/// <summary>
/// Calculates the value of a Bond under the Pelsser model.
/// </summary>
/// <param name='dynamic'>
/// The simulated process.
/// </param>
/// <param name='dates'>
/// The vector of reference dates.
/// </param>
/// <param name='i'>
/// The index at which the state variables must be sampled.
/// </param>
/// <param name='t'>
/// The date in years/fractions at at which the state variables must be sampled.
/// </param>
/// <param name='s'>
/// The maturity of the bond.
/// </param>
/// <returns>The value of the bound at index i using the Pelsser model.</returns>
public double Bond(IReadOnlyMatrixSlice dynamic, double[] dates, int i, double t, double s)
{
// Handles special case.
if (t == s)
{
return(1);
}
// Get the value of the short rate.
double y = Math.Sqrt(dynamic[i, 0]) - this.alphaT0[i];
PelsserKey k = new PelsserKey(t, s);
PelsserCache cachedValue = null;
lock (this.cache)
{
if (this.cache.ContainsKey(k))
{
cachedValue = this.cache[k];
}
else
{
cachedValue = new PelsserCache(t, s, this);
// Insert the value in the cache.
this.cache.Add(k, cachedValue);
}
}
double v = Math.Exp(cachedValue.A - y * cachedValue.B - (y * y) * cachedValue.CtT0);
return(v);
}
/// <summary>
/// Calculates an entire caplets matrix row using Pelsser's model.
/// </summary>
/// <param name="r">The row index.</param>
internal void CalculateRow(int r)
{
double T = this.Mat[r + 1] + this.DeltaK;
PelsserCache pc = new PelsserCache(this.Mat[r + 1], T, this.Model);
double MU0 = this.Model.Mu0(this.Mat[r + 1]);
int rm = r + 1;
double nu = MU0 - pc.B * this.Sigma0s[rm];
double phi = 1 + 2 * this.CCost * this.Sigma0s[rm];
PelsserCache pc0t = new PelsserCache(0, this.Mat[r + 1], this.Model);
PelsserCache pc0tau = new PelsserCache(0, T, this.Model);
// Discount factor
double p0tau = Math.Exp(pc0tau.A);
double p0t = Math.Exp(pc0t.A);
double sqrtSigmaRm = Math.Sqrt(this.Sigma0s[rm]);
// Execute the subsequent operations on all caplets.
for (int c = 0; c < this.K.Length; c++)
{
double d = Math.Pow(pc.B, 2) + 4 * this.CCost * (pc.A - this.LogK[c]);
// Exclude the negative values of the discriminant.
d = Math.Max(0, d);
double el = (-pc.B - Math.Sqrt(d)) / (2 * this.CCost);
double eic = (-pc.B + Math.Sqrt(d)) / (2 * this.CCost);
double nP1 = SpecialFunctions.NormCdf(-(eic * phi - nu) / Math.Sqrt(phi * this.Sigma0s[rm])) + SpecialFunctions.NormCdf((el * phi - nu) / Math.Sqrt(phi * this.Sigma0s[rm]));
double nP2 = SpecialFunctions.NormCdf(-(eic - MU0) / sqrtSigmaRm) + SpecialFunctions.NormCdf((el - MU0) / sqrtSigmaRm);
double put_zc = -p0tau * nP1 + p0t * this.K[c] * nP2;
this.Caplets[r, c] = put_zc;
}
}
/// <summary>
/// Calculates the value of a Bond under the Pelsser model.
/// </summary>
/// <param name='dynamic'>
/// The simulated process.
/// </param>
/// <param name='dates'>
/// The vector of reference dates.
/// </param>
/// <param name='i'>
/// The index at which the state variables must be sampled.
/// </param>
/// <param name='t'>
/// The date in years/fractions at at which the state variables must be sampled.
/// </param>
/// <param name='s'>
/// The maturity of the bond.
/// </param>
/// <returns>The value of the bound at index i using the Pelsser model.</returns>
public double Bond(IReadOnlyMatrixSlice dynamic, double[] dates, int i, double t, double s)
{
// Handles special case.
if (t == s)
return 1;
// Get the value of the short rate.
double y = Math.Sqrt(dynamic[i, 0]) - this.alphaT0[i];
PelsserKey k = new PelsserKey(t, s);
PelsserCache cachedValue = null;
lock (this.cache)
{
if (this.cache.ContainsKey(k))
cachedValue = this.cache[k];
else
{
cachedValue = new PelsserCache(t, s, this);
// Insert the value in the cache.
this.cache.Add(k, cachedValue);
}
}
double v = Math.Exp(cachedValue.A - y * cachedValue.B - (y * y) * cachedValue.CtT0);
return v;
}