//public spotStar
/// <summary>
///
/// </summary>
/// <param name="myZero"></param>
/// <param name="myDivList"></param>
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));
}
}
SetDiv(idx, temp, dt * idx);
}
}
else //missing either div or zero, load in 0 for _div on tree
{
for (int idx = 0; idx <= Gridsteps; idx++)
{
SetDiv(idx, 0.0, dt * idx);
}
}
}
//public MakeGrid
/// <summary>
///
/// </summary>
/// <param name="myZero"></param>
/// <param name="myDivList"></param>
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 + GetDiv(0));
//now march foraward in time
for (int idx = 1; idx <= Gridsteps; idx++)
{
for (int jdx = 0; jdx <= idx; jdx++)
{
sv = _spotstar * Math.Pow(GetUp(idx - 1), jdx) * Math.Pow(GetDn(idx - 1), idx - jdx);
sv += idx == Gridsteps ? 0.0 : GetDiv(idx);
//get_div(idx);
SetSpotMatrix(idx, jdx, sv);
}
}
}
/// <summary>
///
/// </summary>
/// <param name="spotT"></param>
/// <param name="priceT"></param>
/// <param name="myZero"></param>
/// <param name="myDiv"></param>
public void MakeTheta(ITree spotT, Pricer priceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(spotT, priceT);
var type = spotT.GetType();
ITree t1 = (ITree)Activator.CreateInstance(type);
ITree t2 = (ITree)Activator.CreateInstance(type);
t1.Tau = Tau;
t1.Gridsteps = Gridsteps;
t1.Sig = Sig;
t1.Spot = Spot;
t1.MakeGrid(myZero, myDiv);
priceT.MakeGrid(t1);
double p1 = priceT.Price();
DivList shiftDiv = new DivList {
Divpoints = myDiv.Divpoints
};
shiftDiv.MakeArrays();
for (int idx = 0; idx < myDiv.Divpoints; idx++)
{
shiftDiv.SetD(idx, myDiv.GetD(idx), myDiv.GetT(idx) - 1 / 365.0);
}
double t = Tau - 1.00 / 365.00;
t2.Tau = t;
t2.Gridsteps = Gridsteps;
t2.Sig = Sig;
t2.Spot = Spot;
t2.MakeGrid(myZero, shiftDiv);
priceT.MakeGrid(t2);
double p2 = priceT.Price();
Theta = (p2 - p1);
}
/// <summary>
///
/// </summary>
/// <param name="myZero"></param>
/// <param name="myDivList"></param>
/// <param name="spot"></param>
/// <param name="t"></param>
/// <returns></returns>
public static double GetATMfwd(ZeroCurve myZero, DivList myDivList, double spot, double t)
{
double spotstar = 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));
spotstar -= d1 * t1;
}
}
}
//gross up to expiry to get atfwd
if (myZero != null)
{
double r = myZero.LinInterp(t);
return(spotstar * Math.Exp(r * t));
}
return(0);
}
/// <summary>
///
/// </summary>
/// <param name="spotT"></param>
/// <param name="priceT"></param>
/// <param name="myZero"></param>
/// <param name="myDiv"></param>
public void MakeVega(ITree spotT, Pricer priceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(spotT, priceT);
var type = spotT.GetType();
ITree t1 = (ITree)Activator.CreateInstance(type);
ITree t2 = (ITree)Activator.CreateInstance(type);
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);
}
}
/// <summary>
///
/// </summary>
/// <param name="spotT"></param>
/// <param name="priceT"></param>
/// <param name="myZero"></param>
/// <param name="myDiv"></param>
public void MakeDeltaGamma(ITree spotT, Pricer priceT, ZeroCurve myZero, DivList myDiv)
{
SetParam(spotT, priceT);
var type = spotT.GetType();
ITree treeD = (ITree)Activator.CreateInstance(type);
treeD.Gridsteps = Gridsteps + 2;
treeD.Spot = Spot;
treeD.Sig = Sig;
treeD.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]);
double u = treeD.GetUp(0);
double d = treeD.GetDn(0);
double est1 = (c[2] - c[0]) / (s[2] - s[0]);
double est2 = (priceT.GetPriceMatrix(4, 4) - priceT.GetPriceMatrix(4, 0)) / (treeD.GetSpotMatrix(4, 4) - treeD.GetSpotMatrix(4, 0));
