FdmBlackScholesOp Class Reference

#include <qle/methods/fdmblackscholesop.hpp>

Inheritance diagram for FdmBlackScholesOp:

Collaboration diagram for FdmBlackScholesOp:

Public Member Functions
	FdmBlackScholesOp (const ext::shared_ptr< FdmMesher > &mesher, const ext::shared_ptr< GeneralizedBlackScholesProcess > &process, Real strike=Null< Real >(), bool localVol=false, Real illegalLocalVolOverwrite=-Null< Real >(), Size direction=0, const ext::shared_ptr< FdmQuantoHelper > &quantoHelper=ext::shared_ptr< FdmQuantoHelper >(), const bool discounting=true, const bool ensureNonNegativeForwardVariance=false)
Size	size () const override
void	setTime (Time t1, Time t2) override
Array	apply (const Array &r) const override
Array	apply_mixed (const Array &r) const override
Array	apply_direction (Size direction, const Array &r) const override
Array	solve_splitting (Size direction, const Array &r, Real s) const override
Array	preconditioner (const Array &r, Real s) const override
std::vector< QuantLib::SparseMatrix >	toMatrixDecomp () const override

Private Attributes
const ext::shared_ptr< FdmMesher >	mesher_
const ext::shared_ptr< YieldTermStructure >	rTS_
const ext::shared_ptr< YieldTermStructure >	qTS_
const ext::shared_ptr< BlackVolTermStructure >	volTS_
const ext::shared_ptr< LocalVolTermStructure >	localVol_
const Array	x_
const FirstDerivativeOp	dxMap_
const TripleBandLinearOp	dxxMap_
TripleBandLinearOp	mapT_
const Real	strike_
const Real	illegalLocalVolOverwrite_
const Size	direction_
const ext::shared_ptr< FdmQuantoHelper >	quantoHelper_
const Real	initialValue_
const bool	discounting_
const bool	ensureNonNegativeForwardVariance_

Detailed Description

Definition at line 47 of file fdmblackscholesop.hpp.

Constructor & Destructor Documentation

FdmBlackScholesOp()

FdmBlackScholesOp	(	const ext::shared_ptr< FdmMesher > &	mesher,
		const ext::shared_ptr< GeneralizedBlackScholesProcess > &	process,
		Real	strike = Null<Real>(),
		bool	localVol = false,
		Real	illegalLocalVolOverwrite = -Null<Real>(),
		Size	direction = 0,
		const ext::shared_ptr< FdmQuantoHelper > &	quantoHelper = ext::shared_ptr<FdmQuantoHelper>(),
		const bool	discounting = true,
		const bool	ensureNonNegativeForwardVariance = false
	)

Definition at line 30 of file fdmblackscholesop.cpp.

    : mesher_(mesher), rTS_(bsProcess->riskFreeRate().currentLink()), qTS_(bsProcess->dividendYield().currentLink()),
      volTS_(bsProcess->blackVolatility().currentLink()),
      localVol_((localVol) ? bsProcess->localVolatility().currentLink() : ext::shared_ptr<LocalVolTermStructure>()),
      x_((localVol) ? Array(Exp(mesher->locations(direction))) : Array()), dxMap_(FirstDerivativeOp(direction, mesher)),
      dxxMap_(SecondDerivativeOp(direction, mesher)), mapT_(direction, mesher), strike_(strike),
      illegalLocalVolOverwrite_(illegalLocalVolOverwrite), direction_(direction), quantoHelper_(quantoHelper),
      initialValue_(bsProcess->x0()), discounting_(discounting),
      ensureNonNegativeForwardVariance_(ensureNonNegativeForwardVariance) {}

Member Function Documentation

size()

Size size ( ) const

override

Definition at line 98 of file fdmblackscholesop.cpp.

{ return 1u; }

setTime()

void setTime ( Time  t1, Time  t2  )

override

Definition at line 44 of file fdmblackscholesop.cpp.

                                                {
    const Rate r = rTS_->forwardRate(t1, t2, Continuous).rate();
    const Rate q = qTS_->forwardRate(t1, t2, Continuous).rate();
    Rate discountRate = discounting_ ? r : 0.0;
 
    if (localVol_) {
        const ext::shared_ptr<FdmLinearOpLayout> layout = mesher_->layout();
        const FdmLinearOpIterator endIter = layout->end();
 
        Array v(layout->size());
        for (FdmLinearOpIterator iter = layout->begin(); iter != endIter; ++iter) {
            const Size i = iter.index();
 
            if (illegalLocalVolOverwrite_ < 0.0) {
                v[i] = squared(localVol_->localVol(0.5 * (t1 + t2), x_[i], true));
            } else {
                try {
                    v[i] = squared(localVol_->localVol(0.5 * (t1 + t2), x_[i], true));
                } catch (Error&) {
                    v[i] = squared(illegalLocalVolOverwrite_);
                }
            }
        }
 
