public override Lattice tree(TimeGrid grid)
{
TermStructureFittingParameter phi = new TermStructureFittingParameter(termStructure());
ShortRateDynamics numericDynamics =
new Dynamics(phi, a(), sigma());
TrinomialTree trinomial =
new TrinomialTree(numericDynamics.process(), grid);
ShortRateTree numericTree =
new ShortRateTree(trinomial, numericDynamics, grid);
TermStructureFittingParameter.NumericalImpl impl =
(TermStructureFittingParameter.NumericalImpl)phi.implementation();
impl.reset();
double value = 1.0;
double vMin = -50.0;
double vMax = 50.0;
for (int i = 0; i < (grid.size() - 1); i++)
{
double discountBond = termStructure().link.discount(grid[i + 1]);
double xMin = trinomial.underlying(i, 0);
double dx = trinomial.dx(i);
Helper finder = new Helper(i, xMin, dx, discountBond, numericTree);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
impl.setvalue(grid[i], value);
}
return(numericTree);
}
/// <summary>
/// Calculate the Option Adjusted Spread (OAS)
/// <remarks>
/// Calculates the spread that needs to be added to the the
/// reference curve so that the theoretical model value
/// matches the marketPrice.
/// </remarks>
/// </summary>
/// <param name="cleanPrice"></param>
/// <param name="engineTS"></param>
/// <param name="dayCounter"></param>
/// <param name="compounding"></param>
/// <param name="frequency"></param>
/// <param name="settlement"></param>
/// <param name="accuracy"></param>
/// <param name="maxIterations"></param>
/// <param name="guess"></param>
/// <returns></returns>
public double OAS(double cleanPrice,
Handle <YieldTermStructure> engineTS,
DayCounter dayCounter,
Compounding compounding,
Frequency frequency,
Date settlement = null,
double accuracy = 1.0e-10,
int maxIterations = 100,
double guess = 0.0)
{
if (settlement == null)
{
settlement = settlementDate();
}
double dirtyPrice = cleanPrice + accruedAmount(settlement);
var f = new NpvSpreadHelper(this);
OasHelper obj = new OasHelper(f, dirtyPrice);
Brent solver = new Brent();
solver.setMaxEvaluations(maxIterations);
double step = 0.001;
double oas = solver.solve(obj, accuracy, guess, step);
return(continuousToConv(oas,
this,
engineTS,
dayCounter,
compounding,
frequency));
}
private double strikeFromPrice(double price, Option.Type optionType, double referenceStrike)
{
double a, b, min, max, k;
if (optionType == Option.Type.Call)
{
a = swapRateValue_;
min = referenceStrike;
b = max = k = Math.Min(smileSection_.maxStrike(), shiftedUpperBound_);
}
else
{
a = min = k = Math.Max(smileSection_.minStrike(), shiftedLowerBound_);
b = swapRateValue_;
max = referenceStrike;
}
PriceHelper h = new PriceHelper(smileSection_, optionType, price);
Brent solver = new Brent();
try
{
k = solver.solve(h, 1.0E-5, swapRateValue_, a, b);
}
catch (Exception)
{
// use default value set above
}
return(Math.Min(Math.Max(k, min), max));
}
//! Black volatility implied by the model
public double impliedVolatility(double targetValue,
double accuracy, int maxEvaluations, double minVol, double maxVol)
{
ImpliedVolatilityHelper f = new ImpliedVolatilityHelper(this, targetValue);
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
return(solver.solve(f, accuracy, volatility_.link.value(), minVol, maxVol));
}
public double MonthlyYield()
{
Brent solver = new Brent();
solver.setMaxEvaluations(100);
List <CashFlow> cf = expectedCashflows();
MonthlyYieldFinder objective = new MonthlyYieldFinder(notional(settlementDate()), cf, settlementDate());
return(solver.solve(objective, 1.0e-10, 0.02, 0.0, 1.0) / 100);
}
public static double calculate(Instrument instrument, IPricingEngine engine, SimpleQuote volQuote,
double targetValue, double accuracy, int maxEvaluations, double minVol, double maxVol)
{
instrument.setupArguments(engine.getArguments());
engine.getArguments().validate();
PriceError f = new PriceError(engine, volQuote, targetValue);
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
double guess = (minVol + maxVol) / 2.0;
double result = solver.solve(f, accuracy, guess, minVol, maxVol);
return(result);
}
private List <double> spreadsVolImplied()
{
Brent solver = new Brent();
List <double> result = new InitializedList <double>(nOptionExpiries_, 0.0);
double guess = 0.0001, minSpread = -0.1, maxSpread = 0.1;
for (int j = 0; j < nOptionExpiries_; ++j)
{
ObjectiveFunction f = new ObjectiveFunction(stripper1_, caps_[j], atmCapFloorPrices_[j]);
solver.setMaxEvaluations(maxEvaluations_);
double root = solver.solve(f, accuracy_, guess, minSpread, maxSpread);
result[j] = root;
}
return(result);
}
