/// <summary>
/// Simulate a realization of the stochastic process driven by the noise matrix noise.
/// </summary>
/// <remarks>
/// This function is called once for realization.
/// </remarks>
/// <param name="dates">
/// The dates (in years fractions) at which the process must be simulated.
/// </param>
/// <param name="noise">The matrix of IID normal realizations.</param>
/// <param name="outDynamic">Where the dynamic should be written.</param>
public void Simulate(double[] dates, IReadOnlyMatrixSlice noise, IMatrixSlice outDynamic)
{
switch (OperatingMode)
{
case OperatingMode.TranslateHistoricalRealizationsForward:
for (int i = 0; i < dates.Length; i++)
{
int dateIndex;
if (!this.simulationDateIndexes.TryGetValue(dates[i], out dateIndex))
{
dateIndex = 0;
}
Tuple <DateTime, Vector> value = this.fileContent[dateIndex];
for (int j = 0; j < value.Item2.Length - 1; j++)
{
outDynamic[i, j] = value.Item2[j];
}
}
break;
case OperatingMode.Bootstrap:
this.bootstrap.Simulate(dates, outDynamic);
break;
}
}
/// <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);
}
public void Simulate(double[] Dates, IReadOnlyMatrixSlice Noise, IMatrixSlice OutDynamic)
{
OutDynamic[0, 0] = spot.fV();
for (int i = 1; i < Dates.Length; i++)
{
OutDynamic[i, 0] = a * OutDynamic[i - 1, 0] + b + c * Noise[i - 1, 0];
}
}
/// <summary>
/// Calculates the value of a Bond under the Hull and White 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 variable must be sampled.
/// </param>
/// <param name='t'>
/// The date in years/fractions at at which the state variable must be sampled.
/// </param>
/// <param name='T'>
/// The maturity of the bond.
/// </param>
/// <returns>The value of the bound at index i using the HW model.</returns>
public virtual double Bond(IReadOnlyMatrixSlice dynamic, double[] dates, int i, double t, double T)
{
#if TFORWARDFORMULATION
double y = dynamic[i, 0] - this.alphaT[i];
return(Math.Exp(A(t, T, this.alpha1Temp, this.sigma1Temp, this.zeroRateCurve) - y * B(T - t, this.alpha1Temp)));
#else
throw new NotImplementedException();
#endif
}
/// <summary>
/// Calculates the value of a Bond under the Cox-Ingersoll-Ross 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 variable must be sampled.
/// </param>
/// <param name='t'>
/// The date in years/fractions at at which the state variable must be sampled.
/// </param>
/// <param name='s'>
/// The maturity of the bond.
/// </param>
/// <returns>
/// The value of the bound at index i using the Cox-Ingersoll-Ross model.
