public Fdm1DimSolver(FdmSolverDesc solverDesc,
FdmSchemeDesc schemeDesc,
FdmLinearOpComposite op)
{
solverDesc_ = solverDesc;
schemeDesc_ = schemeDesc;
op_ = op;
thetaCondition_ = new FdmSnapshotCondition(
0.99 * Math.Min(1.0 / 365.0,
solverDesc.condition.stoppingTimes().empty()
? solverDesc.maturity
: solverDesc.condition.stoppingTimes().First()));
conditions_ = FdmStepConditionComposite.joinConditions(thetaCondition_,
solverDesc.condition);
x_ = new InitializedList <double>(solverDesc.mesher.layout().size());
initialValues_ = new InitializedList <double>(solverDesc.mesher.layout().size());
resultValues_ = new Vector(solverDesc.mesher.layout().size());
FdmMesher mesher = solverDesc.mesher;
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter;
++iter)
{
initialValues_[iter.index()]
= solverDesc_.calculator.avgInnerValue(iter,
solverDesc.maturity);
x_[iter.index()] = mesher.location(iter, 0);
}
}
public FdmBackwardSolver(FdmLinearOpComposite map,
FdmBoundaryConditionSet bcSet,
FdmStepConditionComposite condition,
FdmSchemeDesc schemeDesc)
{
map_ = map;
bcSet_ = bcSet;
condition_ = condition;
schemeDesc_ = schemeDesc;
}
public static FdmStepConditionComposite joinConditions(FdmSnapshotCondition c1,
FdmStepConditionComposite c2)
{
List <List <double> > stoppingTimes = new List <List <double> >();
stoppingTimes.Add(c2.stoppingTimes());
stoppingTimes.Add(new InitializedList <double>(1, c1.getTime()));
List <IStepCondition <Vector> > conditions = new List <IStepCondition <Vector> >();
conditions.Add(c2);
conditions.Add(c1);
return(new FdmStepConditionComposite(stoppingTimes, conditions));
}
public override void calculate()
{
// 1. Mesher
HestonProcess process = model_.currentLink().process();
double maturity = process.time(arguments_.exercise.lastDate());
// 1.1 The variance mesher
int tGridMin = 5;
int tGridAvgSteps = Math.Max(tGridMin, tGrid_ / 50);
FdmHestonLocalVolatilityVarianceMesher varianceMesher
= new FdmHestonLocalVolatilityVarianceMesher(vGrid_, process, leverageFct_, maturity, tGridAvgSteps);
// 1.2 the equity mesher
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
double?xMin = null;
double?xMax = null;
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
xMin = Math.Log(arguments_.barrier.Value);
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
xMax = Math.Log(arguments_.barrier.Value);
}
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(xGrid_,
FdmBlackScholesMesher.processHelper(process.s0(),
process.dividendYield(),
process.riskFreeRate(),
varianceMesher.volaEstimate()),
maturity,
payoff.strike(),
xMin,
xMax,
0.0001,
1.5,
new Pair <double?, double?>(),
arguments_.cashFlow);
FdmMesher mesher =
new FdmMesherComposite(equityMesher, varianceMesher);
// 2. Calculator
StrikedTypePayoff rebatePayoff =
new CashOrNothingPayoff(Option.Type.Call, 0.0, arguments_.rebate.Value);
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(rebatePayoff, mesher, 0);
// 3. Step conditions
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European,
() => "only european style option are supported");
FdmStepConditionComposite conditions =
FdmStepConditionComposite.vanillaComposite(
arguments_.cashFlow, arguments_.exercise,
mesher, calculator,
process.riskFreeRate().currentLink().referenceDate(),
process.riskFreeRate().currentLink().dayCounter());
// 4. Boundary conditions
FdmBoundaryConditionSet boundaries = new FdmBoundaryConditionSet();
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
boundaries.Add(new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Lower));
