/// <summary>
/// Price of a zcb at t > 0 with maturity TT > t
/// as a function of the rate R, of the factor u at t
/// and of the current zr curve (ZR)
/// using the Hull & White two-factor model
/// <para>
/// dr = (theta(t) + u - a * r) * dt + sigma1 * dz1
/// du = -b * du * dt + sigma2 * dz2
/// with dz1 * dz2 = rho * dt
/// </para>
/// (see Hull-White (1994) Journal of Derivatives).
/// </summary>
/// <param name="context">The underlying project context.</param>
/// <param name="cache">Data structure where pre-calculated values are stored.</param>
/// <param name="hw2">An HW2Context object to use for the evaluation.</param>
/// <param name="R">Rate of return from time t to t+dt.</param>
/// <param name="u">Factor u at t.</param>
/// <param name="PT">Current price of a zcb maturing at TT.</param>
/// <param name="P_t">Current price of a zcb maturing at t.</param>
/// <param name="Pdt">Current price of a zcb maturing at t + dt.</param>
/// <param name="TT">The bond maturity.</param>
/// <param name="t">The initial date of the zcb.</param>
/// <param name="dt">The length of time steps.</param>
/// <returns>The value of the bond using the HW2 model.</returns>
private static double BondHW2(Project context, SPCache cache, HW2Context hw2, double R, double u, double PT, double P_t, double Pdt, double TT, double t, double dt)
{
double a_a_b = +hw2.alpha1 * (hw2.alpha1 - hw2.alpha2);
double b_a_b = +hw2.alpha2 * (hw2.alpha1 - hw2.alpha2);
double ab = hw2.alpha1 * hw2.alpha2;
double TT_t = TT - t;
int t_idx = context.DiscreteTime(t);
int TT_idx = context.DiscreteTime(TT);
double aHat = 0;
double bHat = 0;
double cHat = 0;
#if _USE_CACHE_
#if !_SWAPTIONW_
lock (cache)
#endif
{
if (!cache.IsCached_Eta[t_idx])
{
cache.Cached_Eta[t_idx] = Eta(t, t + dt, a, b, sigma1, sigma2, rho);
cache.IsCached_Eta[t_idx] = true;
}
}
int TT_idx_rel = TT_idx - t_idx;
if (cache.cache.J > TT_idx_rel)
{
HWCache2 cached_element = null;
#if !_SWAPTIONW_
lock (cache.cache)
#endif
{
if (!cache.cache.IsCached(t_idx, TT_idx_rel))
{
cached_element = cache.cache.InsertToCache(t_idx, TT_idx_rel);
cached_element.Eta2 = Eta(t, TT, a, b, sigma1, sigma2, rho);
cached_element.Bhat = BHat(t, TT, dt, a);
cached_element.Chat = CHat(t, TT, dt, a, b, cached_element.Bhat);
double BtT = (1 - Math.Exp(-a * (TT_t))) / a;
double Btdt = (1 - Math.Exp(-a * (dt))) / a;
cached_element.Ahat = PT / P_t * Math.Exp(-BtT / Btdt * Math.Log(Pdt / P_t)
- cached_element.Eta2
+ BtT / Btdt * cache.Cached_Eta[t_idx]);
}
}
cached_element = cache.cache.Get(t_idx, TT_idx_rel);
bHat = cached_element.Bhat;
cHat = cached_element.Chat;
aHat = cached_element.Ahat;
}
else
{
double BtT = (1 - Math.Exp(-a * (TT_t))) / a;
double Btdt = (1 - Math.Exp(-a * (dt))) / a;
aHat = PT / P_t * Math.Exp(-BtT / Btdt * Math.Log(Pdt / P_t)
- Eta(t, TT, a, b, sigma1, sigma2, rho)
+ BtT / Btdt * cache.Cached_Eta[t_idx]);
bHat = BHat(t, TT, dt, a);
cHat = CHat(t, TT, dt, a, b, bHat);
}
#else
double BtT = (1 - Math.Exp(-hw2.alpha1 * (TT_t))) / hw2.alpha1;
double Btdt = (1 - Math.Exp(-hw2.alpha1 * (dt))) / hw2.alpha1;
double l_Pdt_Pt = Math.Log(Pdt / P_t);
double eta_TT = hw2.Eta(t, TT);
double eta_dt = hw2.Eta(t, t + dt);
double arg = -BtT / Btdt * (l_Pdt_Pt - eta_dt) - eta_TT;
if (Engine.Log)
{
if (SolverContext.SimulationRealization == 0)
{
Log.Write(string.Format("arg {0} eta_TT {1} eta_dt {2}", arg, eta_TT, eta_dt));
}
}
aHat = (PT / P_t) * Math.Exp(arg);
bHat = hw2.BHat(t, TT, dt);
cHat = hw2.CHat(t, TT, dt, bHat);
#endif
double bond = aHat * Math.Exp(-bHat * R - cHat * u);
#if _CHECK_OWERFLOWS_
if (Double.IsInfinity(bond))
{
bond = Double.MaxValue / 1000000;
}
#endif
return(bond);
}
/// <summary>
/// Price of a zcb at t > 0 with maturity TT > t
/// as a function of the rate R, of the factor u at t
/// and of the current zr curve (ZR)
/// using the Hull & White two-factor model
/// <para>
/// dr = (theta(t) + u - a * r) * dt + sigma1 * dz1
/// du = -b * du * dt + sigma2 * dz2
/// with dz1 * dz2 = rho * dt
/// </para>
/// (see Hull-White (1994) Journal of Derivatives).
