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);

            // correct timesteps to ensure a (local) minimum, using Boyle and Lau
            // approach. See Journal of Derivatives, 1/1994,
            // "Bumping up against the barrier with the binomial method"
            // Note: this approach works only for CoxRossRubinstein lattices, so
            // is disabled if T is not a CoxRossRubinstein or derived from it.
            int optimum_steps = timeSteps_;

            if (maxTimeSteps_ > timeSteps_ && s0 > 0 && arguments_.barrier > 0) // boost::is_base_of<CoxRossRubinstein, T>::value &&
            {
                double divisor;
                if (s0 > arguments_.barrier)
                {
                    divisor = Math.Pow(Math.Log(s0 / arguments_.barrier.Value), 2);
                }
                else
                {
                    divisor = Math.Pow(Math.Log(arguments_.barrier.Value / s0), 2);
                }
                if (!Utils.close(divisor, 0))
                {
                    for (int i = 1; i < timeSteps_; ++i)
                    {
                        int optimum = (int)((i * i * v * v * maturity) / divisor);
                        if (timeSteps_ < optimum)
                        {
                            optimum_steps = optimum;
                            break; // found first minimum with iterations>=timesteps
                        }
                    }
                }

                if (optimum_steps > maxTimeSteps_)
                {
                    optimum_steps = maxTimeSteps_; // too high, limit
                }
            }

            TimeGrid grid = new TimeGrid(maturity, optimum_steps);

            ITree tree = getTree_(bs, maturity, optimum_steps, payoff.strike());

            BlackScholesLattice <ITree> lattice = new BlackScholesLattice <ITree>(tree, r, maturity, optimum_steps);

            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];
        }
Ejemplo n.º 2
0
        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];
        }