/// </returns>
public double Bond(IReadOnlyMatrixSlice dynamic, double[] dates, int i, double t, double s)
{
double r = dynamic[i, 0];
double T = s - t;
double den = (this.alphaTemp + this.d) * (Math.Exp(this.d * T) - 1.0) + 2.0 * this.d;
double A = Math.Pow(2.0 * this.d * Math.Exp(0.5 * (this.alphaTemp + this.d) * T) / den, this.nu);
double B = 2.0 * (Math.Exp(this.d * T) - 1.0) / den;
return(A * Math.Exp(-r * B));
}
public void Simulate(double[] Dates, IReadOnlyMatrixSlice Noise, IMatrixSlice OutDynamic)
{
OutDynamic[0, 0] = x0[0];
for (int i = 1; i < Dates.Length; i++)
{
double dt = Dates[i] - Dates[i - 1];
double rdt = Math.Sqrt(dt);
double th = theta(Dates[i], dt);
OutDynamic[i, 0] = OutDynamic[i - 1, 0] + (th - alpha1Temp * OutDynamic[i - 1, 0]) * dt + sigma1Temp * Noise[i - 1, 0] * rdt;
}
}
/// <summary>
/// Manage the simulation of the variance gamma process
/// </summary>
/// <param name="Dates">Simulation dates</param>
/// <param name="Noise">Gaussian noise for a single path</param>
/// <param name="OutDynamic">Single path process realization</param>
public void Simulate(double[] Dates, IReadOnlyMatrixSlice Noise, IMatrixSlice OutDynamic)
{
int steps = OutDynamic.R;
double GammaNoise, dt;
OutDynamic[0, 0] = this.s0.fV();
for (int i = 1; i < steps; i++)
{
dt = Dates[i] - Dates[i - 1];
this.gamma = new Fairmat.Statistics.Gamma(dt / this.nu.fV(), 1.0 / this.nu.fV());
GammaNoise = this.gamma.Draw(Engine.Generator);
OutDynamic[i, 0] = OutDynamic[i - 1, 0] * Math.Exp(this.drift * dt +
this.theta.fV() * GammaNoise + this.sigma.fV() * Math.Sqrt(GammaNoise) * Noise[i - 1, 0]);
}
}
/// <summary>
/// Calculates the value of a Bond under the Hull and White Two factors 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 bond at index i using the HW2 model.</returns>
public double Bond(IReadOnlyMatrixSlice dynamic, double[] dates, int i, double t, double s)
{
double R = dynamic[i, 0];
double U = dynamic[i, 1];
double dt = this.context.timeDiscretization.dt(i);
double Ps = ZCB(s);
double Pt = ZCB(t);
double Pdt = ZCB(t + dt);
if (Engine.Log)
{
if (SolverContext.SimulationRealization == 0)
{
Log.Write(string.Format("BOND i={0} Ps={1} Pt={2}", i, Ps, Pt));
}
}
return(BondHW2(this.context, this.cache, this, R, U, Ps, Pt, Pdt, s, t, dt));
}
/// <summary>
/// Calculates the probability of a default at date t (conditional
/// of being in a given state (realization) of process s1, s2),
/// being on period s = dates[j].
/// </summary>
/// <param name="dynamic">The underlying's realizations.</param>
/// <param name="dates">The corresponding underlying's dates.</param>
/// <param name="j">The wanted date index.</param>
/// <param name="t">The date at which we want to estimate the default prob.</param>
/// <returns>The default probability estimation.</returns>
public double CDSDefaultP(IReadOnlyMatrixSlice dynamic, double[] dates, int j, double t)
{
double tau = t - dates[j];
double RRate = 0.4;
double s1 = dynamic[j, 0];
double s2 = dynamic[j, 1];
double final = t;
double ZR = GetZR(final);
// PTau.
double discf = Math.Exp(-ZR * tau);
double num_A1 = 2 * this.gamma1 * Math.Exp((this.k1.fV() + this.gamma1) * tau / 2.0);
double num_A2 = 2 * this.gamma2 * Math.Exp((this.k2.fV() + this.gamma2) * tau / 2.0);
double eg1 = Math.Exp(this.gamma1 * tau) - 1;
double eg2 = Math.Exp(this.gamma2 * tau) - 1;
double den_A1 = (this.k1.fV() + this.gamma1) * eg1 + 2 * this.gamma1;
double den_A2 = (this.k2.fV() + this.gamma2) * eg2 + 2 * this.gamma2;
double A1 = Math.Pow(num_A1 / den_A1, (2 * this.k1.fV() * this.theta1.fV()) / this.sigma12);
double A2 = Math.Pow(num_A2 / den_A2, (2 * this.k2.fV() * this.theta2.fV()) / this.sigma22);
double B1 = 2.0 * eg1 / den_A1;
double B2 = 2.0 * eg2 / den_A2;
double gg = discf * A1 * Math.Exp(-B1 * s1) * A2 * Math.Exp(-B2 * s2);
double gd = RRate * discf + (1 - RRate) * gg;
double y = -(1.0 / tau) * Math.Log(gd);
double sd = y - ZR;
double pdcum = (1 - Math.Exp(-sd * tau)) / (1.0 - RRate);
return(pdcum);
}
/// <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 the probability of a default at date t (conditional
/// of being in a given state (realization) of process s1, s2),
/// being on period s = dates[j].