double est3 = (priceT.GetPriceMatrix(6, 6) - priceT.GetPriceMatrix(6, 0)) / (treeD.GetSpotMatrix(6, 6) - treeD.GetSpotMatrix(6, 0));
double temp = (Math.Pow(u, 2) + Math.Pow(d, 2) + Math.Pow(u, 2) * Math.Pow(d, 2)) * est1 -
(Math.Pow(u, 2) + Math.Pow(d, 2) + 1) * est2 + est3;
Delta = 1 / Math.Pow(u, 2) / Math.Pow(d, 2) * temp;
//Delta = 1/
}
/// <summary>
///
/// </summary>
/// <param name="today"></param>
/// <param name="expiry"></param>
/// <param name="dates"></param>
/// <param name="amts"></param>
/// <returns></returns>
/// <exception cref="Exception"></exception>
public DivList UnpackDiv(DateTime today, DateTime expiry, DateTime[] dates, double[] amts)
{
int n1 = dates.Length;
int n2 = dates.Length;
double timetoexp = expiry.Subtract(today).Days / 365.0;
if (n1 != n2)
{
throw new Exception("Rate ranges must be of the same length");
}
var dl = new DivList {
Divpoints = n1
};
dl.MakeArrays();
for (int idx = 0; idx < n1; idx++)
{
double time = dates[idx].Subtract(today).Days / 365.0;
double rate = amts[idx];
if (time > 0 & time <= timetoexp)
{
dl.SetD(_kdx, rate, time);
_kdx++;
}
}
return(dl);
}
/// <summary>
/// Gets the AT mforward.
/// </summary>
/// <param name="zeroDates"></param>
/// <param name="zeroRates">The zero curve.</param>
/// <param name="divDates"></param>
/// <param name="divAms">The div curve.</param>
/// <param name="expiry"></param>
/// <param name="spot">The spot.</param>
/// <param name="today"></param>
/// <returns></returns>
public static double GetForward(DateTime today, DateTime expiry, double spot, DateTime[] zeroDates, double[] zeroRates, DateTime[] divDates, double[] divAms)
{
var wrapper = new Wrapper();
ZeroCurve myZero = wrapper.UnpackZero(today, zeroDates, zeroRates);
DivList myDiv = wrapper.UnpackDiv(today, expiry, divDates, divAms);
double t = expiry.Subtract(today).Days / 365.0;
double temp = Collar.GetATMfwd(myZero, myDiv, spot, t);
return(temp);
}
/// <summary>
///
/// </summary>
/// <param name="spot"></param>
/// <param name="strike"></param>
/// <param name="vol"></param>
/// <param name="paystyle"></param>
/// <param name="today"></param>
/// <param name="expiry"></param>
/// <param name="zeroDates"></param>
/// <param name="zeroRates"></param>
/// <param name="divDates"></param>
/// <param name="divAms"></param>
/// <returns></returns>
public static double BlackScholesPricer(double spot, double strike, double vol, string paystyle, DateTime today, DateTime expiry,
DateTime[] zeroDates, double[] zeroRates, DateTime[] divDates, double[] divAms)
{
double t = expiry.Subtract(today).Days / 365.0;
var wrapper = new Wrapper();
ZeroCurve myZero = wrapper.UnpackZero(today, zeroDates, zeroRates);
DivList myDiv = wrapper.UnpackDiv(today, expiry, divDates, divAms);
double fwd = Collar.GetATMfwd(myZero, myDiv, spot, t);
double r = myZero.LinInterp(t);
//create default pricer
var myPrice = new Pricer {
Strike = strike, Payoff = paystyle
};
double pr = myPrice.BSprice(fwd, t, strike, r, vol, paystyle);
return(pr);
}
//public spotStar
private void MakeSpotStar(ZeroCurve myZero, DivList myDivList)
{
_spotstar = 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));
_spotstar -= d1 * t1;
}
}
}
}
/// <summary>
///
/// </summary>
/// <param name="style"></param>
/// <param name="spot"></param>
/// <param name="strike"></param>
/// <param name="vol"></param>
/// <param name="today"></param>
/// <param name="expiry"></param>
/// <param name="paystyle"></param>
/// <param name="zeroDates"></param>
