public void NonFlatRates()
{
ZeroCurve myZero = new ZeroCurve();
myZero.Ratepoints = 2;
myZero.MakeArrays();
myZero.SetR(0, 0.05, 1.0);
myZero.SetR(1, 0.075, 2.0);
//test interpolation priot to point 0
double tTime = 0.5;
double val = myZero.LinInterp(tTime);
Assert.IsTrue(val > 0.0499999999);
Assert.IsTrue(val < 0.050000001);
//test interpolation prior to point 1
tTime = 1.5;
val = myZero.LinInterp(tTime);
Assert.IsTrue(val > 0.062499999999);
Assert.IsTrue(val < 0.06250000001);
//test interpolation post point 1
tTime = 2.5;
val = myZero.LinInterp(tTime);
Assert.IsTrue(val > 0.07499999999);
Assert.IsTrue(val < 0.0750000001);
//test forward rates
//test interpolation priot to point 0
double tl = 0.25;
tTime = 0.5;
val = myZero.ForwardRate(tl, tTime);
Assert.IsTrue(val > 0.0499999999);
Assert.IsTrue(val < 0.050000001);
//test interpolation prior to point 1
tTime = 1.5;
val = myZero.ForwardRate(tl, tTime);
Assert.IsTrue(val > 0.06499999); /// 0.065
Assert.IsTrue(val < 0.065000001);
//test interpolation post point 1
tTime = 2.5;
val = myZero.ForwardRate(tl, tTime); ///0.077778
Assert.IsTrue(val > 0.0777777);
Assert.IsTrue(val < 0.07777778);
}
//public spotStar
private void MakeDivArray(ZeroCurve myZero, DivList myDivList)
{
double dt = Tau / Gridsteps;
if ((myDivList != null) && (myZero != null))
{
for (int idx = 0; idx < Gridsteps; idx++)
{
double temp = 0.0;
for (int kdx = 0; kdx < myDivList.Divpoints; kdx++)
{
if ((myDivList.GetT(kdx) > idx * dt) && (myDivList.GetT(kdx) < Tau))
{
temp += myDivList.GetD(kdx) * Math.Exp(-myZero.ForwardRate(idx * dt, myDivList.GetT(kdx)) *
(myDivList.GetT(kdx) - idx * dt));
}
}
set_div(idx, temp, dt * idx);
}
}
else //missing either div or zero, load in 0 for _div on tree
{
for (int idx = 0; idx <= Gridsteps; idx++)
{
set_div(idx, 0.0, dt * idx);
}
}
}
//compute Sstar for the BC's
private double ComputeDiscDiv(double tTemp, double T, ZeroCurve myZero, DivList mydiv)
{
double temp = 0.0;
for (int idx = 0; idx < mydiv.Divpoints; idx++)
{
if ((tTemp < mydiv.GetT(idx)) && (mydiv.GetT(idx) < T))
{
double fwdRate = myZero.ForwardRate(tTemp, mydiv.GetT(idx));
temp += mydiv.GetD(idx) * Math.Exp(-fwdRate * (mydiv.GetT(idx) - tTemp));
}
}
return temp;
}
//fill grid forward rates
private void FillForwardRate(ZeroCurve myZero)
{
double dt = Tau / Gridsteps;
if (myZero != null)
{
if (flatFlag)
{
flatRate = myZero.LinInterp(Tau);
}
for (int idx = 0; idx < Gridsteps; idx++)
{
SetR(idx, flatFlag ? flatRate : myZero.ForwardRate(idx * dt, (idx + 1) * dt));
}
}
}
/// <summary>
/// main pricer
/// </summary>
/// <param name="myZero"></param>
/// <param name="myDiv"></param>
/// <param name="greeks"></param>
/// <param name="bGreeks"></param>
/// <returns></returns>
public double Pricer(ZeroCurve myZero, DivList myDiv, ref double[] greeks, bool bGreeks)
{
_x = new List<double>();
_v = new List<double>();
double tTemp = T; //real time
double tau = 0.0; //backward time
double dtnom = T / (double) NTsteps;
double dt = dtnom;
double tempInt=0.0;
//start the pricer
CreateGrid();
TerminalCondition();
while( tau < T)
{
//set the increment
double t1 = tTemp - dtnom;
t1 = (t1 >= 0.0) ? t1 : 0.0; //make sure t1 >= 0.0
double divPay = 0.0;
dt = CheckBetweenDiv(t1, tTemp, ref divPay, myDiv);
//compute the real time and backward time tau
tTemp -= dt;
tau = T - tTemp;
//compute the increment forward rate
_domR = myZero.ForwardRate(tTemp, tTemp + dt);
_forR = 0.0;
//compute the forward rate from real time tTemp to expiry for the BC'c