        if (quantoHelper_) {
            mapT_.axpyb(r - q - 0.5 * v - quantoHelper_->quantoAdjustment(Sqrt(v), t1, t2), dxMap_,
                        dxxMap_.mult(0.5 * v), Array(1, -discountRate));
        } else {
            mapT_.axpyb(r - q - 0.5 * v, dxMap_, dxxMap_.mult(0.5 * v), Array(1, -discountRate));
        }
    } else {
        Real k1, k2;
        if (strike_ == Null<Real>()) {
            k1 = initialValue_ * qTS_->discount(t1) / rTS_->discount(t1);
            k2 = initialValue_ * qTS_->discount(t2) / rTS_->discount(t2);
        } else {
            k1 = k2 = strike_;
        }
        Real v = ((close_enough(t2, 0.0) ? 0.0 : volTS_->blackVariance(t2, k2)) -
                  (close_enough(t1, 0.0) ? 0.0 : volTS_->blackVariance(t1, k1))) /
                 (t2 - t1);
        if (ensureNonNegativeForwardVariance_)
            v = std::max(v, 0.0);
 
        if (quantoHelper_) {
            mapT_.axpyb(Array(1, r - q - 0.5 * v) - quantoHelper_->quantoAdjustment(Array(1, std::sqrt(v)), t1, t2),
                        dxMap_, dxxMap_.mult(0.5 * Array(mesher_->layout()->size(), v)), Array(1, -discountRate));
        } else {
            mapT_.axpyb(Array(1, r - q - 0.5 * v), dxMap_, dxxMap_.mult(0.5 * Array(mesher_->layout()->size(), v)),
                        Array(1, -discountRate));
        }
    }
}

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apply()

Array apply ( const Array &  r ) const

override

Definition at line 100 of file fdmblackscholesop.cpp.

{ return mapT_.apply(u); }

apply_mixed()

Array apply_mixed ( const Array &  r ) const

override

Definition at line 111 of file fdmblackscholesop.cpp.

                                                         {
    Array retVal(r.size(), 0.0);
    return retVal;
}

apply_direction()

Array apply_direction ( Size  direction, const Array &  r  ) const

override

Definition at line 102 of file fdmblackscholesop.cpp.

                                                                             {
    if (direction == direction_)
        return mapT_.apply(r);
    else {
        Array retVal(r.size(), 0.0);
        return retVal;
    }
}

solve_splitting()

Array solve_splitting ( Size  direction, const Array &  r, Real  s  ) const

override

Definition at line 116 of file fdmblackscholesop.cpp.

                                                                                      {
    if (direction == direction_)
        return mapT_.solve_splitting(r, dt, 1.0);
    else {
        Array retVal(r);
        return retVal;
    }
}

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preconditioner()

Array preconditioner ( const Array &  r, Real  s  ) const

override

Definition at line 125 of file fdmblackscholesop.cpp.

                                                                     {
    return solve_splitting(direction_, r, dt);
}

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toMatrixDecomp()

std::vector< QuantLib::SparseMatrix > toMatrixDecomp ( ) const

override

Definition at line 130 of file fdmblackscholesop.cpp.

                                                                            {
        std::vector<QuantLib::SparseMatrix> retVal(1, mapT_.toMatrix());
    return retVal;
}

Member Data Documentation

mesher_

const ext::shared_ptr<FdmMesher> mesher_

private

Definition at line 68 of file fdmblackscholesop.hpp.

rTS_

const ext::shared_ptr<YieldTermStructure> rTS_

private

Definition at line 69 of file fdmblackscholesop.hpp.

qTS_

const ext::shared_ptr<YieldTermStructure> qTS_

private

Definition at line 69 of file fdmblackscholesop.hpp.

volTS_

const ext::shared_ptr<BlackVolTermStructure> volTS_

private

Definition at line 70 of file fdmblackscholesop.hpp.

localVol_

const ext::shared_ptr<LocalVolTermStructure> localVol_

private

Definition at line 71 of file fdmblackscholesop.hpp.

x_

const Array x_

private

Definition at line 72 of file fdmblackscholesop.hpp.

dxMap_

const FirstDerivativeOp dxMap_

private

Definition at line 73 of file fdmblackscholesop.hpp.

dxxMap_

const TripleBandLinearOp dxxMap_

private

Definition at line 74 of file fdmblackscholesop.hpp.

mapT_

TripleBandLinearOp mapT_

private

Definition at line 75 of file fdmblackscholesop.hpp.

strike_

const Real strike_

private

Definition at line 76 of file fdmblackscholesop.hpp.

illegalLocalVolOverwrite_

const Real illegalLocalVolOverwrite_

private

Definition at line 77 of file fdmblackscholesop.hpp.

direction_

const Size direction_

private

Definition at line 78 of file fdmblackscholesop.hpp.

quantoHelper_

const ext::shared_ptr<FdmQuantoHelper> quantoHelper_

private

Definition at line 79 of file fdmblackscholesop.hpp.

initialValue_

const Real initialValue_

private

Definition at line 80 of file fdmblackscholesop.hpp.

discounting_

const bool discounting_

private

Definition at line 81 of file fdmblackscholesop.hpp.

ensureNonNegativeForwardVariance_

const bool ensureNonNegativeForwardVariance_

private

Definition at line 82 of file fdmblackscholesop.hpp.