Esempio n. 1
0
        static void Main(string[] args)
        {
            const int xSteps       = 100;
            const int tSteps       = 25;
            const int dampingSteps = 0;

            Date today = new Date(15, Month.January, 2020);

            Settings.instance().setEvaluationDate(today);

            DayCounter dc = new Actual365Fixed();

            YieldTermStructureHandle rTS = new YieldTermStructureHandle(
                new FlatForward(today, 0.06, dc));
            YieldTermStructureHandle qTS = new YieldTermStructureHandle(
                new FlatForward(today, 0.02, dc));

            const double      strike = 110.0;
            StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, strike);

            Date   maturityDate = today.Add(new Period(1, TimeUnit.Years));
            double maturity     = dc.yearFraction(today, maturityDate);

            Exercise exercise = new AmericanExercise(today, maturityDate);

            Instrument vanillaOption = new VanillaOption(payoff, exercise);

            QuoteHandle spot = new QuoteHandle(new SimpleQuote(100.0));
            BlackVolTermStructureHandle volatility = new BlackVolTermStructureHandle(
                new BlackConstantVol(today, new TARGET(), 0.20, dc));

            BlackScholesMertonProcess process =
                new BlackScholesMertonProcess(spot, qTS, rTS, volatility);

            vanillaOption.setPricingEngine(new FdBlackScholesVanillaEngine(
                                               process, tSteps, xSteps, dampingSteps));

            double expected = vanillaOption.NPV();

            // build an PDE engine from scratch
            Fdm1dMesher equityMesher = new FdmBlackScholesMesher(
                xSteps, process, maturity, strike,
                nullDouble(), nullDouble(), 0.0001, 1.5,
                new DoublePair(strike, 0.1));

            FdmMesherComposite mesher = new FdmMesherComposite(equityMesher);

            FdmLinearOpComposite op = new FdmBlackScholesOp(mesher, process, strike);

            FdmInnerValueCalculator calc = new FdmLogInnerValue(payoff, mesher, 0);

            QlArray x   = new QlArray(equityMesher.size());
            QlArray rhs = new QlArray(equityMesher.size());

            FdmLinearOpIterator iter = mesher.layout().begin();

            for (uint i = 0; i < rhs.size(); ++i, iter.increment())
            {
                x.set(i, mesher.location(iter, 0));
                rhs.set(i, calc.avgInnerValue(iter, maturity));
            }

            FdmBoundaryConditionSet bcSet = new FdmBoundaryConditionSet();

            FdmStepConditionComposite stepCondition =
                FdmStepConditionComposite.vanillaComposite(
                    new DividendSchedule(), exercise, mesher, calc, today, dc);


            FdmLinearOpComposite proxyOp = new FdmLinearOpCompositeProxy(
                new FdmBSDelegate(op));

            FdmBackwardSolver solver = new FdmBackwardSolver(
                proxyOp, bcSet, stepCondition, FdmSchemeDesc.Douglas());

            solver.rollback(rhs, maturity, 0.0, tSteps, dampingSteps);

            double logS = Math.Log(spot.value());

            double calculated = new CubicNaturalSpline(x, rhs).call(logS);

            Console.WriteLine("Homebrew PDE engine        : {0:0.0000}", calculated);
            Console.WriteLine("FdBlackScholesVanillaEngine: {0:0.0000}", expected);
        }