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
boundaries.Add(new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Upper));
}
// 5. Solver
FdmSolverDesc solverDesc = new FdmSolverDesc();
solverDesc.mesher = mesher;
solverDesc.bcSet = boundaries;
solverDesc.condition = conditions;
solverDesc.calculator = calculator;
solverDesc.maturity = maturity;
solverDesc.dampingSteps = dampingSteps_;
solverDesc.timeSteps = tGrid_;
FdmHestonSolver solver =
new FdmHestonSolver(
new Handle <HestonProcess>(process),
solverDesc, schemeDesc_,
new Handle <FdmQuantoHelper>(),
leverageFct_);
double spot = process.s0().currentLink().value();
results_.value = solver.valueAt(spot, process.v0());
results_.delta = solver.deltaAt(spot, process.v0());
results_.gamma = solver.gammaAt(spot, process.v0());
results_.theta = solver.thetaAt(spot, process.v0());
}
public override void calculate()
{
// 1. Mesher
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
double maturity = process_.time(arguments_.exercise.lastDate());
double?xMin = null;
double?xMax = null;
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
xMin = Math.Log(arguments_.barrier.Value);
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
xMax = Math.Log(arguments_.barrier.Value);
}
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(xGrid_, process_, maturity,
payoff.strike(), xMin, xMax, 0.0001, 1.5,
new Pair <double?, double?>(),
arguments_.cashFlow);
FdmMesher mesher =
new FdmMesherComposite(equityMesher);
// 2. Calculator
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(payoff, mesher, 0);
// 3. Step conditions
List <IStepCondition <Vector> > stepConditions = new List <IStepCondition <Vector> >();
List <List <double> > stoppingTimes = new List <List <double> >();
// 3.1 Step condition if discrete dividends
FdmDividendHandler dividendCondition =
new FdmDividendHandler(arguments_.cashFlow, mesher,
process_.riskFreeRate().currentLink().referenceDate(),
process_.riskFreeRate().currentLink().dayCounter(), 0);
if (!arguments_.cashFlow.empty())
{
stepConditions.Add(dividendCondition);
stoppingTimes.Add(dividendCondition.dividendTimes());
}
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European,
() => "only european style option are supported");
FdmStepConditionComposite conditions =
new FdmStepConditionComposite(stoppingTimes, stepConditions);
// 4. Boundary conditions
FdmBoundaryConditionSet boundaries = new FdmBoundaryConditionSet();
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
boundaries.Add(
new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Lower));
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
boundaries.Add(
new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Upper));
}
// 5. Solver
FdmSolverDesc solverDesc = new FdmSolverDesc();
solverDesc.mesher = mesher;
solverDesc.bcSet = boundaries;
solverDesc.condition = conditions;
solverDesc.calculator = calculator;
solverDesc.maturity = maturity;
solverDesc.dampingSteps = dampingSteps_;
solverDesc.timeSteps = tGrid_;
FdmBlackScholesSolver solver =
new FdmBlackScholesSolver(
new Handle <GeneralizedBlackScholesProcess>(process_),
payoff.strike(), solverDesc, schemeDesc_,
localVol_, illegalLocalVolOverwrite_);
double spot = process_.x0();
results_.value = solver.valueAt(spot);
results_.delta = solver.deltaAt(spot);
results_.gamma = solver.gammaAt(spot);
results_.theta = solver.thetaAt(spot);
// 6. Calculate vanilla option and rebate for in-barriers
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.UpIn)
