public void MakeVega(Tree SpotT, Pricer PriceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(SpotT, PriceT);
Tree T1 = new Tree(), T2 = new Tree();
T1.Tau = tau;
T1.Gridsteps = Gridsteps;
T1.Sig = .99 * sig;
T1.Spot = spot;
T1.MakeGrid(myZero, myDiv);
PriceT.MakeGrid(T1);
double P1 = PriceT.Price();
T2.Tau = tau;
T2.Gridsteps = Gridsteps;
T2.Sig = 1.01 * sig;
T2.Spot = spot;
T2.MakeGrid(myZero, myDiv);
PriceT.MakeGrid(T2);
double P2 = PriceT.Price();
if (sig != 0)
{
Vega = 0.01 * (P2 - P1) / (2 * 0.01 * sig);
}
}
public void MakeTheta(Tree SpotT, Pricer PriceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(SpotT, PriceT);
Tree T1 = new Tree(), T2 = new Tree();
T1.Tau = tau;
T1.Gridsteps = Gridsteps;
T1.Sig = sig;
T1.Spot = spot;
T1.MakeGrid(myZero, myDiv);
PriceT.MakeGrid(T1);
double P1 = PriceT.Price();
double t = tau - 1.00 / 365.00;
T2.Tau = t;
T2.Gridsteps = Gridsteps;
T2.Sig = sig;
T2.Spot = spot;
T2.MakeGrid(myZero, myDiv);
PriceT.MakeGrid(T2);
double P2 = PriceT.Price();
Theta = (P2 - P1);
}
public void MakeDeltaGamma(Tree spotT, Pricer priceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(spotT, priceT);
Tree treeD = new Tree
{
GridSteps = GridSteps + 2,
Spot = Spot,
Sig = Sigma,
Tau = Tau * (1 + 2 / GridSteps)
};
treeD.MakeGrid(myZero, myDiv);
priceT.MakeGrid(treeD);
double[] s = new double[3];
double[] c = new double[3];
for (int i = 0; i <= 2; ++i)
{
s[i] = treeD.GetSpotMatrix(2, i);
c[i] = priceT.GetPriceMatrix(2, i);
}
Delta = (s[0] * (2 * s[1] - s[0]) * (c[1] - c[2]) +
(s[1] * s[1]) * (c[2] - c[0]) + s[2] * (2 * s[1] - s[2]) * (c[0] - c[1]))
/ (s[1] - s[0]) / (s[2] - s[0]) / (s[2] - s[1]);
Gamma = 2 * (s[0] * (c[1] - c[2]) + s[1] * (c[2] - c[0]) + s[2] * (c[0] - c[1]))
/ (s[1] - s[0]) / (s[2] - s[0]) / (s[2] - s[1]);
}
public void MakeDeltaGamma(Tree SpotT, Pricer PriceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(SpotT, PriceT);
Tree treeD = new Tree
{
Gridsteps = Gridsteps + 2,
Spot = spot,
Sig = sig,
Tau = tau * (1 + 2 / Gridsteps)
};
treeD.MakeGrid(myZero, myDiv);
PriceT.MakeGrid(treeD);
double[] S = new double[3];
double[] C = new double[3];
for (int i = 0; i <= 2; ++i)
{
S[i] = treeD.GetSpotMatrix(2, i);
C[i] = PriceT.Get_PriceMatrix(2, i);
}
Delta = (S[0] * (2 * S[1] - S[0]) * (C[1] - C[2]) +
(S[1] * S[1]) * (C[2] - C[0]) + S[2] * (2 * S[1] - S[2]) * (C[0] - C[1]))
/ (S[1] - S[0]) / (S[2] - S[0]) / (S[2] - S[1]);
Gamma = 2 * (S[0] * (C[1] - C[2]) + S[1] * (C[2] - C[0]) + S[2] * (C[0] - C[1]))
/ (S[1] - S[0]) / (S[2] - S[0]) / (S[2] - S[1]);
}
public void MakeVega(Tree spotT, Pricer priceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(spotT, priceT);
Tree t1 = new Tree(), t2 = new Tree();
t1.Tau = Tau;
t1.GridSteps = GridSteps;
t1.Sig = .99 * Sigma;
t1.Spot = Spot;
t1.MakeGrid(myZero, myDiv);
priceT.MakeGrid(t1);
double p1 = priceT.Price();
t2.Tau = Tau;
t2.GridSteps = GridSteps;
t2.Sig = 1.01 * Sigma;
t2.Spot = Spot;
t2.MakeGrid(myZero, myDiv);
priceT.MakeGrid(t2);
double p2 = priceT.Price();
if (Sigma != 0)
{
Vega = 0.01 * (p2 - p1) / (2 * 0.01 * Sigma);
}
}
//public MakeGrid
public void MakeGrid(ZeroCurve myZero, DivList myDivList)
{
EmptyArrays();
MakeArrays();
MakeSpotStar(myZero, myDivList);
MakeDivArray(myZero, myDivList);
FillForwardRate(myZero);
FillUpDown(Sig);
//make the spot grid
double sv = Spotstar;
SetSpotMatrix(0, 0, sv + get_div(0));
//now march forward in time
for (int idx = 1; idx <= Gridsteps; idx++)
{
