public FdmBlackScholesMesher(int size,
GeneralizedBlackScholesProcess process,
double maturity, double strike,
double?xMinConstraint = null,
double?xMaxConstraint = null,
double eps = 0.0001,
double scaleFactor = 1.5,
Pair <double?, double?> cPoint
= null,
DividendSchedule dividendSchedule = null,
FdmQuantoHelper fdmQuantoHelper = null,
double spotAdjustment = 0.0)
: base(size)
{
double S = process.x0();
Utils.QL_REQUIRE(S > 0.0, () => "negative or null underlying given");
dividendSchedule = dividendSchedule == null ? new DividendSchedule() : dividendSchedule;
List <pair_double> intermediateSteps = new List <pair_double>();
for (int i = 0; i < dividendSchedule.Count &&
process.time(dividendSchedule[i].date()) <= maturity; ++i)
{
intermediateSteps.Add(
new pair_double(
process.time(dividendSchedule[i].date()),
dividendSchedule[i].amount()
));
}
int intermediateTimeSteps = (int)Math.Max(2, 24.0 * maturity);
for (int i = 0; i < intermediateTimeSteps; ++i)
{
intermediateSteps.Add(
new pair_double((i + 1) * (maturity / intermediateTimeSteps), 0.0));
}
intermediateSteps.Sort();
Handle <YieldTermStructure> rTS = process.riskFreeRate();
Handle <YieldTermStructure> qTS = fdmQuantoHelper != null
? new Handle <YieldTermStructure>(
new QuantoTermStructure(process.dividendYield(),
process.riskFreeRate(),
new Handle <YieldTermStructure>(fdmQuantoHelper.foreignTermStructure()),
process.blackVolatility(),
strike,
new Handle <BlackVolTermStructure>(fdmQuantoHelper.fxVolatilityTermStructure()),
fdmQuantoHelper.exchRateATMlevel(),
fdmQuantoHelper.equityFxCorrelation()))
: process.dividendYield();
double lastDivTime = 0.0;
double fwd = S + spotAdjustment;
double mi = fwd, ma = fwd;
for (int i = 0; i < intermediateSteps.Count; ++i)
{
double divTime = intermediateSteps[i].first;
double divAmount = intermediateSteps[i].second;
fwd = fwd / rTS.currentLink().discount(divTime) * rTS.currentLink().discount(lastDivTime)
* qTS.currentLink().discount(divTime) / qTS.currentLink().discount(lastDivTime);
mi = Math.Min(mi, fwd); ma = Math.Max(ma, fwd);
fwd -= divAmount;
mi = Math.Min(mi, fwd); ma = Math.Max(ma, fwd);
lastDivTime = divTime;
}
// Set the grid boundaries
double normInvEps = new InverseCumulativeNormal().value(1 - eps);
double sigmaSqrtT
= process.blackVolatility().currentLink().blackVol(maturity, strike)
* Math.Sqrt(maturity);
double?xMin = Math.Log(mi) - sigmaSqrtT * normInvEps * scaleFactor;
double?xMax = Math.Log(ma) + sigmaSqrtT * normInvEps * scaleFactor;
if (xMinConstraint != null)
{
xMin = xMinConstraint;
}
if (xMaxConstraint != null)
{
xMax = xMaxConstraint;
}
Fdm1dMesher helper;
if (cPoint != null &&
cPoint.first != null &&
Math.Log(cPoint.first.Value) >= xMin && Math.Log(cPoint.first.Value) <= xMax)
{
helper = new Concentrating1dMesher(xMin.Value, xMax.Value, size,
new Pair <double?, double?>(Math.Log(cPoint.first.Value), cPoint.second));
}
else
{
helper = new Uniform1dMesher(xMin.Value, xMax.Value, size);
}
locations_ = helper.locations();
for (int i = 0; i < locations_.Count; ++i)
{
dplus_[i] = helper.dplus(i);
dminus_[i] = helper.dminus(i);
}
}
public override void calculate()
{
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
Calendar volcal = process_.blackVolatility().link.calendar();
double s0 = process_.stateVariable().link.value();
Utils.QL_REQUIRE(s0 > 0.0, () => "negative or null underlying given");
double v = process_.blackVolatility().link.blackVol(arguments_.exercise.lastDate(), s0);
Date maturityDate = arguments_.exercise.lastDate();
double r = process_.riskFreeRate().link.zeroRate(maturityDate, rfdc, Compounding.Continuous, Frequency.NoFrequency).rate();
double q = process_.dividendYield().link.zeroRate(maturityDate, divdc, Compounding.Continuous, Frequency.NoFrequency).rate();
Date referenceDate = process_.riskFreeRate().link.referenceDate();
// binomial trees with constant coefficient
var flatRiskFree = new Handle <YieldTermStructure>(new FlatForward(referenceDate, r, rfdc));
var flatDividends = new Handle <YieldTermStructure>(new FlatForward(referenceDate, q, divdc));
var flatVol = new Handle <BlackVolTermStructure>(new BlackConstantVol(referenceDate, volcal, v, voldc));
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-plain payoff given");
double maturity = rfdc.yearFraction(referenceDate, maturityDate);
StochasticProcess1D bs =
new GeneralizedBlackScholesProcess(process_.stateVariable(), flatDividends, flatRiskFree, flatVol);
TimeGrid grid = new TimeGrid(maturity, timeSteps_);
T tree = FastActivator <T> .Create().factory(bs, maturity, timeSteps_, payoff.strike());
BlackScholesLattice <T> lattice = new BlackScholesLattice <T>(tree, r, maturity, timeSteps_);
DiscretizedVanillaOption option = new DiscretizedVanillaOption(arguments_, process_, grid);
option.initialize(lattice, maturity);
// Partial derivatives calculated from various points in the
// binomial tree (Odegaard)
// Rollback to third-last step, and get underlying price (s2) &
// option values (p2) at this point
option.rollback(grid[2]);
Vector va2 = new Vector(option.values());
Utils.QL_REQUIRE(va2.size() == 3, () => "Expect 3 nodes in grid at second step");
double p2h = va2[2]; // high-price
double s2 = lattice.underlying(2, 2); // high price
// Rollback to second-last step, and get option value (p1) at
// this point
option.rollback(grid[1]);
Vector va = new Vector(option.values());
Utils.QL_REQUIRE(va.size() == 2, () => "Expect 2 nodes in grid at first step");
double p1 = va[1];
// Finally, rollback to t=0
option.rollback(0.0);
double p0 = option.presentValue();
double s1 = lattice.underlying(1, 1);
// Calculate partial derivatives
double delta0 = (p1 - p0) / (s1 - s0); // dp/ds
double delta1 = (p2h - p1) / (s2 - s1); // dp/ds
// Store results
results_.value = p0;
results_.delta = delta0;
results_.gamma = 2.0 * (delta1 - delta0) / (s2 - s0); //d(delta)/ds
results_.theta = Utils.blackScholesTheta(process_,
results_.value.GetValueOrDefault(),
results_.delta.GetValueOrDefault(),
results_.gamma.GetValueOrDefault());
}
public YoYInflationIndex clone(Handle <YoYInflationTermStructure> h)
{
return(new YoYInflationIndex(familyName_, region_, revised_,
interpolated_, ratio_, frequency_,
availabilityLag_, currency_, h));
}