{
// Cast the payoff
StrikedTypePayoff castedPayoff = arguments_.payoff as StrikedTypePayoff;
// Calculate the vanilla option
DividendVanillaOption vanillaOption =
new DividendVanillaOption(castedPayoff, arguments_.exercise,
dividendCondition.dividendDates(),
dividendCondition.dividends());
vanillaOption.setPricingEngine(
new FdBlackScholesVanillaEngine(
process_, tGrid_, xGrid_,
0, // dampingSteps
schemeDesc_, localVol_, illegalLocalVolOverwrite_));
// Calculate the rebate value
DividendBarrierOption rebateOption =
new DividendBarrierOption(arguments_.barrierType,
arguments_.barrier.Value,
arguments_.rebate.Value,
castedPayoff, arguments_.exercise,
dividendCondition.dividendDates(),
dividendCondition.dividends());
int min_grid_size = 50;
int rebateDampingSteps
= (dampingSteps_ > 0) ? Math.Min(1, dampingSteps_ / 2) : 0;
rebateOption.setPricingEngine(new FdBlackScholesRebateEngine(
process_, tGrid_, Math.Max(min_grid_size, xGrid_ / 5),
rebateDampingSteps, schemeDesc_, localVol_,
illegalLocalVolOverwrite_));
results_.value = vanillaOption.NPV() + rebateOption.NPV()
- results_.value;
results_.delta = vanillaOption.delta() + rebateOption.delta()
- results_.delta;
results_.gamma = vanillaOption.gamma() + rebateOption.gamma()
- results_.gamma;
results_.theta = vanillaOption.theta() + rebateOption.theta()
- results_.theta;
}
}
public FdmSolverDesc getSolverDesc(double x)
{
// 1. Mesher
HestonProcess process = model_.currentLink().process();
double maturity = process.time(arguments_.exercise.lastDate());
// 1.1 The variance mesher
int tGridMin = 5;
FdmHestonVarianceMesher varianceMesher =
new FdmHestonVarianceMesher(vGrid_, process,
maturity, Math.Max(tGridMin, tGrid_ / 50));
// 1.2 The equity mesher
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Fdm1dMesher equityMesher;
if (strikes_.empty())
{
equityMesher = new FdmBlackScholesMesher(
xGrid_,
FdmBlackScholesMesher.processHelper(
process.s0(), process.dividendYield(),
process.riskFreeRate(), varianceMesher.volaEstimate()),
maturity, payoff.strike(),
null, null, 0.0001, x,
new Pair <double?, double?>(payoff.strike(), 0.1),
arguments_.cashFlow);
}
else
{
Utils.QL_REQUIRE(arguments_.cashFlow.empty(), () => "multiple strikes engine "
+ "does not work with discrete dividends");
equityMesher = new FdmBlackScholesMultiStrikeMesher(
xGrid_,
FdmBlackScholesMesher.processHelper(
process.s0(), process.dividendYield(),
process.riskFreeRate(), varianceMesher.volaEstimate()),
maturity, strikes_, 0.0001, x,
new Pair <double?, double?>(payoff.strike(), 0.075));
}
FdmMesher mesher = new FdmMesherComposite(equityMesher, varianceMesher);
// 2. Calculator
FdmInnerValueCalculator calculator = new FdmLogInnerValue(arguments_.payoff, mesher, 0);
// 3. Step conditions
FdmStepConditionComposite conditions =
FdmStepConditionComposite.vanillaComposite(
arguments_.cashFlow, arguments_.exercise,
mesher, calculator,
process.riskFreeRate().currentLink().referenceDate(),
process.riskFreeRate().currentLink().dayCounter());
// 4. Boundary conditions
FdmBoundaryConditionSet boundaries = new FdmBoundaryConditionSet();
// 5. Solver
FdmSolverDesc solverDesc = new FdmSolverDesc();
solverDesc.mesher = mesher;
solverDesc.bcSet = boundaries;
solverDesc.condition = conditions;
solverDesc.calculator = calculator;
solverDesc.maturity = maturity;
solverDesc.dampingSteps = dampingSteps_;
solverDesc.timeSteps = tGrid_;
return(solverDesc);
}
public override void calculate()
{
// 1. Mesher
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
