protected override double CalcPv(IOption option, IMarketCondition market, double timeIncrement = 0.0)
{
var dayCount = market.DiscountCurve.Value.DayCount;
var startDate = market.ValuationDate;
var maturityDate = option.ExerciseDates.Last();
var t = dayCount.CalcDayCountFraction(market.ValuationDate, maturityDate) + timeIncrement;
var bsProcess = new BlackScholesProcess(
market.DiscountCurve.Value.ZeroRate(startDate, maturityDate),
market.DividendCurves.Value.Values.First().ZeroRate(startDate, maturityDate),
market.VolSurfaces.Value.Values.First().GetValue(maturityDate, option.Strike));
var pdeSolver = new SecondOrderPdeCrankNicolson(
bsProcess.Drift,
(t0, s) => 0.5 * Math.Pow(bsProcess.Diffusion(t0, s), 2.0),
market.DiscountCurve.Value.GetSpotRate);
double[] x;
double[] xGrid;
InitializeGrid(market.SpotPrices.Value.Values.First(), option.Strike, bsProcess.Diffusion(0, 0), t, out x, out xGrid);
var dt = t / _steps;
return(pdeSolver.Solve(
Enumerable.Range(0, _steps + 1).Select(i => i * dt).ToArray(),
xGrid,
x,
price => option.GetPayoff(new[] { price })[0].PaymentAmount
)[0][_gridSize]);
}
public LeisenReimerBinomialTree(BlackScholesProcess process, double x0, double strike, double tend, int steps = 200, int peizerPrattMethod = 1)
: base(process, x0, tend, (steps % 2 == 0 ? steps + 1 : steps))
{
_strike = strike;
Dx = process.StdDeviation(0, X0, Dt); // sigma * sqrt(dt)
var drift = process.Drift(0, X0, Dt); // r - q - 0.5 * sigma * sigma
var sigma = process.Diffusion(0, X0); // sigma
var d1 = (Math.Log(X0 / _strike) + (drift + sigma * sigma) * tend) / (sigma * Math.Sqrt(tend)); // d+
var d2 = (Math.Log(X0 / _strike) + drift * tend) / (sigma * Math.Sqrt(tend)); // d-
var p1 = ProbabilityHelper(d1, NumberOfSteps, peizerPrattMethod);
var p2 = ProbabilityHelper(d2, NumberOfSteps, peizerPrattMethod);
var tmp = Math.Exp((drift + 0.5 * sigma * sigma) * Dt);
var u = tmp * p1 / p2;
var d = (tmp - p2 * u) / (1 - p2);
PUp = p2;
PDown = 1 - PUp;
_steps = steps % 2 == 0 ? steps + 1 : steps; // only use odd number
_stateValues = new double[_steps + 1][];
for (int i = 0; i < _steps + 1; ++i)
{
_stateValues[i] = new double[i + 1];
for (int j = 0; j < i + 1; ++j)
{
_stateValues[i][j] = X0 * Math.Pow(u, j) * Math.Pow(d, i - j);
}
}
}
