private BsEqtySimulatorStepDatas StepSimulDatas(DateTime start, DateTime end, BlackScholesModel model, DiscountCurve assetDiscount, DateTime horizon)
{
DiscreteLocalDividend[] stepDividends = model.Dividends
.Where(div => start < div.Date && div.Date <= end)
.OrderBy(div => div.Date)
.ToArray();
//If step end date is not a div date, we insert a fictious zero dividend
if (!(stepDividends.Any() && end.Equals(stepDividends.Last().Date)))
{
stepDividends = stepDividends.Union(new[] { DiscreteLocalDividend.ZeroDiv(end) }).ToArray();
}
var variance = (model.Sigma * model.Sigma).Integral(0.0);
var stepVols = new double[stepDividends.Length];
var stepVarDrifts = new double[stepDividends.Length];
for (int i = 0; i < stepDividends.Length; i++)
{
var subStepStart = i > 0 ? stepDividends[i - 1].Date : start;
var subStepEnd = stepDividends[i].Date;
var subStep = RealInterval.Compact(model.Time[subStepStart], model.Time[subStepEnd]);
var stepVariance = variance.Eval(subStep.Sup) - variance.Eval(subStep.Inf);
var stepVarDrift = -0.5 * stepVariance;
stepVols[i] = Math.Sqrt(stepVariance / subStep.Length);
stepVarDrifts[i] = stepVarDrift;
}
var horizonDiscount = assetDiscount.Zc(horizon);
var discounts = stepDividends.Map(div => horizonDiscount / assetDiscount.Zc(div.Date));
var dates = model.Time[stepDividends.Map(div => div.Date)];
var step = RealInterval.Compact(model.Time[start], model.Time[end]);
return(new BsEqtySimulatorStepDatas(step, dates, stepDividends, discounts, stepVols, stepVarDrifts));
}
public static DiscreteLocalDividend DivModel(this DividendQuote divQuote)
{
return(DiscreteLocalDividend.AffineDividend(divQuote.Date, divQuote.Cash, divQuote.Yield));
}