/// <summary>
/// Determine present value of swaption from fiven paths of
/// forward LIBOR rates and numeraire adjusted discount factors
/// </summary>
/// <param name="paths"></param>
/// <returns>Payoff at exercise date</returns>
public double DiscountedPayoff(LiborMarketModelPath paths)
{
// European swaption, hence there is no path dependence
// therefore only we only need state of model at the
// exercise date
var j = Array.IndexOf(paths.Dates, ExerciseDate);
var forwardRates = paths.ForwardRates.Column(j);
var numeraireAdjustedDiscountFactors = paths.NumeraireAdjustedDiscountFactors.Column(j);
// present value of the underling swap at exercise date
var presentValue = PresentValueUnderlyingSwap(paths.InitialNumeraire, paths.Tenors,
forwardRates, numeraireAdjustedDiscountFactors,
Strike, Nominal);
// payoff of the swaption
return(Math.Max(presentValue, 0));
}
/// <summary>
/// Discounted payoff of caplet
/// Payoff P(T+alpha) = max(N * alpha * L(T,T,T+alpa) - K, 0)
/// </summary>
/// <param name="paths"></param>
/// <returns>Payoff at exercise date</returns>
public double DiscountedPayoff(LiborMarketModelPath paths)
{
// Choose L(T,T, T + alpha)
var j = Array.IndexOf(paths.Dates, FixingDate);
var i = Array.IndexOf(paths.TenorStructure, FixingDate);
var forwardRate = paths.ForwardRates[i, j];
// Choose D(T+alpha) = B(T+alpha,T+alpha)/B(T+alpha,Tk)
var jj = Array.IndexOf(paths.Dates, ExpiryDate);
var ii = Array.IndexOf(paths.TenorStructure, ExpiryDate);
var numeraireAdjustedDiscountFactor = paths.NumeraireAdjustedDiscountFactors[ii, jj];
// payoff of the swaption
return(paths.InitialNumeraire * numeraireAdjustedDiscountFactor * Math.Max(Tenor * Principal * forwardRate - CapRate, 0));
}
/// <summary>
/// Discounted payoff of caplet
/// Payoff P(T+alpha) = max(N * alpha * L(T,T,T+alpa) - K, 0)
/// </summary>
/// <param name="paths"></param>
/// <returns>Payoff at exercise date</returns>
public double DiscountedPayoff(LiborMarketModelPath paths)
{
return(Caplets.Sum(caplet => caplet.DiscountedPayoff(paths)));
}
