1],
guess[2], guess[3],
isParameterFixed_[0],
isParameterFixed_[1],
isParameterFixed_[2],
isParameterFixed_[3],
vegaWeightedSmileFit_,
endCriteria_,
optMethod_,
errorAccept_,
useMaxError_,
maxGuesses_,
shiftTmp,
volatilityType());// shiftTmp
sabrInterpolation.update();
double rmsError = sabrInterpolation.rmsError();
double maxError = sabrInterpolation.maxError();
alphas [j, k] = sabrInterpolation.alpha();
betas [j, k] = sabrInterpolation.beta();
nus [j, k] = sabrInterpolation.nu();
rhos [j, k] = sabrInterpolation.rho();
forwards [j, k] = atmForward;
errors [j, k] = rmsError;
maxErrors [j, k] = maxError;
endCriteria[j, k] = (double)sabrInterpolation.endCriteria();
Utils.QL_REQUIRE(endCriteria[j, k].IsNotEqual((double)EndCriteria.Type.MaxIterations), () =>
"global swaptions calibration failed: " +
"MaxIterations reached: " + "\n" +
"option maturity = " + optionDates[j] + ", \n" +
"swap tenor = " + swapTenors[k] + ", \n" +
"error = " + (errors[j, k]) + ", \n" +
"max error = " + (maxErrors[j, k]) + ", \n" +
" alpha = " + alphas[j, k] + "n" +
" beta = " + betas[j, k] + "\n" +
" nu = " + nus[j, k] + "\n" +
" rho = " + rhos[j, k] + "\n"
);
Utils.QL_REQUIRE(useMaxError_ ? maxError > 0 : rmsError < maxErrorTolerance_, () =>
"global swaptions calibration failed: " +
"option tenor " + optionDates[j] +
", swap tenor " + swapTenors[k] +
(useMaxError_ ? ": max error " : ": error") +
(useMaxError_ ? maxError : rmsError) +
" alpha = " + alphas[j, k] + "\n" +
" beta = " + betas[j, k] + "\n" +
" nu = " + nus[j, k] + "\n" +
" rho = " + rhos[j, k] + "\n" +
(useMaxError_ ? ": error" : ": max error ") +
(useMaxError_ ? rmsError : maxError)
);
}
}
Cube sabrParametersCube = new Cube(optionDates, swapTenors, optionTimes, swapLengths, 8, true, backwardFlat_);
sabrParametersCube.setLayer(0, alphas);
sabrParametersCube.setLayer(1, betas);
sabrParametersCube.setLayer(2, nus);
sabrParametersCube.setLayer(3, rhos);
sabrParametersCube.setLayer(4, forwards);
sabrParametersCube.setLayer(5, errors);
sabrParametersCube.setLayer(6, maxErrors);
sabrParametersCube.setLayer(7, endCriteria);
return(sabrParametersCube);
}
public TqrEigenDecomposition(Vector diag, Vector sub, EigenVectorCalculation calc = EigenVectorCalculation.WithEigenVector,
ShiftStrategy strategy = ShiftStrategy.CloseEigenValue)
{
iter_ = 0;
d_ = new Vector(diag);
int row = calc == EigenVectorCalculation.WithEigenVector ? d_.size() :
calc == EigenVectorCalculation.WithoutEigenVector ? 0 : 1;
ev_ = new Matrix(row, d_.size(), 0.0);
int n = diag.size();
Utils.QL_REQUIRE(n == sub.size() + 1, () => "Wrong dimensions");
Vector e = new Vector(n, 0.0);
int i;
for (i = 1; i < e.Count; ++i)
{
e[i] = sub[i - 1];
}
for (i = 0; i < ev_.rows(); ++i)
{
ev_[i, i] = 1.0;
}
for (int k = n - 1; k >= 1; --k)
{
while (!offDiagIsZero(k, e))
{
int l = k;
while (--l > 0 && !offDiagIsZero(l, e))
{
;
}
iter_++;
double q = d_[l];
if (strategy != ShiftStrategy.NoShift)
{
// calculated eigenvalue of 2x2 sub matrix of
// [ d_[k-1] e_[k] ]
// [ e_[k] d_[k] ]
// which is closer to d_[k+1].
// FLOATING_POINT_EXCEPTION
double t1 = Math.Sqrt(
0.25 * (d_[k] * d_[k] + d_[k - 1] * d_[k - 1])
- 0.5 * d_[k - 1] * d_[k] + e[k] * e[k]);
double t2 = 0.5 * (d_[k] + d_[k - 1]);
double lambda = (Math.Abs(t2 + t1 - d_[k]) < Math.Abs(t2 - t1 - d_[k]))?