double maturity = process_.time(arguments_.exercise.lastDate());
double?xMin = null;
double?xMax = null;
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
xMin = Math.Log(arguments_.barrier.Value);
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
xMax = Math.Log(arguments_.barrier.Value);
}
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(xGrid_, process_, maturity,
payoff.strike(), xMin, xMax, 0.0001, 1.5,
new Pair <double?, double?>(),
arguments_.cashFlow);
FdmMesher mesher =
new FdmMesherComposite(equityMesher);
// 2. Calculator
StrikedTypePayoff rebatePayoff =
new CashOrNothingPayoff(Option.Type.Call, 0.0, arguments_.rebate.Value);
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(rebatePayoff, mesher, 0);
// 3. Step conditions
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European,
() => "only european style option are supported");
FdmStepConditionComposite conditions =
FdmStepConditionComposite.vanillaComposite(
arguments_.cashFlow, arguments_.exercise,
mesher, calculator,
process_.riskFreeRate().currentLink().referenceDate(),
process_.riskFreeRate().currentLink().dayCounter());
// 4. Boundary conditions
FdmBoundaryConditionSet boundaries = new FdmBoundaryConditionSet();
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
boundaries.Add(new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Lower));
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
boundaries.Add(new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Upper));
}
// 5. Solver
FdmSolverDesc solverDesc = new FdmSolverDesc();
solverDesc.mesher = mesher;
solverDesc.bcSet = boundaries;
solverDesc.condition = conditions;
solverDesc.calculator = calculator;
solverDesc.maturity = maturity;
solverDesc.dampingSteps = dampingSteps_;
solverDesc.timeSteps = tGrid_;
FdmBlackScholesSolver solver =
new FdmBlackScholesSolver(
new Handle <GeneralizedBlackScholesProcess>(process_),
payoff.strike(), solverDesc, schemeDesc_,
localVol_, illegalLocalVolOverwrite_);
double spot = process_.x0();
results_.value = solver.valueAt(spot);
results_.delta = solver.deltaAt(spot);
results_.gamma = solver.gammaAt(spot);
results_.theta = solver.thetaAt(spot);
}
public override void calculate()
{
// 1. Term structure
Handle <YieldTermStructure> ts = model_.currentLink().termStructure();
// 2. Mesher
DayCounter dc = ts.currentLink().dayCounter();
Date referenceDate = ts.currentLink().referenceDate();
double maturity = dc.yearFraction(referenceDate,
arguments_.exercise.lastDate());
OrnsteinUhlenbeckProcess process = new OrnsteinUhlenbeckProcess(model_.currentLink().a(), model_.currentLink().sigma());
Fdm1dMesher shortRateMesher =
new FdmSimpleProcess1DMesher(xGrid_, process, maturity, 1, invEps_);
FdmMesher mesher = new FdmMesherComposite(shortRateMesher);
// 3. Inner Value Calculator
List <Date> exerciseDates = arguments_.exercise.dates();
Dictionary <double, Date> t2d = new Dictionary <double, Date>();
for (int i = 0; i < exerciseDates.Count; ++i)
{
double t = dc.yearFraction(referenceDate, exerciseDates[i]);
Utils.QL_REQUIRE(t >= 0, () => "exercise dates must not contain past date");
t2d.Add(t, exerciseDates[i]);
}
Handle <YieldTermStructure> disTs = model_.currentLink().termStructure();
Handle <YieldTermStructure> fwdTs
= arguments_.swap.iborIndex().forwardingTermStructure();
Utils.QL_REQUIRE(fwdTs.currentLink().dayCounter() == disTs.currentLink().dayCounter(),
() => "day counter of forward and discount curve must match");