/// </summary>
/// <param name="context">The underlying project context.</param>
/// <param name="cache">Data structure where pre-calculated values are stored.</param>
/// <param name="hw2">An HW2Context object to use for the evaluation.</param>
/// <param name="R">Rate of return from time t to t+dt.</param>
/// <param name="u">Factor u at t.</param>
/// <param name="PT">Current price of a zcb maturing at TT.</param>
/// <param name="P_t">Current price of a zcb maturing at t.</param>
/// <param name="Pdt">Current price of a zcb maturing at t + dt.</param>
/// <param name="TT">The bond maturity.</param>
/// <param name="t">The initial date of the zcb.</param>
/// <param name="dt">The length of time steps.</param>
/// <returns>The value of the bond using the HW2 model.</returns>
private static double BondHW2(Project context, SPCache cache, HW2Context hw2, double R, double u, double PT, double P_t, double Pdt, double TT, double t, double dt)
{
double a_a_b = +hw2.alpha1 * (hw2.alpha1 - hw2.alpha2);
double b_a_b = +hw2.alpha2 * (hw2.alpha1 - hw2.alpha2);
double ab = hw2.alpha1 * hw2.alpha2;
double TT_t = TT - t;
int t_idx = context.DiscreteTime(t);
int TT_idx = context.DiscreteTime(TT);
double aHat = 0;
double bHat = 0;
double cHat = 0;
#if _USE_CACHE_
#if !_SWAPTIONW_
lock (cache)
#endif
{
if (!cache.IsCached_Eta[t_idx])
{
cache.Cached_Eta[t_idx] = Eta(t, t + dt, a, b, sigma1, sigma2, rho);
cache.IsCached_Eta[t_idx] = true;
}
}
int TT_idx_rel= TT_idx-t_idx;
if(cache.cache.J>TT_idx_rel)
{
HWCache2 cached_element = null;
#if !_SWAPTIONW_
lock (cache.cache)
#endif
{
if (!cache.cache.IsCached(t_idx, TT_idx_rel))
{
cached_element = cache.cache.InsertToCache(t_idx, TT_idx_rel);
cached_element.Eta2 = Eta(t, TT, a, b, sigma1, sigma2, rho);
cached_element.Bhat = BHat(t, TT, dt, a);
cached_element.Chat = CHat(t, TT, dt, a, b, cached_element.Bhat);
double BtT = (1 - Math.Exp(-a * (TT_t))) / a;
double Btdt = (1 - Math.Exp(-a * (dt))) / a;
cached_element.Ahat = PT / P_t * Math.Exp(-BtT / Btdt * Math.Log(Pdt / P_t)
- cached_element.Eta2
+ BtT / Btdt * cache.Cached_Eta[t_idx]);
}
}
cached_element=cache.cache.Get(t_idx,TT_idx_rel);
bHat=cached_element.Bhat;
cHat=cached_element.Chat;
aHat=cached_element.Ahat;
}
else
{
double BtT = (1 - Math.Exp(-a*(TT_t)))/a;
double Btdt = (1 - Math.Exp(-a*(dt)))/a;
aHat = PT/P_t *Math.Exp( -BtT/Btdt * Math.Log( Pdt/P_t )
- Eta(t,TT,a,b,sigma1,sigma2,rho)
+ BtT/Btdt * cache.Cached_Eta[t_idx]);
bHat=BHat(t,TT,dt,a);
cHat=CHat(t,TT,dt,a,b,bHat);
}
#else
double BtT = (1 - Math.Exp(-hw2.alpha1 * (TT_t))) / hw2.alpha1;
double Btdt = (1 - Math.Exp(-hw2.alpha1 * (dt))) / hw2.alpha1;
double l_Pdt_Pt = Math.Log(Pdt / P_t);
double eta_TT = hw2.Eta(t, TT);
double eta_dt = hw2.Eta(t, t + dt);
double arg = -BtT / Btdt * (l_Pdt_Pt - eta_dt) - eta_TT;
if (Engine.Log)
if (SolverContext.SimulationRealization == 0)
Log.Write(string.Format("arg {0} eta_TT {1} eta_dt {2}", arg, eta_TT, eta_dt));
aHat = (PT / P_t) * Math.Exp(arg);
bHat = hw2.BHat(t, TT, dt);
cHat = hw2.CHat(t, TT, dt, bHat);
#endif
double bond = aHat * Math.Exp(-bHat * R - cHat * u);
#if _CHECK_OWERFLOWS_
if(Double.IsInfinity(bond))
bond= Double.MaxValue/1000000;
#endif
return bond;
}