/// <param name="zeroRates"></param>
/// <param name="divDates"></param>
/// <param name="divAms"></param>
/// <param name="gridsteps"></param>
/// <param name="smoo"></param>
/// <param name="flatFlag"></param>
/// <returns></returns>
public static double[,] BinomialRelativeGetGreeks(string style, double spot, double strike, double vol, DateTime today, DateTime expiry,
string paystyle, DateTime[] zeroDates, double[] zeroRates, DateTime[] divDates, double[] divAms, double gridsteps, string smoo, bool flatFlag)
{
const int arrsize = 4;
gridsteps = (gridsteps == 0.0) ? 20 : gridsteps;
int nGridsteps = Convert.ToInt32(gridsteps);
string smoothing = (smoo.ToLower().Equals("n")) ? "n" : "y";
var retArray = new double[arrsize, arrsize];
double t = expiry.Subtract(today).Days / 365.0;
ZeroCurve myZero = (new Wrapper()).UnpackZero(today, zeroDates, zeroRates);
DivList myDiv = (new Wrapper()).UnpackDiv(today, expiry, divDates, divAms);
//create the tree
var myTree = new PropTree(t, vol, spot, nGridsteps, true)
{
Gridsteps = nGridsteps
};
myTree.MakeGrid(myZero, myDiv);
//create pricer
var myPrice = new Pricer(strike, paystyle, smoothing, style);
myPrice.MakeGrid(myTree);
myPrice.Price();
var myGreeks = new Greeks();
myGreeks.MakeDeltaGamma(myTree, myPrice, myZero, myDiv);
double delta = myGreeks.Delta;
double gamma = myGreeks.Gamma;
myGreeks.MakeVega(myTree, myPrice, myZero, myDiv);
double vega = myGreeks.Vega;
myGreeks.MakeTheta(myTree, myPrice, myZero, myDiv);
double theta = myGreeks.Theta;
retArray[0, 0] = delta;
retArray[0, 1] = gamma;
retArray[0, 2] = vega;
retArray[0, 3] = theta;
return(retArray);
}
/// <summary>
///
/// </summary>
/// <param name="myZero"></param>
/// <param name="myDivList"></param>
public void MakeGrid(ZeroCurve myZero, DivList myDivList)
{
EmptyArrays();
MakeArrays();
MakeSpotZero(myZero, myDivList);
MakeDivArray(myZero, myDivList);
FillForwardRate(myZero);
FillUpDown(Sig);
decimal deltaT = Convert.ToDecimal(Tau) / Convert.ToDecimal(Gridsteps);
//make the spot grid
SetSpotMatrix(0, 0, _spot0);
//now march foraward in time
for (int idx = 1; idx <= Gridsteps; idx++)
{
for (int jdx = 0; jdx <= idx; jdx++)
{
var sv = _spot0 * Math.Pow(GetUp(idx - 1), jdx) * Math.Pow(GetDn(idx - 1), idx - jdx);
//sv += (idx == Gridsteps) ? 0.0 : get_div(idx);
//get_div(idx);
SetSpotMatrix(idx, jdx, sv);
}
}
for (int idx = 1; idx <= Gridsteps; idx++)
{
for (int jdx = 0; jdx <= idx; jdx++)
{
int kdx = myDivList.Divpoints - 1;
while (kdx >= 0)
{
decimal t1 = Convert.ToDecimal(myDivList.GetT(kdx));
if (t1 / idx > deltaT)
{
SetSpotMatrix(idx, jdx, GetSpotMatrix(idx, jdx) / (1 - _ratio[kdx]));
}
kdx--;
}
}
}
SetSpotMatrix(0, 0, Spot);
}
/// <summary>
///
/// </summary>
/// <param name="myZero"></param>
/// <param name="myDiv"></param>
/// <param name="orcParams"></param>
/// <param name="t"></param>
/// <param name="strike"></param>
/// <param name="spot"></param>
/// <param name="style"></param>
/// <param name="paystyle"></param>
/// <param name="gridsteps"></param>
/// <returns></returns>
public static double FindPrice(ZeroCurve myZero, DivList myDiv, double[] orcParams, double t,
double strike, double spot, string style, string paystyle, double gridsteps)
{
//get the atfwd
double atFwd = GetATMfwd(myZero, myDiv, spot, t);
//unpack the orc paramters
//double currentVol = OrcParams[0];
//double slopeRef = OrcParams[1];
//double putCurve = OrcParams[2];
//double callCurve = OrcParams[3];
//double dnCutOff = OrcParams[4];
//double upCutOff = OrcParams[5];