protected override double blackVolImpl(double t, double strike)
{
HestonProcess process = hestonModel_.link.process();
double df = process.riskFreeRate().link.discount(t, true);
double div = process.dividendYield().link.discount(t, true);
double spotPrice = process.s0().link.value();
double fwd = spotPrice
* process.dividendYield().link.discount(t, true)
/ process.riskFreeRate().link.discount(t, true);
var payoff = new PlainVanillaPayoff(fwd > strike ? Option.Type.Put : Option.Type.Call, strike);
double kappa = hestonModel_.link.kappa();
double theta = hestonModel_.link.theta();
double rho = hestonModel_.link.rho();
double sigma = hestonModel_.link.sigma();
double v0 = hestonModel_.link.v0();
AnalyticHestonEngine.ComplexLogFormula cpxLogFormula = AnalyticHestonEngine.ComplexLogFormula.Gatheral;
AnalyticHestonEngine hestonEnginePtr = null;
double?npv = null;
int evaluations = 0;
AnalyticHestonEngine.doCalculation(
df, div, spotPrice, strike, t,
kappa, theta, sigma, v0, rho,
payoff, integration_, cpxLogFormula,
hestonEnginePtr, ref npv, ref evaluations);
if (npv <= 0.0)
{
return(Math.Sqrt(theta));
}
Brent solver = new Brent();
solver.setMaxEvaluations(10000);
double guess = Math.Sqrt(theta);
double accuracy = Const.QL_EPSILON;
var f = new ImpliedVolHelper(payoff.optionType(), strike, fwd, t, df, npv.Value);
return(solver.solve(f, accuracy, guess, 0.01));
}
/// <summary>
/// Returns the Black implied forward yield volatility
/// <remarks>
/// the forward yield volatility, see Hull, Fourth Edition,
/// Chapter 20, pg 536). Relevant only to European put/call
/// schedules
/// </remarks>
/// </summary>
/// <param name="targetValue"></param>
/// <param name="discountCurve"></param>
/// <param name="accuracy"></param>
/// <param name="maxEvaluations"></param>
/// <param name="minVol"></param>
/// <param name="maxVol"></param>
/// <returns></returns>
public double impliedVolatility(double targetValue,
Handle <YieldTermStructure> discountCurve,
double accuracy,
int maxEvaluations,
double minVol,
double maxVol)
{
calculate();
Utils.QL_REQUIRE(!isExpired(), () => "instrument expired");
double guess = 0.5 * (minVol + maxVol);
blackDiscountCurve_.linkTo(discountCurve, false);
ImpliedVolHelper f = new ImpliedVolHelper(this, targetValue);
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
return(solver.solve(f, accuracy, guess, minVol, maxVol));
}
public double value(double x)
{
// first find the right side of the interval
double upper = guess_;
int evaluations = maxEvaluations_;
while (nonCentralDist_.value(upper) < x && evaluations > 0)
{
upper *= 2.0;
--evaluations;
}
// use a brent solver for the rest
Brent solver = new Brent();
solver.setMaxEvaluations(evaluations);
return(solver.solve(new IncChiQuareFinder(x, nonCentralDist_.value),
accuracy_, 0.75 * upper, (evaluations == maxEvaluations_) ? 0.0 : 0.5 * upper,
upper));
}
public double value(double x)
{
CumulativeNormalDistribution phi = new CumulativeNormalDistribution();
double temp = (x - mux_) / sigmax_;
double txy = Math.Sqrt(1.0 - rhoxy_ * rhoxy_);
Vector lambda = new Vector(size_);
int i;
for (i = 0; i < size_; i++)
{
double tau = (i == 0 ? t_[0] - T_ : t_[i] - t_[i - 1]);
double c = (i == size_ - 1 ? (1.0 + rate_ * tau) : rate_ * tau);
lambda[i] = c * A_[i] * Math.Exp(-Ba_[i] * x);
}
SolvingFunction function = new SolvingFunction(lambda, Bb_);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
double yb = s1d.solve(function, 1e-6, 0.00, -100.0, 100.0);
double h1 = (yb - muy_) / (sigmay_ * txy) -
rhoxy_ * (x - mux_) / (sigmax_ * txy);
double value = phi.value(-w_ * h1);
for (i = 0; i < size_; i++)
{
double h2 = h1 +
Bb_[i] * sigmay_ *Math.Sqrt(1.0 - rhoxy_ *rhoxy_);
double kappa = -Bb_[i] *
(muy_ - 0.5 * txy * txy * sigmay_ * sigmay_ * Bb_[i] +
rhoxy_ * sigmay_ * (x - mux_) / sigmax_);
value -= lambda[i] * Math.Exp(kappa) * phi.value(-w_ * h2);
}
return(Math.Exp(-0.5 * temp * temp) * value /
(sigmax_ * Math.Sqrt(2.0 * QLCore.Const.M_PI)));
}
//! Tree build-up + numerical fitting to term-structure
public ShortRateTree(TrinomialTree tree, ShortRateDynamics dynamics, TermStructureFittingParameter.NumericalImpl theta,
TimeGrid timeGrid)
: base(timeGrid, tree.size(1))
{
tree_ = tree;
dynamics_ = dynamics;
theta.reset();
double value = 1.0;
double vMin = -100.0;
double vMax = 100.0;
for (int i = 0; i < (timeGrid.size() - 1); i++)
{
double discountBond = theta.termStructure().link.discount(t_[i + 1]);
Helper finder = new Helper(i, discountBond, theta, this);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
theta.change(value);
}
}
//! implied Z-spread.