/// </summary>
/// <param name="dynamic">The underlying's realizations.</param>
/// <param name="dates">The corresponding underlying's dates.</param>
/// <param name="j">The wanted date index.</param>
/// <param name="t">The date at which we want to estimate the default prob.</param>
/// <returns>The default probability estimation.</returns>
public double CDSDefaultP(IReadOnlyMatrixSlice dynamic, double[] dates, int j, double t)
{
double tau = t - dates[j];
double RRate = 0.4;
double s1 = dynamic[j, 0];
double s2 = dynamic[j, 1];
double final = t;
double ZR = GetZR(final);
// PTau.
double discf = Math.Exp(-ZR * tau);
double num_A1 = 2 * this.gamma1 * Math.Exp((this.k1.fV() + this.gamma1) * tau / 2.0);
double num_A2 = 2 * this.gamma2 * Math.Exp((this.k2.fV() + this.gamma2) * tau / 2.0);
double eg1 = Math.Exp(this.gamma1 * tau) - 1;
double eg2 = Math.Exp(this.gamma2 * tau) - 1;
double den_A1 = (this.k1.fV() + this.gamma1) * eg1 + 2 * this.gamma1;
double den_A2 = (this.k2.fV() + this.gamma2) * eg2 + 2 * this.gamma2;
double A1 = Math.Pow(num_A1 / den_A1, (2 * this.k1.fV() * this.theta1.fV()) / this.sigma12);
double A2 = Math.Pow(num_A2 / den_A2, (2 * this.k2.fV() * this.theta2.fV()) / this.sigma22);
double B1 = 2.0 * eg1 / den_A1;
double B2 = 2.0 * eg2 / den_A2;
double gg = discf * A1 * Math.Exp(-B1 * s1) * A2 * Math.Exp(-B2 * s2);
double gd = RRate * discf + (1 - RRate) * gg;
double y = -(1.0 / tau) * Math.Log(gd);
double sd = y - ZR;
double pdcum = (1 - Math.Exp(-sd * tau)) / (1.0 - RRate);
return pdcum;
}
/// <summary>
/// Manage the simulation of the variance gamma process
/// </summary>
/// <param name="Dates">Simulation dates</param>
/// <param name="Noise">Gaussian noise for a single path</param>
/// <param name="OutDynamic">Single path process realization</param>
public void Simulate(double[] Dates, IReadOnlyMatrixSlice Noise, IMatrixSlice OutDynamic)
{
int steps = OutDynamic.R;
double GammaNoise, dt;
OutDynamic[0, 0] = this.s0.fV();
for (int i = 1; i < steps; i++)
{
dt = Dates[i] - Dates[i - 1];
this.gamma = new Fairmat.Statistics.Gamma(dt / this.nu.fV(), 1.0 / this.nu.fV());
GammaNoise = this.gamma.Draw(Engine.Generator);
OutDynamic[i, 0] = OutDynamic[i - 1, 0] * Math.Exp(this.drift * dt +
this.theta.fV() * GammaNoise + this.sigma.fV() * Math.Sqrt(GammaNoise) * Noise[i - 1, 0]);
}
}
public void Simulate(double[] Dates, IReadOnlyMatrixSlice Noise, IMatrixSlice OutDynamic)
{
OutDynamic[0, 0] = x0[0];
for (int i = 1; i < Dates.Length; i++)
{
double dt= Dates[i]-Dates[i-1];
double rdt=Math.Sqrt(dt);
double th = theta(Dates[i], dt);
OutDynamic[i, 0] = OutDynamic[i-1, 0]+(th - alpha1Temp * OutDynamic[i - 1, 0]) * dt + sigma1Temp * Noise[i - 1, 0] * rdt;
}
}
/// <summary>
/// Calculates the value of a Bond under the Hull and White 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 variable must be sampled.
