public static double GetATMfwd(ZeroCurve myZero, DivList myDivList, double spot, double t)
{
double spotStart = spot;
//compute the discounted dividends and take off spot
if ((myDivList != null) && (myZero != null))
{
for (int idx = 0; idx < myDivList.Divpoints; idx++)
{
if (myDivList.GetT(idx) <= t)
{
double d1 = myDivList.GetD(idx);
double r1 = myZero.LinInterp(myDivList.GetT(idx));
double t1 = Math.Exp(-r1 * myDivList.GetT(idx));
spotStart -= d1 * t1;
}
}
}
//gross up to expiry to get atfwd
if (myZero != null)
{
double r = myZero.LinInterp(t);
return(spotStart * Math.Exp(r * t));
}
return(0);
}
public static double FindZeroCostCall(ZeroCurve myZero, DivList myDiv, OrcWingVol myVol, double t,
double strike, double spot, string style, string payStyle, double gridSteps)
{
//compute the cost of the put
double callPrice = 0.0;
double putPrice = FindPrice(myZero, myDiv, myVol, t, strike, spot, style, "p", gridSteps);
//start looking for the call using the ATM strike
//double callStrike = GetATMfwd(myZero, myDiv, spot, t);
double callStrike = strike;
const double tol = 0.0001;
for (int idx = 0; idx < 1000; idx++)
{
callPrice = FindPrice(myZero, myDiv, myVol, t, callStrike, spot, style, "c", gridSteps);
if (Math.Abs(callPrice - putPrice) < tol)
{
break;
}
//apply newton
double dk = 0.001 * callStrike;
double callPriceUp = FindPrice(myZero, myDiv, myVol, t, callStrike + dk, spot, style, "c", gridSteps);
callStrike -= (callPrice - putPrice) * dk / (callPriceUp - callPrice);
}
if (Math.Abs(callPrice - putPrice) > tol)
{
throw new Exception("Price did not converge");
}
return(callStrike);
}
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 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);
}
}
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));
}
}
SetDividends(idx, temp, dt * idx);
}
}
else //missing either div or zero, load in 0 for _div on tree
{
for (int idx = 0; idx <= GridSteps; idx++)
{
SetDividends(idx, 0.0, dt * idx);
}
}
}
//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 = SpotStart;
SetSpotMatrix(0, 0, sv + GetDividends(0));
//now march forward in time
for (int idx = 1; idx <= GridSteps; idx++)
{
for (int jdx = 0; jdx <= idx; jdx++)
{
sv = SpotStart * Math.Pow(GetUp(idx - 1), jdx) * Math.Pow(GetDn(idx - 1), idx - jdx);
sv += (idx == GridSteps) ? 0.0 : GetDividends(idx);
//get_div(idx);
SetSpotMatrix(idx, jdx, sv);
}
}
}
//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;
}
//determine if dt needs adjusted because a div occurs in proposed interval
private double CheckBetweenDiv(double t1, double t2, ref double discDiv, DivList myDiv) //t1 & t2 are real times
{
double temp = t2-t1;
for (int idx = 0; idx < myDiv.Divpoints; idx++)
{
if ((t1 <= myDiv.GetT(idx)) && (t2 > myDiv.GetT(idx)))
{
temp = t2 - myDiv.GetT(idx);
discDiv = myDiv.GetD(idx);
break;
}
}
return temp;
}
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;
}
}
}
}
/// <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 static double FindPrice(ZeroCurve myZero, DivList myDiv, OrcWingVol myVol, double t,
double strike, double spot, string style, string paystyle, double gridsteps)
{
//get the atfwd
double atFwd = GetATMfwd(myZero, myDiv, spot, t);
//set up the tree
var myTree = new Tree();
int numGridSteps = (gridsteps < 20.0) ? 20 : Convert.ToInt32(gridsteps);
myTree.GridSteps = numGridSteps;
myTree.Tau = t;
myTree.Sig = myVol.orcvol(atFwd, strike);
myTree.Spot = spot;
myTree.MakeGrid(myZero, myDiv);
//create pricer
var myPrice = new Pricer {
Strike = strike, Payoff = paystyle, Smoothing = "y", Style = style
};
myPrice.MakeGrid(myTree);
double pr = myPrice.Price();
return(pr);
}
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;
}