//double refFwd = OrcParams[6];
//double refVol = OrcParams[7];
//double vcr = OrcParams[8];
//double scr = OrcParams[9];
//double ssr = OrcParams[10];
//double dsr = OrcParams[11];
//double usr = OrcParams[12];
//set up the tree
var myTree = new DiscreteTree();
var myVol = new OrcWingVol();
int nGridsteps = (gridsteps < 20.0) ? 20 : Convert.ToInt32(gridsteps);
myTree.Gridsteps = nGridsteps;
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);
}
/// <summary>
///
/// </summary>
/// <param name="style"></param>
/// <param name="spot"></param>
/// <param name="strike"></param>
/// <param name="vol"></param>
/// <param name="today"></param>
/// <param name="expiry"></param>
/// <param name="paystyle"></param>
/// <param name="zeroDates"></param>
/// <param name="zeroRates"></param>
/// <param name="divDates"></param>
/// <param name="divAms"></param>
/// <param name="gridsteps"></param>
/// <param name="smoo"></param>
/// <param name="flatFlag"></param>
/// <returns></returns>
public static double BinomialRelativePricer(string style, double spot, double strike, double vol, DateTime today, DateTime expiry,
string paystyle, DateTime[] zeroDates, double[] zeroRates, DateTime[] divDates, double[] divAms, double gridsteps, string smoo, bool flatFlag)
{
gridsteps = (gridsteps == 0.0) ? 20 : gridsteps;
int nGridsteps = Convert.ToInt32(gridsteps);
string smoothing = (smoo.ToLower().Equals("n")) ? "n" : "y";
double t = expiry.Subtract(today).Days / 365.0;
var wrapper = new Wrapper();
ZeroCurve myZero = wrapper.UnpackZero(today, zeroDates, zeroRates);
DivList myDiv = wrapper.UnpackDiv(today, expiry, divDates, divAms);
//create the tree
var myTree = new PropTree(t, vol, spot, nGridsteps, true);
myTree.MakeGrid(myZero, myDiv);
//create pricer
var myPrice = new Pricer(strike, paystyle, smoothing, style);
myPrice.MakeGrid(myTree);
double pr = myPrice.Price();
return(pr);
}
//public spotStar
private void MakeSpotZero(ZeroCurve myZero, DivList myDivList)
{
_spot0 = Spot;
_ratio = new double[myDivList.Divpoints];
if (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));
_ratio[idx] = d1 * t1 / _spot0;
if (_ratio[idx] > 1)
{
throw new Exception("Dividend greater than spot");
}
_spot0 = _spot0 * (1 - _ratio[idx]);
}
}
}
}
/// <summary>
///
/// </summary>
/// <param name="myZero"></param>
/// <param name="myDiv"></param>
/// <param name="orcParams"></param>
/// <param name="t"></param>
/// <param name="strike"></param>
/// <param name="spot"></param>
/// <param name="style"></param>
/// <param name="paystyle"></param>
/// <param name="gridsteps"></param>
/// <returns></returns>
public static double FindZeroCostPut(ZeroCurve myZero, DivList myDiv, double[] orcParams, double t,
double strike, double spot, string style, string paystyle, double gridsteps)
{
//compute the cost of the put
double putPrice = 0.0;
double callPrice = FindPrice(myZero, myDiv, orcParams, t, strike, spot, style, "c", gridsteps);
//start looking for the call using the ATM strike
double putStrike = GetATMfwd(myZero, myDiv, spot, t);
const double tol = 0.0001;
for (int idx = 0; idx < 20; idx++)
{
putPrice = FindPrice(myZero, myDiv, orcParams, t, putStrike, spot, style, "p", gridsteps);
if (Math.Abs(callPrice - putPrice) < tol)
{
break;
}
//apply newton
double dk = 0.01 * putStrike;
double putPriceUp = FindPrice(myZero, myDiv, orcParams, t, putStrike - dk, spot, style, "p", gridsteps);
putStrike += (callPrice - putPrice) * dk / (putPriceUp - putPrice);
}
return(putPrice);
}