public static double zSpread(Leg leg, double npv, YieldTermStructure discount, DayCounter dayCounter, Compounding compounding,
Frequency frequency, bool includeSettlementDateFlows, Date settlementDate = null,
Date npvDate = null, double accuracy = 1.0e-10, int maxIterations = 100, double guess = 0.0)
{
if (settlementDate == null)
{
settlementDate = Settings.Instance.evaluationDate();
}
if (npvDate == null)
{
npvDate = settlementDate;
}
Brent solver = new Brent();
solver.setMaxEvaluations(maxIterations);
ZSpreadFinder objFunction = new ZSpreadFinder(leg, discount, npv, dayCounter, compounding, frequency,
includeSettlementDateFlows, settlementDate, npvDate);
double step = 0.01;
return(solver.solve(objFunction, accuracy, guess, step));
}
// alternative delta type
private double strikeFromDelta(double delta, DeltaVolQuote.DeltaType dt)
{
double res = 0.0;
double arg = 0.0;
InverseCumulativeNormal f = new InverseCumulativeNormal();
Utils.QL_REQUIRE(delta * phi_ >= 0.0, () => "Option type and delta are incoherent.");
switch (dt)
{
case DeltaVolQuote.DeltaType.Spot:
Utils.QL_REQUIRE(Math.Abs(delta) <= fDiscount_, () => "Spot delta out of range.");
arg = -phi_ *f.value(phi_ *delta / fDiscount_) * stdDev_ + 0.5 * stdDev_ * stdDev_;
res = forward_ * Math.Exp(arg);
break;
case DeltaVolQuote.DeltaType.Fwd:
Utils.QL_REQUIRE(Math.Abs(delta) <= 1.0, () => "Forward delta out of range.");
arg = -phi_ *f.value(phi_ *delta) * stdDev_ + 0.5 * stdDev_ * stdDev_;
res = forward_ * Math.Exp(arg);
break;
case DeltaVolQuote.DeltaType.PaSpot:
case DeltaVolQuote.DeltaType.PaFwd:
// This has to be solved numerically. One of the
// problems is that the premium adjusted call delta is
// not monotonic in strike, such that two solutions
// might occur. The one right to the max of the delta is
// considered to be the correct strike. Some proper
// interval bounds for the strike need to be chosen, the
// numerics can otherwise be very unreliable and
// unstable. I've chosen Brent over Newton, since the
// interval can be specified explicitly and we can not
// run into the area on the left of the maximum. The
// put delta doesn't have this property and can be
// solved without any problems, but also numerically.
BlackDeltaPremiumAdjustedSolverClass f1 = new BlackDeltaPremiumAdjustedSolverClass(
ot_, dt, spot_, dDiscount_, fDiscount_, stdDev_, delta);
Brent solver = new Brent();
solver.setMaxEvaluations(1000);
double accuracy = 1.0e-10;
double rightLimit = 0.0;
double leftLimit = 0.0;
// Strike of not premium adjusted is always to the right of premium adjusted
if (dt == DeltaVolQuote.DeltaType.PaSpot)
{
rightLimit = strikeFromDelta(delta, DeltaVolQuote.DeltaType.Spot);
}
else
{
rightLimit = strikeFromDelta(delta, DeltaVolQuote.DeltaType.Fwd);
}
if (phi_ < 0)
{
// if put
res = solver.solve(f1, accuracy, rightLimit, 0.0, spot_ * 100.0);
break;
}
else
{
// find out the left limit which is the strike
// corresponding to the value where premium adjusted
// deltas have their maximum.
BlackDeltaPremiumAdjustedMaxStrikeClass g = new BlackDeltaPremiumAdjustedMaxStrikeClass(
ot_, dt, spot_, dDiscount_, fDiscount_, stdDev_);
leftLimit = solver.solve(g, accuracy, rightLimit * 0.5, 0.0, rightLimit);
double guess = leftLimit + (rightLimit - leftLimit) * 0.5;
res = solver.solve(f1, accuracy, guess, leftLimit, rightLimit);
} // end if phi<0 else
break;
default:
Utils.QL_FAIL("invalid delta type");
break;
}
return(res);
}
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 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;
}