for (int jdx = 0; jdx <= idx; jdx++)
{
sv = Spotstar * Math.Pow(get_up(idx - 1), jdx) * Math.Pow(get_dn(idx - 1), idx - jdx);
sv += (idx == Gridsteps) ? 0.0 : get_div(idx);
//get_div(idx);
SetSpotMatrix(idx, jdx, sv);
}
}
}
public static ZeroCurve as_zerocurve(YieldTermStructure curve)
{
ZeroCurve ret = new ZeroCurve(NQuantLibcPINVOKE.as_zerocurve(YieldTermStructure.getCPtr(curve)), true);
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
return(ret);
}
//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;
}
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 void NonFlatRates()
{
ZeroCurve myZero = new ZeroCurve();
myZero.ratepoints = 2;
myZero.makeArrays();
myZero.set_r(0, 0.05, 1.0);
myZero.set_r(1, 0.075, 2.0);
//test interpolation priot to point 0
double tTime = 0.5;
double val = myZero.linInterp(tTime);
Assert.Greater(val, 0.0499999999);
Assert.Less(val, 0.050000001);
//test interpolation prior to point 1
tTime = 1.5;
val = myZero.linInterp(tTime);
Assert.Greater(val, 0.062499999999);
Assert.Less(val, 0.06250000001);
//test interpolation post point 1
tTime = 2.5;
val = myZero.linInterp(tTime);
Assert.Greater(val, 0.07499999999);
Assert.Less(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.Greater(val, 0.0499999999);
Assert.Less(val, 0.050000001);
//test interpolation prior to point 1
tTime = 1.5;
val = myZero.forwardRate(tl, tTime);
Assert.Greater(val, 0.06499999); /// 0.065
Assert.Less(val, 0.065000001);
//test interpolation post point 1
tTime = 2.5;
val = myZero.forwardRate(tl, tTime); ///0.077778
Assert.Greater(val, 0.0777777);
Assert.Less(val, 0.07777778);
}
//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));
}
}
}
private void MakeSpotStar(ZeroCurve myZero, DivList myDivList)
{
SpotStart = Spot;
if ((myDivList != null) && (myZero != null))
{
for (int idx = 0; idx < myDivList.Divpoints; idx++)
{
if (myDivList.GetT(idx) <= Tau)
{
double d1 = myDivList.GetD(idx);
double r1 = myZero.LinInterp(myDivList.GetT(idx));
double t1 = Math.Exp(-r1 * myDivList.GetT(idx));
SpotStart -= d1 * t1;
}
}
}
}
public void ADivSlopingZero()
{
DivList mydiv = new DivList();
mydiv.Divpoints = 1;
mydiv.MakeArrays();
mydiv.SetD(0, 5, 0.5);
ZeroCurve myZero = new ZeroCurve();
myZero.Ratepoints = 2;
myZero.MakeArrays();
myZero.SetR(0, 0.075, 0.5);
myZero.SetR(1, 0.05, 2);
//create the tree
Tree myTree = new Tree();
myTree.Gridsteps = 100;
myTree.Tau = 1.0;
myTree.Sig = 0.25;
myTree.Spot = 100.0;
//myTree.flatFlag = false;
myTree.MakeGrid(myZero, mydiv);
//create pricer
Pricer myPrice = new Pricer();
myPrice.Strike = 100;
myPrice.Payoff = "c";
myPrice.Smoothing = "y";
myPrice.Style = "a";
myPrice.MakeGrid(myTree);
double prc = myPrice.Price();
myPrice.Payoff = "p";
myPrice.MakeGrid(myTree);
double prp = myPrice.Price();
Assert.IsTrue(prc > 10.37); //Orc pr = 10.38
Assert.IsTrue(prc < 10.39);
Assert.IsTrue(prp > 9.42); //Orc pr = 9.43
Assert.IsTrue(prp < 9.44);
}
public void EDivFlatZero()
{
DivList mydiv = new DivList();
mydiv.Divpoints = 1;
mydiv.MakeArrays();
mydiv.SetD(0, 5, 0.5);
ZeroCurve myZero = new ZeroCurve();
myZero.Ratepoints = 1;
myZero.MakeArrays();
myZero.SetR(0, 0.05, 1.0);
//create the tree
Tree myTree = new Tree();
myTree.Gridsteps = 100;
myTree.Tau = 1.0;
myTree.Sig = 0.25;
myTree.Spot = 100.0;
//myTree.flatFlag = false;
myTree.MakeGrid(myZero, mydiv);
//create pricer
Pricer myPrice = new Pricer();
myPrice.Strike = 100;
myPrice.Payoff = "c";
myPrice.Smoothing = "y";
myPrice.Style = "e";