t2 + t1 : t2 - t1;
if (strategy == ShiftStrategy.CloseEigenValue)
{
q -= lambda;
}
else
{
q -= ((k == n - 1) ? 1.25 : 1.0) * lambda;
}
}
// the QR transformation
double sine = 1.0;
double cosine = 1.0;
double u = 0.0;
bool recoverUnderflow = false;
for (i = l + 1; i <= k && !recoverUnderflow; ++i)
{
double h = cosine * e[i];
double p = sine * e[i];
e[i - 1] = Math.Sqrt(p * p + q * q);
if (e[i - 1].IsNotEqual(0.0))
{
sine = p / e[i - 1];
cosine = q / e[i - 1];
double g = d_[i - 1] - u;
double t = (d_[i] - g) * sine + 2 * cosine * h;
u = sine * t;
d_[i - 1] = g + u;
q = cosine * t - h;
for (int j = 0; j < ev_.rows(); ++j)
{
double tmp = ev_[j, i - 1];
ev_[j, i - 1] = sine * ev_[j, i] + cosine * tmp;
ev_[j, i] = cosine * ev_[j, i] - sine * tmp;
}
}
else
{
// recover from underflow
d_[i - 1] -= u;
e[l] = 0.0;
recoverUnderflow = true;
}
}
if (!recoverUnderflow)
{
d_[k] -= u;
e[k] = q;
e[l] = 0.0;
}
}
}
// sort (eigenvalues, eigenvectors),
// code taken from symmetricSchureDecomposition.cpp
List <KeyValuePair <double, List <double> > > temp = new InitializedList <KeyValuePair <double, List <double> > >(n);
List <double> eigenVector = new InitializedList <double>(ev_.rows());
for (i = 0; i < n; i++)
{
if (ev_.rows() > 0)
{
eigenVector = ev_.column(i);
}
temp[i] = new KeyValuePair <double, List <double> >(d_[i], eigenVector);
}
temp.Sort(KeyValuePairCompare);
// first element is positive
for (i = 0; i < n; i++)
{
d_[i] = temp[i].Key;
double sign = 1.0;
if (ev_.rows() > 0 && temp[i].Value[0] < 0.0)
{
sign = -1.0;
}
for (int j = 0; j < ev_.rows(); ++j)
{
ev_[j, i] = sign * temp[i].Value[j];
}
}
}
protected List <double> spreadVolInterpolation(Date atmOptionDate, Period atmSwapTenor)
{
double atmOptionTime = timeFromReference(atmOptionDate);
double atmTimeLength = swapLength(atmSwapTenor);
List <double> result = new List <double>();
List <double> optionTimes = sparseParameters_.optionTimes();
List <double> swapLengths = sparseParameters_.swapLengths();
List <Date> optionDates = sparseParameters_.optionDates();
List <Period> swapTenors = sparseParameters_.swapTenors();
double optionTimesPreviousNode, swapLengthsPreviousNode;
optionTimesPreviousNode = optionTimes_.First(x => x >= Math.Min(atmOptionTime, optionTimes_.Max()));
int optionTimesPreviousIndex = optionTimes_.IndexOf(optionTimesPreviousNode);
swapLengthsPreviousNode = swapLengths_.First(x => x >= Math.Min(atmTimeLength, swapLengths_.Max()));
int swapLengthsPreviousIndex = swapLengths_.IndexOf(swapLengthsPreviousNode);
if (optionTimesPreviousIndex > 0)
{
optionTimesPreviousIndex--;
}
if (swapLengthsPreviousIndex > 0)
{
swapLengthsPreviousIndex--;
}
List <List <SmileSection> > smiles = new List <List <SmileSection> >();
List <SmileSection> smilesOnPreviousExpiry = new List <SmileSection>();
List <SmileSection> smilesOnNextExpiry = new List <SmileSection>();
Utils.QL_REQUIRE(optionTimesPreviousIndex + 1 < sparseSmiles_.Count, () =>
"optionTimesPreviousIndex+1 >= sparseSmiles_.size()");
Utils.QL_REQUIRE(swapLengthsPreviousIndex + 1 < sparseSmiles_[0].Count, () =>
"swapLengthsPreviousIndex+1 >= sparseSmiles_[0].size()");
smilesOnPreviousExpiry.Add(sparseSmiles_[optionTimesPreviousIndex][swapLengthsPreviousIndex]);
smilesOnPreviousExpiry.Add(sparseSmiles_[optionTimesPreviousIndex][swapLengthsPreviousIndex + 1]);
smilesOnNextExpiry.Add(sparseSmiles_[optionTimesPreviousIndex + 1][swapLengthsPreviousIndex]);
smilesOnNextExpiry.Add(sparseSmiles_[optionTimesPreviousIndex + 1][swapLengthsPreviousIndex + 1]);
smiles.Add(smilesOnPreviousExpiry);
smiles.Add(smilesOnNextExpiry);
List <double> optionsNodes = new InitializedList <double>(2);
optionsNodes[0] = optionTimes[optionTimesPreviousIndex];
optionsNodes[1] = optionTimes[optionTimesPreviousIndex + 1];
List <Date> optionsDateNodes = new InitializedList <Date>(2);
optionsDateNodes[0] = optionDates[optionTimesPreviousIndex];
optionsDateNodes[1] = optionDates[optionTimesPreviousIndex + 1];
List <double> swapLengthsNodes = new InitializedList <double>(2);
swapLengthsNodes[0] = swapLengths[swapLengthsPreviousIndex];