/// </param>
/// <param name='t'>
/// The date in years/fractions at at which the state variable must be sampled.
/// </param>
/// <param name='T'>
/// The maturity of the bond.
/// </param>
/// <returns>The value of the bound at index i using the HW model.</returns>
public virtual double Bond(IReadOnlyMatrixSlice dynamic, double[] dates, int i, double t, double T)
{
#if TFORWARDFORMULATION
double y = dynamic[i, 0] - this.alphaT[i];
return Math.Exp(A(t, T, this.alpha1Temp, this.sigma1Temp, this.zeroRateCurve) - y * B(T - t, this.alpha1Temp));
#else
throw new NotImplementedException();
#endif
}
/// <summary>
/// Calculates the value of a Bond under the Cox-Ingersoll-Ross 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 variable must be sampled.
/// </param>
/// <param name='t'>
/// The date in years/fractions at at which the state variable must be sampled.
/// </param>
/// <param name='s'>
/// The maturity of the bond.
/// </param>
/// <returns>
/// The value of the bound at index i using the Cox-Ingersoll-Ross model.
/// </returns>
public double Bond(IReadOnlyMatrixSlice dynamic, double[] dates, int i, double t, double s)
{
double r = dynamic[i, 0];
double T = s - t;
double den = (this.alphaTemp + this.d) * (Math.Exp(this.d * T) - 1.0) + 2.0 * this.d;
double A = Math.Pow(2.0 * this.d * Math.Exp(0.5 * (this.alphaTemp + this.d) * T) / den, this.nu);
double B = 2.0 * (Math.Exp(this.d * T) - 1.0) / den;
return A * Math.Exp(-r * B);
}
/// <summary>
/// Simulate a realization of the stochastic process driven by the noise matrix noise.
/// </summary>
/// <remarks>
/// This function is called once for realization.
/// </remarks>
/// <param name="dates">
/// The dates (in years fractions) at which the process must be simulated.
/// </param>
/// <param name="noise">The matrix of IID normal realizations.</param>
/// <param name="outDynamic">Where the dynamic should be written.</param>
public void Simulate(double[] dates, IReadOnlyMatrixSlice noise, IMatrixSlice outDynamic)
{
switch (OperatingMode)
{
case OperatingMode.TranslateHistoricalRealizationsForward:
for (int i = 0; i < dates.Length; i++)
{
int dateIndex;
if (!this.simulationDateIndexes.TryGetValue(dates[i], out dateIndex))
dateIndex = 0;
Tuple<DateTime, Vector> value = this.fileContent[dateIndex];
for (int j = 0; j < value.Item2.Length - 1; j++)
{
outDynamic[i, j] = value.Item2[j];
}
}
break;
case OperatingMode.Bootstrap:
this.bootstrap.Simulate(dates, outDynamic);
break;
}
}
/// <summary>
/// Calculates the value of a Bond under the Hull and White Two factors 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 bond at index i using the HW2 model.</returns>
public double Bond(IReadOnlyMatrixSlice dynamic, double[] dates, int i, double t, double s)
{
double R = dynamic[i, 0];
double U = dynamic[i, 1];
double dt = this.context.timeDiscretization.dt(i);
double Ps = ZCB(s);
double Pt = ZCB(t);
double Pdt = ZCB(t + dt);
if (Engine.Log)
if (SolverContext.SimulationRealization == 0)
Log.Write(string.Format("BOND i={0} Ps={1} Pt={2}", i, Ps, Pt));
return BondHW2(this.context, this.cache, this, R, U, Ps, Pt, Pdt, s, t, dt);
}