Utils.QL_REQUIRE(fwdTs.currentLink().referenceDate() == disTs.currentLink().referenceDate(),
() => "reference date of forward and discount curve must match");
HullWhite fwdModel =
new HullWhite(fwdTs, model_.currentLink().a(), model_.currentLink().sigma());
FdmInnerValueCalculator calculator =
new FdmAffineModelSwapInnerValue <HullWhite>(
model_.currentLink(), fwdModel,
arguments_.swap, t2d, mesher, 0);
// 4. Step conditions
FdmStepConditionComposite conditions =
FdmStepConditionComposite.vanillaComposite(
new DividendSchedule(), arguments_.exercise,
mesher, calculator, referenceDate, dc);
// 5. Boundary conditions
FdmBoundaryConditionSet boundaries = new FdmBoundaryConditionSet();
// 6. Solver
FdmSolverDesc solverDesc = new FdmSolverDesc();
solverDesc.mesher = mesher;
solverDesc.bcSet = boundaries;
solverDesc.condition = conditions;
solverDesc.calculator = calculator;
solverDesc.maturity = maturity;
solverDesc.timeSteps = tGrid_;
solverDesc.dampingSteps = dampingSteps_;
FdmHullWhiteSolver solver =
new FdmHullWhiteSolver(model_, solverDesc, schemeDesc_);
results_.value = solver.valueAt(0.0);
}
public override void calculate()
{
// 0. Cash dividend model
Date exerciseDate = arguments_.exercise.lastDate();
double maturity = process_.time(exerciseDate);
Date settlementDate = process_.riskFreeRate().currentLink().referenceDate();
double spotAdjustment = 0.0;
DividendSchedule dividendSchedule = new DividendSchedule();
switch (cashDividendModel_)
{
case CashDividendModel.Spot:
dividendSchedule = arguments_.cashFlow;
break;
case CashDividendModel.Escrowed:
foreach (Dividend divIter in dividendSchedule)
{
Date divDate = divIter.date();
if (divDate <= exerciseDate && divDate >= settlementDate)
{
double divAmount = divIter.amount();
double discount =
process_.riskFreeRate().currentLink().discount(divDate) /
process_.dividendYield().currentLink().discount(divDate);
spotAdjustment -= divAmount * discount;
}
}
Utils.QL_REQUIRE(process_.x0() + spotAdjustment > 0.0,
() => "spot minus dividends becomes negative");
break;
default:
Utils.QL_FAIL("unknwon cash dividend model");
break;
}
// 1. Mesher
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(
xGrid_, process_, maturity, payoff.strike(),
null, null, 0.0001, 1.5,
new Pair <double?, double?>(payoff.strike(), 0.1),
dividendSchedule, quantoHelper_,
spotAdjustment);
FdmMesher mesher =
new FdmMesherComposite(equityMesher);
// 2. Calculator
FdmInnerValueCalculator calculator = new FdmLogInnerValue(payoff, mesher, 0);
// 3. Step conditions
FdmStepConditionComposite conditions = FdmStepConditionComposite.vanillaComposite(
arguments_.cashFlow, arguments_.exercise,
mesher, calculator,
process_.riskFreeRate().currentLink().referenceDate(),
process_.riskFreeRate().currentLink().dayCounter());
// 4. Boundary conditions
FdmBoundaryConditionSet boundaries = new FdmBoundaryConditionSet();
// 5. Solver
FdmSolverDesc solverDesc = new FdmSolverDesc();
solverDesc.mesher = mesher;
solverDesc.bcSet = boundaries;
solverDesc.condition = conditions;
solverDesc.calculator = calculator;
solverDesc.maturity = maturity;
solverDesc.dampingSteps = dampingSteps_;
solverDesc.timeSteps = tGrid_;
FdmBlackScholesSolver solver =
new FdmBlackScholesSolver(
new Handle <GeneralizedBlackScholesProcess>(process_),
payoff.strike(), solverDesc, schemeDesc_,
localVol_, illegalLocalVolOverwrite_);
double spot = process_.x0();
results_.value = solver.valueAt(spot);
results_.delta = solver.deltaAt(spot);
results_.gamma = solver.gammaAt(spot);
results_.theta = solver.thetaAt(spot);
}