double domRbc = myZero.ForwardRate(tTemp, T);
//compute discounted dividends for the bc's
double DiscDiv = ComputeDiscDiv(tTemp, T, myZero, myDiv);
//save the value at the spot for use in theta calcuation
int nKeyInt = (int)((Math.Log(Spot) - XL) / _dx);
double fracInt = (Math.Log(Spot) - _x[nKeyInt]) / (_x[nKeyInt + 1] - _x[nKeyInt]);
tempInt = _v[nKeyInt] * (1.0 - fracInt) + _v[nKeyInt + 1] * fracInt;
//get the fwd
_lnfwd = Math.Log(GetATMfwd(myZero, myDiv, tTemp));
//build the matrix
OneStepSetUp(dt, tTemp);
//compute the q vec
MakeQVec();
if (SStyle.ToUpper().Equals("E"))
{
// set the exlicit BC
_v[0] = MakeLowerBC(tau, Math.Exp(_x[0]), domRbc, DiscDiv);
_v[Steps - 1] = MakeUpperBC(tau, Math.Exp(_x[Steps - 1]), domRbc, DiscDiv);
SORmethod();
//subract from q(1) and q(_steps-2) for explicit BC
//'_q[1] -= _SubDiagL[0] * _v[0];
//'_q[_msteps - 1] -= _SuperDiagL[_steps - 1] * _v[_steps - 1];
//this commented out info is used for the zero curvature condition
//_DiagL[1] += 2.0 * _SubDiagL[1];
//_SuperDiagL[1] -= _SubDiagL[1];
//_DiagL[_steps - 2] += 2.0 * _SuperDiagL[_steps - 2];
//_SubDiagL[_steps - 2] -= _SuperDiagL[_steps - 2];
//call LU decomp
//LUDecomp();
//Call the LU sOlver
//LUSolution();
//for zero curvature
//_v[0] = 2.0 * _v[1] - _v[2];
//_v[_steps - 1] = 2.0 * _v[_steps - 2] - _v[_steps - 3];
}
else
{
_v[0] = MakeLowerBC(tau, Math.Exp(_x[0]), domRbc, DiscDiv);
_v[Steps - 1] = MakeUpperBC(tau, Math.Exp(_x[Steps - 1]), domRbc, DiscDiv);
SORmethod();
}
//after having incremented back, apply a grid shift if needed
if (divPay != 0.0)
{
ApplyGridShift(tau, divPay, domRbc, DiscDiv);
}
}
int nKey = (int) ((Math.Log(Spot) - XL) / _dx);
double frac = (Math.Log(Spot) - _x[nKey])/ (_x[nKey+1] - _x[nKey]);
double temp = _v[nKey] * (1.0 - frac) + _v[nKey+1] * frac;
if (bGreeks)
{
double[,] a = new double[4, 4];
double[] b = new double[4];
a[0,0] = 1.0;
a[1,0] = 1.0;
a[2,0] = 1.0;
a[3,0] = 1.0;
a[0, 1] = Math.Exp(_x[nKey-1]);
a[1, 1] = Math.Exp(_x[nKey]);
a[2, 1] = Math.Exp(_x[nKey +1]);
a[3, 1] = Math.Exp(_x[nKey +2]);
a[0, 2] = Math.Exp(_x[nKey - 1]) * Math.Exp(_x[nKey - 1]);
a[1, 2] = Math.Exp(_x[nKey]) * Math.Exp(_x[nKey]);
a[2, 2] = Math.Exp(_x[nKey + 1])*Math.Exp(_x[nKey + 1]);
a[3, 2] = Math.Exp(_x[nKey + 2]) * Math.Exp(_x[nKey + 1]);
a[0, 3] = Math.Exp(_x[nKey - 1])*Math.Exp(_x[nKey - 1])*Math.Exp(_x[nKey - 1]);
a[1, 3] = Math.Exp(_x[nKey]) * Math.Exp(_x[nKey]) * Math.Exp(_x[nKey]);
a[2, 3] = Math.Exp(_x[nKey + 1]) * Math.Exp(_x[nKey + 1]) * Math.Exp(_x[nKey +1]);
a[3, 3] = Math.Exp(_x[nKey + 2] )* Math.Exp(_x[nKey + 2] )* Math.Exp(_x[nKey + 2]);
b[0] = _v[nKey-1];
b[1] = _v[nKey];
b[2] = _v[nKey+1];
b[3] = _v[nKey+2];
int info = NewtonGauss(4, ref a, ref b);
greeks[0] = b[1] + 2.0 * b[2] * Spot +3.0 * b[3] * Spot * Spot;
greeks[1] =2.0*b[2] +6.0* b[3] * Spot ;
greeks[2] = (tempInt - temp) / (365.0 * dt);
/*
nKey = (int)((Math.Log(_spot) * 1.001 - _xl) / _dx);
frac = (Math.Log(_spot )* 1.001 - _x[nKey]) / (_x[nKey + 1] - _x[nKey]);
double tempUp = _v[nKey] * (1.0 - frac) + _v[nKey + 1] * frac;
nKey = (int)((Math.Log(_spot) * 0.999 - _xl) / _dx);
frac = (Math.Log(_spot) * 0.999 - _x[nKey]) / (_x[nKey + 1] - _x[nKey]);
double tempDn = _v[nKey] * (1.0 - frac) + _v[nKey + 1] * frac;
greeks[0] = (tempUp - tempDn) / (0.002 *Math.Log(spot))/spot ;
greeks[1] = (tempUp + tempDn - 2.0 * temp) / Math.Pow(0.001 * _spot * Math.Log(_spot), 2.0) - greeks[0]/_spot;
greeks[2] = (tempInt - temp) / (365.0 * dt);
*/
}
return temp;
}
