void FDEuropeanEngine<Scheme>::calculate() const {
setupArguments(&arguments_);
setGridLimits();
initializeInitialCondition();
initializeOperator();
initializeBoundaryConditions();
FiniteDifferenceModel<Scheme<TridiagonalOperator> > model(
finiteDifferenceOperator_, BCs_);
prices_ = intrinsicValues_;
model.rollback(prices_.values(), getResidualTime(),
0, timeSteps_);
results_.value = prices_.valueAtCenter();
results_.delta = prices_.firstDerivativeAtCenter();
results_.gamma = prices_.secondDerivativeAtCenter();
results_.theta = blackScholesTheta(process_,
results_.value,
results_.delta,
results_.gamma);
results_.additionalResults["priceCurve"] = prices_;
}
void BinomialVanillaEngine<T>::calculate() const {
DayCounter rfdc = process_->riskFreeRate()->dayCounter();
DayCounter divdc = process_->dividendYield()->dayCounter();
DayCounter voldc = process_->blackVolatility()->dayCounter();
Calendar volcal = process_->blackVolatility()->calendar();
Real s0 = process_->stateVariable()->value();
QL_REQUIRE(s0 > 0.0, "negative or null underlying given");
Volatility v = process_->blackVolatility()->blackVol(
arguments_.exercise->lastDate(), s0);
Date maturityDate = arguments_.exercise->lastDate();
Rate r = process_->riskFreeRate()->zeroRate(maturityDate,
rfdc, Continuous, NoFrequency);
Rate q = process_->dividendYield()->zeroRate(maturityDate,
divdc, Continuous, NoFrequency);
Date referenceDate = process_->riskFreeRate()->referenceDate();
// binomial trees with constant coefficient
Handle<YieldTermStructure> flatRiskFree(
boost::shared_ptr<YieldTermStructure>(
new FlatForward(referenceDate, r, rfdc)));
Handle<YieldTermStructure> flatDividends(
boost::shared_ptr<YieldTermStructure>(
new FlatForward(referenceDate, q, divdc)));
Handle<BlackVolTermStructure> flatVol(
boost::shared_ptr<BlackVolTermStructure>(
new BlackConstantVol(referenceDate, volcal, v, voldc)));
boost::shared_ptr<PlainVanillaPayoff> payoff =
boost::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-plain payoff given");
Time maturity = rfdc.yearFraction(referenceDate, maturityDate);
boost::shared_ptr<StochasticProcess1D> bs(
new GeneralizedBlackScholesProcess(
process_->stateVariable(),
flatDividends, flatRiskFree, flatVol));
TimeGrid grid(maturity, timeSteps_);
boost::shared_ptr<T> tree(new T(bs, maturity, timeSteps_,
payoff->strike()));
boost::shared_ptr<BlackScholesLattice<T> > lattice(
new BlackScholesLattice<T>(tree, r, maturity, timeSteps_));
DiscretizedVanillaOption option(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]);
Array va2(option.values());
QL_ENSURE(va2.size() == 3, "Expect 3 nodes in grid at second step");
Real p2h = va2[2]; // high-price
Real s2 = lattice->underlying(2, 2); // high price
// Rollback to second-last step, and get option value (p1) at
// this point
option.rollback(grid[1]);
Array va(option.values());
QL_ENSURE(va.size() == 2, "Expect 2 nodes in grid at first step");
Real p1 = va[1];
// Finally, rollback to t=0
option.rollback(0.0);
Real p0 = option.presentValue();
Real s1 = lattice->underlying(1, 1);
// Calculate partial derivatives
Real delta0 = (p1-p0)/(s1-s0); // dp/ds
Real 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 = blackScholesTheta(process_,
results_.value,
results_.delta,
results_.gamma);
}