swapLengthsNodes[1] = swapLengths[swapLengthsPreviousIndex + 1];
List <Period> swapTenorNodes = new InitializedList <Period>(2);
swapTenorNodes[0] = swapTenors[swapLengthsPreviousIndex];
swapTenorNodes[1] = swapTenors[swapLengthsPreviousIndex + 1];
double atmForward = atmStrike(atmOptionDate, atmSwapTenor);
double shift = atmVol_.link.shift(atmOptionTime, atmTimeLength);
Matrix atmForwards = new Matrix(2, 2, 0.0);
Matrix atmShifts = new Matrix(2, 2, 0.0);
Matrix atmVols = new Matrix(2, 2, 0.0);
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
atmForwards[i, j] = atmStrike(optionsDateNodes[i], swapTenorNodes[j]);
atmShifts[i, j] = atmVol_.link.shift(optionsNodes[i], swapLengthsNodes[j]);
atmVols[i, j] = atmVol_.link.volatility(optionsDateNodes[i], swapTenorNodes[j], atmForwards[i, j]);
/* With the old implementation the interpolated spreads on ATM
* volatilities were null even if the spreads on ATM volatilities to be
* interpolated were non-zero. The new implementation removes
* this behaviour, but introduces a small ERROR in the cube:
* even if no spreads are applied on any cube ATM volatility corresponding
* to quoted smile sections (that is ATM volatilities in sparse cube), the
* cube ATM volatilities corresponding to not quoted smile sections (that
* is ATM volatilities in dense cube) are no more exactly the quoted values,
* but that ones PLUS the linear interpolation of the fit errors on the ATM
* volatilities in sparse cube whose spreads are used in the calculation.
* A similar imprecision is introduced to the volatilities in dense cube
* whith moneyness near to 1.
* (See below how spreadVols are calculated).
* The extent of this error depends on the quality of the fit: in case of
* good fits it is negligibile.
*/
}
}
for (int k = 0; k < nStrikes_; k++)
{
double strike = Math.Max(atmForward + strikeSpreads_[k], cutoffStrike_ - shift);
double moneyness = (atmForward + shift) / (strike + shift);
Matrix strikes = new Matrix(2, 2, 0.0);
Matrix spreadVols = new Matrix(2, 2, 0.0);
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
strikes[i, j] = (atmForwards[i, j] + atmShifts[i, j]) / moneyness - atmShifts[i, j];
spreadVols[i, j] = smiles[i][j].volatility(strikes[i, j]) - atmVols[i, j];
}
}
Cube localInterpolator = new Cube(optionsDateNodes, swapTenorNodes, optionsNodes, swapLengthsNodes, 1);
localInterpolator.setLayer(0, spreadVols);
localInterpolator.updateInterpolators();
result.Add(localInterpolator.value(atmOptionTime, atmTimeLength)[0]);
}
return(result);
}
public LinearInterpolationImpl(List <double> xBegin, int size, List <double> yBegin)
: base(xBegin, size, yBegin)
{
primitiveConst_ = new InitializedList <double>(size_);
s_ = new InitializedList <double>(size_);
}
protected void rkqs(List <double> y,
List <double> dydx,
ref double x,
double htry,
double eps,
List <double> yScale,
ref double hdid,
ref double hnext,
OdeFct derivs)
{
int n = y.Count;
double errmax, xnew;
List <double> yerr = new InitializedList <double>(n), ytemp = new InitializedList <double>(n);
double h = htry;
for (;;)
{
rkck(y, dydx, ref x, h, ref ytemp, ref yerr, derivs);
errmax = 0.0;
for (int i = 0; i < n; i++)
{
errmax = Math.Max(errmax, Math.Abs(yerr[i] / yScale[i]));
}
errmax /= eps;
if (errmax > 1.0)
{
double htemp1 = ADAPTIVERK_SAFETY * h * Math.Pow(errmax, ADAPTIVERK_PSHRINK);
double htemp2 = h / 10;
// These would be std::min and std::max, of course,
// but VC++14 had problems inlining them and caused
// the wrong results to be calculated. The problem
// seems to be fixed in update 3, but let's keep this
// implementation for compatibility.
double max_positive = htemp1 > htemp2 ? htemp1 : htemp2;
double max_negative = htemp1 < htemp2 ? htemp1 : htemp2;
h = ((h >= 0.0) ? max_positive : max_negative);
xnew = x + h;
if (xnew.IsEqual(x))
{
Utils.QL_FAIL("Stepsize underflow (" + h + " at x = " + x
+ ") in AdaptiveRungeKutta::rkqs");
}
continue;
}
else
{
if (errmax > ADAPTIVERK_ERRCON)
{
hnext = ADAPTIVERK_SAFETY * h * Math.Pow(errmax, ADAPTIVERK_PGROW);
}
else
{
hnext = 5.0 * h;
}
x += (hdid = h);
for (int i = 0; i < n; i++)
{
y[i] = ytemp[i];
}
break;
}
}
}