myPrice.MakeGrid(myTree);
double prc = myPrice.Price();
myPrice.Payoff = "p";
myPrice.MakeGrid(myTree);
double prp = myPrice.Price();
Assert.IsTrue(prc > 9.455); //BS pr = 9.46277
Assert.IsTrue(prc < 9.475);
Assert.IsTrue(prp > 9.462); //BS pr = 9.46226
Assert.IsTrue(prp < 9.475);
}
public void ANoDivFlatZero()
{
DivList mydiv = new DivList();
mydiv.Divpoints = 1;
mydiv.MakeArrays();
mydiv.SetD(0, 0.0, 1.0);
ZeroCurve myZero = new ZeroCurve();
myZero.Ratepoints = 1;
myZero.MakeArrays();
myZero.SetR(0, 0.05, 1.0);
//create the tree
Tree myTree = new Tree();
myTree.Gridsteps = 100;
myTree.Tau = 1.0;
myTree.Sig = 0.25;
myTree.Spot = 100.0;
//myTree.flatFlag = false;
myTree.MakeGrid(myZero, mydiv);
//create pricer
Pricer myPrice = new Pricer();
myPrice.Strike = 100;
myPrice.Payoff = "c";
myPrice.Smoothing = "y";
myPrice.Style = "a";
myPrice.MakeGrid(myTree);
double prc = myPrice.Price();
myPrice.Payoff = "p";
myPrice.MakeGrid(myTree);
double prp = myPrice.Price();
Assert.IsTrue(prc > 12.33); //Orc pr = 12.34
Assert.IsTrue(prc < 12.35);
Assert.IsTrue(prp > 7.98); //Orc pr = 7.99
Assert.IsTrue(prp < 8.00);
}
public void DivFlatZero()
{
DivList mydiv = new DivList();
mydiv.divpoints = 1;
mydiv.makeArrays();
mydiv.set_d(0, 5, 0.5);
ZeroCurve myZero = new ZeroCurve();
myZero.ratepoints = 1;
myZero.makeArrays();
myZero.set_r(0, 0.05, 1.0);
//create the tree
DiscreteTree myTree = new DiscreteTree();
myTree.Gridsteps = 100;
myTree.tau = 1.0;
myTree.sig = 0.25;
myTree.Spot = 100.0;
//myTree.flatFlag = false;
myTree.MakeGrid(myZero, mydiv);
//create pricer
Pricer myPrice = new Pricer();
myPrice.Strike = 100;
myPrice.Payoff = "c";
myPrice.Smoothing = "y";
myPrice.Style = "e";
myPrice.MakeGrid(myTree);
double prc = myPrice.Price();
myPrice.Payoff = "p";
myPrice.MakeGrid(myTree);
double prp = myPrice.Price();
Assert.Greater(prc, 9.455); //BS pr = 9.46277
Assert.Less(prc, 9.475);
Assert.Greater(prp, 9.462); //BS pr = 9.46226
Assert.Less(prp, 9.475);
}
/// <summary>
///
/// </summary>
/// <param name="price"></param>
/// <param name="myZero"></param>
/// <param name="myDiv"></param>
/// <returns></returns>
public double ImpVol(double price, ZeroCurve myZero, DivList myDiv)
{
double[] greeks = new double[4];
double temp = Pricer(myZero, myDiv, ref greeks, false);
for (int idx = 0; idx < 20; idx++)
{
temp = Pricer(myZero, myDiv, ref greeks, false);
if (Math.Abs(temp - price) < 0.0001) break;
double sigold = Sig;
double dsig = 0.01 * Sig;
Sig += dsig;
double tempUp = Pricer(myZero, myDiv, ref greeks, false);
sigold -= (temp - price) * dsig / (tempUp - temp);
Sig = sigold;
}
return Sig;
}
public void MakeTheta(Tree spotT, Pricer priceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(spotT, priceT);
Tree t1 = new Tree(), t2 = new Tree();
t1.Tau = Tau;
t1.GridSteps = GridSteps;
t1.Sig = Sigma;
t1.Spot = Spot;
t1.MakeGrid(myZero, myDiv);
priceT.MakeGrid(t1);
double p1 = priceT.Price();
double t = Tau - 1.00 / 365.00;
t2.Tau = t;
t2.GridSteps = GridSteps;
t2.Sig = Sigma;
t2.Spot = Spot;
t2.MakeGrid(myZero, myDiv);
priceT.MakeGrid(t2);
double p2 = priceT.Price();
Theta = (p2 - p1);
}
/// <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;
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(ZeroCurve obj) {
return (obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr;
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(ZeroCurve obj)
{
return((obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr);
}