mat33 randomInertiaMatrix() {
// generate random valid inertia matrix by first getting valid components
// along major axes and then rotating by random amount
vec3 principal = randomInertiaPrincipal();
mat33 rot(transformX(randomFloat(-BT_ID_PI, BT_ID_PI)) * transformY(randomFloat(-BT_ID_PI, BT_ID_PI)) *
transformZ(randomFloat(-BT_ID_PI, BT_ID_PI)));
mat33 inertia;
inertia(0, 0) = principal(0);
inertia(0, 1) = 0;
inertia(0, 2) = 0;
inertia(1, 0) = 0;
inertia(1, 1) = principal(1);
inertia(1, 2) = 0;
inertia(2, 0) = 0;
inertia(2, 1) = 0;
inertia(2, 2) = principal(2);
return rot * inertia * rot.transpose();
}
void AnalyticCompoundOptionEngine::calculate() const {
QL_REQUIRE(strikeDaughter()>0.0,
"Daughter strike must be positive");
QL_REQUIRE(strikeMother()>0.0,
"Mother strike must be positive");
QL_REQUIRE(spot() >= 0.0, "negative or null underlying given");
/* Solver Setup ***************************************************/
Date helpDate(process_->riskFreeRate()->referenceDate());
Date helpMaturity=helpDate+(maturityDaughter()-maturityMother())*Days;
Real vol =process_->blackVolatility()->blackVol(helpMaturity,
strikeDaughter());
Time helpTimeToMat=process_->time(helpMaturity);
vol=vol*std::sqrt(helpTimeToMat);
DiscountFactor dividendDiscount =
process_->dividendYield()->discount(helpMaturity);
DiscountFactor riskFreeDiscount =
process_->riskFreeRate()->discount(helpMaturity);
boost::shared_ptr<ImpliedSpotHelper> f(
new ImpliedSpotHelper(dividendDiscount, riskFreeDiscount,
vol, payoffDaughter(), strikeMother()));
Brent solver;
solver.setMaxEvaluations(1000);
Real accuracy = 1.0e-6;
Real X=0.0;
Real sSolved=0.0;
sSolved=solver.solve(*f, accuracy, strikeDaughter(), 1.0e-6, strikeDaughter()*1000.0);
X=transformX(sSolved); // transform stock to return as in Wystup's book
/* Solver Setup Finished*****************************************/
Real phi=typeDaughter(); // -1 or 1
Real w=typeMother(); // -1 or 1
Real rho=std::sqrt(residualTimeMother()/residualTimeDaughter());
BivariateCumulativeNormalDistributionDr78 N2(w*rho) ;
DiscountFactor ddD=dividendDiscountDaughter();
DiscountFactor rdD=riskFreeDiscountDaughter();
//DiscountFactor ddM=dividendDiscountMother();
DiscountFactor rdM=riskFreeDiscountMother();
Real XmSM=X-stdDeviationMother();
Real S=spot();
Real dP=dPlus();
Real dPT12=dPlusTau12(sSolved);
Real vD=volatilityDaughter();
Real dM=dMinus();
Real strD=strikeDaughter();
Real strM=strikeMother();
Real rTM=residualTimeMother();
Real rTD=residualTimeDaughter();
Real rD=riskFreeRateDaughter();
Real dD=dividendRateDaughter();
Real tempRes=0.0;
Real tempDelta=0.0;
Real tempGamma=0.0;
Real tempVega=0.0;
Real tempTheta=0.0;
Real N2XmSM=N2(-phi*w*XmSM,phi*dP);
Real N2X=N2(-phi*w*X,phi*dM);
Real NeX=N_(-phi*w*e(X));
Real NX=N_(-phi*w*X);
Real NT12=N_(phi*dPT12);
Real ndP=n_(dP);
Real nXm=n_(XmSM);
Real invMTime=1/std::sqrt(rTM);
Real invDTime=1/std::sqrt(rTD);
tempRes=phi*w*S*ddD*N2XmSM-phi*w*strD*rdD*N2X-w*strM*rdM*NX;
tempDelta=phi*w*ddD*N2XmSM;
tempGamma=(ddD/(vD*S))*(invMTime*nXm*NT12+w*invDTime*ndP*NeX);
tempVega=ddD*S*((1/invMTime)*nXm*NT12+w*(1/invDTime)*ndP*NeX);
tempTheta+=phi*w*dD*S*ddD*N2XmSM-phi*w*rD*strD*rdD*N2X-w*rD*strM*rdM*NX;
tempTheta-=0.5*vD*S*ddD*(invMTime*nXm*NT12+w*invDTime*ndP*NeX);
results_.value=tempRes;
results_.delta=tempDelta;
results_.gamma=tempGamma;
results_.vega=tempVega;
results_.theta=tempTheta;
}
QPointF ZStTransform::transform(const QPoint &pt) const
{
return QPointF(transformX(pt.x()), transformY(pt.y()));
}
QRectF ZStTransform::transform(const QRectF &rect) const
{
return QRectF(transformX(rect.left()), transformY(rect.top()),
rect.width() * getSx(), rect.height() * getSy());
}
ZPoint ZStTransform::transform(const ZPoint &pt) const
{
return ZPoint(transformX(pt.x()), transformY(pt.y()), transformZ(pt.z()));
}
