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);
}
}
}
/// <summary>
/// Initializes a new instance of the <see cref="BinomialTree"/> class.
/// The underlying process shall be a Black-Schole process with constant r, sigma
/// </summary>
/// <param name="process">The process.</param>
/// <param name="x0">The x0.</param>
/// <param name="tend">The end time in years.</param>
/// <param name="steps">The number of time steps.</param>
//protected BinomialTree(BlackScholesProcess process, double x0, double tend, int steps = 200)
protected BinomialTree(BlackScholesProcess process, double x0, double tend, int steps)
{
Process = process;
X0 = x0;
Dt = tend / steps;
NumberOfSteps = steps;
DriftPerStep = process.Drift(0, x0, Dt) * Dt;
AllBranchDirections = new List <BranchDirection> {
BranchDirection.Down, BranchDirection.Up
};
}
private BinomialTree BuildTree(IMarketCondition market, double tEnd, double strike, double spotPrice, int steps, double vol, double r)
{
//most suitable arrangement to deal with both strike vol and moneyness vol
var process = new BlackScholesProcess(
r: r,
q: 0.0,
sigma: vol
);
return(_binomialTreeType == BinomialTreeType.CoxRossRubinstein
? (BinomialTree) new CoxRossRubinsteinBinomialTree(process, spotPrice, tEnd, steps)
: new LeisenReimerBinomialTree(process, spotPrice, strike, tEnd, steps));
}
private BinomialTree BuildTree(ConvertibleBond convertibleBond, IMarketCondition market)
{
var endDate = convertibleBond.UnderlyingMaturityDate;
//assuming we use a strike vol
var process = new BlackScholesProcess(
market.DiscountCurve.Value.ZeroRate(market.ValuationDate, endDate),
market.DividendCurves.Value.Values.First().ZeroRate(market.ValuationDate, endDate),
market.VolSurfaces.Value.Values.First().GetValue(endDate, market.SpotPrices.Value.Values.First())
);
var dayCount = market.DiscountCurve.Value.DayCount;
var tEnd = dayCount.CalcDayCountFraction(market.ValuationDate, convertibleBond.UnderlyingMaturityDate);
return(new CoxRossRubinsteinBinomialTree(process, market.SpotPrices.Value.Values.First(), tEnd, _steps));
}
public CoxRossRubinsteinBinomialTree(BlackScholesProcess process, double x0, double tend, int steps = 200)
: base(process, x0, tend, steps)
{
Dx = process.StdDeviation(0, X0, Dt); // sigma * sqrt(dt)
// (exp(r*dt) - exp(-sigma*sqrt(dt)) / (exp(sigma*sqrt(dt)) - exp(-sigma*sqrt(dt)))
PUp = 0.5 + 0.5 * DriftPerStep / Dx; //(Math.Exp((Process.GetDiscountRate(0.0) - Process.GetDividendRate(0.0)) * Dt) - Math.Exp(-Dx)) / (Math.Exp(Dx) - Math.Exp(-Dx));
PDown = 1 - PUp;
_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.Exp((2 * j - i) * Dx);
}
}
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(BlackScholesProcess obj)
{
return((obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr);
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(BlackScholesProcess obj) {
return (obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr;
}
