public FdmBlackScholesMultiStrikeMesher(int size,
GeneralizedBlackScholesProcess process,
double maturity,
List <double> strikes,
double eps = 0.0001,
double scaleFactor = 1.5,
Pair <double?, double?> cPoint
= null)
: base(size)
{
double spot = process.x0();
Utils.QL_REQUIRE(spot > 0.0, () => "negative or null underlying given");
double d = process.dividendYield().currentLink().discount(maturity)
/ process.riskFreeRate().currentLink().discount(maturity);
double minStrike = strikes.Min();
double maxStrike = strikes.Max();
double Fmin = spot * spot / maxStrike * d;
double Fmax = spot * spot / minStrike * d;
Utils.QL_REQUIRE(Fmin > 0.0, () => "negative forward given");
// Set the grid boundaries
double normInvEps = new InverseCumulativeNormal().value(1 - eps);
double sigmaSqrtTmin
= process.blackVolatility().currentLink().blackVol(maturity, minStrike)
* Math.Sqrt(maturity);
double sigmaSqrtTmax
= process.blackVolatility().currentLink().blackVol(maturity, maxStrike)
* Math.Sqrt(maturity);
double xMin
= Math.Min(0.8 * Math.Log(0.8 * spot * spot / maxStrike),
Math.Log(Fmin) - sigmaSqrtTmin * normInvEps * scaleFactor
- sigmaSqrtTmin * sigmaSqrtTmin / 2.0);
double xMax
= Math.Max(1.2 * Math.Log(0.8 * spot * spot / minStrike),
Math.Log(Fmax) + sigmaSqrtTmax * normInvEps * scaleFactor
- sigmaSqrtTmax * sigmaSqrtTmax / 2.0);
Fdm1dMesher helper;
if (cPoint.first != null &&
Math.Log(cPoint.first.Value) >= xMin && Math.Log(cPoint.first.Value) <= xMax)
{
helper = new Concentrating1dMesher(xMin, xMax, size,
new Pair <double?, double?>(Math.Log(cPoint.first.Value), cPoint.second));
}
else
{
helper = new Uniform1dMesher(xMin, xMax, size);
}
locations_ = helper.locations();
for (int i = 0; i < locations_.Count; ++i)
{
dplus_[i] = helper.dplus(i);
dminus_[i] = helper.dminus(i);
}
}
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);
}
}