public override void calculate()
{
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
Calendar volcal = process_.blackVolatility().link.calendar();
double s0 = process_.stateVariable().link.value();
Utils.QL_REQUIRE(s0 > 0.0, () => "negative or null underlying given");
double v = process_.blackVolatility().link.blackVol(arguments_.exercise.lastDate(), s0);
Date maturityDate = arguments_.exercise.lastDate();
double r = process_.riskFreeRate().link.zeroRate(maturityDate, rfdc, Compounding.Continuous, Frequency.NoFrequency).value();
double q = process_.dividendYield().link.zeroRate(maturityDate, divdc, Compounding.Continuous, Frequency.NoFrequency).value();
Date referenceDate = process_.riskFreeRate().link.referenceDate();
// binomial trees with constant coefficient
Handle <YieldTermStructure> flatRiskFree = new Handle <YieldTermStructure>(new FlatForward(referenceDate, r, rfdc));
Handle <YieldTermStructure> flatDividends = new Handle <YieldTermStructure>(new FlatForward(referenceDate, q, divdc));
Handle <BlackVolTermStructure> flatVol = new Handle <BlackVolTermStructure>(new BlackConstantVol(referenceDate, volcal, v, voldc));
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-striked payoff given");
double maturity = rfdc.yearFraction(referenceDate, maturityDate);
StochasticProcess1D bs = new GeneralizedBlackScholesProcess(process_.stateVariable(),
flatDividends, flatRiskFree, flatVol);
TimeGrid grid = new TimeGrid(maturity, timeSteps_);
ITree tree = getTree_(bs, maturity, timeSteps_, payoff.strike());
BlackScholesLattice <ITree> lattice = new BlackScholesLattice <ITree>(tree, r, maturity, timeSteps_);
DiscretizedAsset option = getAsset_(arguments_, process_, grid);
option.initialize(lattice, maturity);
// Partial derivatives calculated from various points in the
// binomial tree
// (see J.C.Hull, "Options, Futures and other derivatives", 6th edition, pp 397/398)
// Rollback to third-last step, and get underlying prices (s2) &
// option values (p2) at this point
option.rollback(grid[2]);
Vector va2 = new Vector(option.values());
Utils.QL_REQUIRE(va2.size() == 3, () => "Expect 3 nodes in grid at second step");
double p2u = va2[2]; // up
double p2m = va2[1]; // mid
double p2d = va2[0]; // down (low)
double s2u = lattice.underlying(2, 2); // up price
double s2m = lattice.underlying(2, 1); // middle price
double s2d = lattice.underlying(2, 0); // down (low) price
// calculate gamma by taking the first derivate of the two deltas
double delta2u = (p2u - p2m) / (s2u - s2m);
double delta2d = (p2m - p2d) / (s2m - s2d);
double gamma = (delta2u - delta2d) / ((s2u - s2d) / 2);
// Rollback to second-last step, and get option values (p1) at
// this point
option.rollback(grid[1]);
Vector va = new Vector(option.values());
Utils.QL_REQUIRE(va.size() == 2, () => "Expect 2 nodes in grid at first step");
double p1u = va[1];
double p1d = va[0];
double s1u = lattice.underlying(1, 1); // up (high) price
double s1d = lattice.underlying(1, 0); // down (low) price
double delta = (p1u - p1d) / (s1u - s1d);
// Finally, rollback to t=0
option.rollback(0.0);
double p0 = option.presentValue();
// Store results
results_.value = p0;
results_.delta = delta;
results_.gamma = gamma;
// theta can be approximated by calculating the numerical derivative
// between mid value at third-last step and at t0. The underlying price
// is the same, only time varies.
results_.theta = (p2m - p0) / grid[2];
}
//! computes the present value of an asset. public abstract double presentValue(DiscretizedAsset a);
/*! Roll back an asset until the given time, but do not perform * the final adjustment. */ public abstract void partialRollback(DiscretizedAsset a, double to);
/*! Roll back an asset until the given time, performing any needed adjustment. */ public abstract void rollback(DiscretizedAsset a, double to);
/* Numerical method interface
*
* These methods are to be used by discretized assets and
* must be overridden by developers implementing numerical
* methods. Users are advised to use the corresponding
* methods of DiscretizedAsset instead.
*/
//! initialize an asset at the given time.
public abstract void initialize(DiscretizedAsset a, double time);
public DiscretizedOption(DiscretizedAsset underlying, Exercise.Type exerciseType, List <double> exerciseTimes)
{
underlying_ = underlying;
exerciseType_ = exerciseType;
exerciseTimes_ = exerciseTimes;
}
