/// <summary>
/// Gets the price.
/// </summary>
/// <returns></returns>
public double GetPrice()
{
int numresets = _resetDays.Length;
int readings = _resetAmts.Count(item => (item > 0));
if (readings == numresets)
{
double av = _resetAmts.Average();
double df = EquityAnalytics.GetDFCCLin365(0, _tau, _rtdays, _rtamts);
return((av - _strike) * df);
}
double newstrike = TransformStrike(numresets, readings);
int nleft = numresets - readings;
int[] reset_days = new int[nleft];
double[] vols = new double[nleft];
for (int idx = 0; idx < nleft; idx++)
{
reset_days[idx] = _resetDays[idx + readings];
vols[idx] = _vols[idx + readings];
}
double newprice = GetPrice(newstrike, numresets - readings, reset_days, vols);
return(newprice * (numresets - readings) / numresets);
}
/// <summary>
/// Gets the price.
/// </summary>
/// <param name="strike">The strike.</param>
/// <param name="numResets">The num_resets.</param>
/// <param name="resetDays"></param>
/// <param name="vols">The vols.</param>
/// <returns></returns>
public double GetPrice(double strike, int numResets, int[] resetDays, double[] vols)
{
double bond = 0.0;
int numVols = _vols.Length;
double[] covxxi;
double[] varlogs;
double[] forwards = new double[numResets];
double mu = CalcMu(ref forwards, resetDays, vols);
double sigma = CalcSigma(resetDays, vols);
varlogs = CalcVarLogs(resetDays, vols);
covxxi = CalcCovXXI(varlogs, vols.Length);
if (strike <= 0)
{
bond = System.Math.Abs(strike);
strike = CEpsilon;
}
double z0 = (mu - System.Math.Log(strike)) / sigma;
double i1 = 0.0;
for (int idx = 0; idx < numResets; idx++)
{
double x1 = z0 + (covxxi[idx] / sigma);
double n1 = _nd.CumulativeDistribution(x1);
i1 += n1 * forwards[idx] / (double)numResets;
}
double i2 = strike * _nd.CumulativeDistribution(z0);
double prem = i1 - i2;
double df = EquityAnalytics.GetDFCCLin365(0, _tau, _rtdays, _rtamts);
return((prem + bond) * df);
}
/// <summary>
/// Gets the price.
/// </summary>
/// <returns></returns>
public double GetPrice()
{
double fwd = EquityAnalytics.GetForwardCCLin365(_spot, _tau, _divdays, _divamts, _rtdays, _rtamts);
double rate = EquityAnalytics.GetRateCCLin365(0, _tau, _rtdays, _rtamts);
return(BlackScholesPrice(fwd, _tau, _strike, rate, _vol, _isCall));
}
/// <summary>
/// Gets the vega.
/// </summary>
/// <returns></returns>
public double GetVega()
{
double q = EquityAnalytics.GetYieldCCLin365(_spot, 0, _tau, _divdays, _divamts, _rtdays, _rtamts);
double fwd = EquityAnalytics.GetForwardCCLin365(_spot, _tau, _divdays, _divamts, _rtdays, _rtamts);
double d1 = (System.Math.Log(fwd / _strike) + _vol * _vol * _tau / 2) / _vol / System.Math.Sqrt(_tau);
double lhs = _spot * System.Math.Sqrt(_tau) * _nd.ProbabilityDensity(d1) * 0.01 * System.Math.Exp(-q * _tau);
return(lhs);
}
/// <summary>
/// Gets the gamma.
/// </summary>
/// <returns></returns>
public double GetGamma()
{
double q = EquityAnalytics.GetYieldCCLin365(_spot, 0, _tau, _divdays, _divamts, _rtdays, _rtamts);
double fwd = EquityAnalytics.GetForwardCCLin365(_spot, _tau, _divdays, _divamts, _rtdays, _rtamts);
double d1 = (System.Math.Log(fwd / _strike) + _vol * _vol * _tau / 2) / _vol / System.Math.Sqrt(_tau);
var temp = _nd.ProbabilityDensity(d1);
return(System.Math.Exp(q * _tau) * temp / _spot / _vol / System.Math.Sqrt(_tau));
}
/// <summary>
/// Forwards the rate.
/// </summary>
/// <param name="yearFraction1">The t1.</param>
/// <param name="yearFraction2">The t2.</param>
/// <returns></returns>
private double ForwardRate(double yearFraction1, double yearFraction2)
{
return(EquityAnalytics.GetRateCCLin365(yearFraction1, yearFraction2, _rateDays, _rateAmts));
//double rt1 = _rateInterp.ValueAt(yearFraction1, false);
//double rt2 = _rateInterp.ValueAt(yearFraction2, false);
//if (yearFraction2 > yearFraction1)
// return (rt2 * yearFraction2 - rt1 * yearFraction1) / (yearFraction2 - yearFraction1);
//else
// return 0;
}
/// <summary>
/// Calcs the mu.
/// </summary>
/// <param name="resetDays"></param>
/// <param name="vols">The vols.</param>
/// <param name="forwards">The forwards.</param>
/// <returns></returns>
private double CalcMu(ref double[] forwards, int[] resetDays, double[] vols)
{
double musum = 0;
int numresets = resetDays.Length;
for (int idx = 0; idx < numresets; idx++)
{
double dt0 = Convert.ToDouble(resetDays[idx]) / Daybasis;
double r0 = EquityAnalytics.GetRateCCLin365(0, dt0, _rtdays, _rtamts);
double q0 = EquityAnalytics.GetYieldCCLin365(_spot, 0, dt0, _divdays, _divamts, _rtdays, _rtamts);
musum += System.Math.Log(_spot) + (r0 - q0) * dt0 - vols[idx] * vols[idx] * dt0 / 2;
forwards[idx] = _spot * System.Math.Exp((r0 - q0) * dt0);
}
return(musum / numresets);
}
/// <summary>
/// Gets the delta.
/// </summary>
/// <returns></returns>
public double GetDelta()
{
double q = EquityAnalytics.GetYieldCCLin365(_spot, 0, _tau, _divdays, _divamts, _rtdays, _rtamts);
double fwd = EquityAnalytics.GetForwardCCLin365(_spot, _tau, _divdays, _divamts, _rtdays, _rtamts);
double d1 = (System.Math.Log(fwd / _strike) + _vol * _vol * _tau / 2) / _vol / System.Math.Sqrt(_tau);
double temp;
if (!_isCall)
{
temp = BasicMath.Ndist(d1) - 1;
}
else
{
temp = BasicMath.Ndist(d1);
}
return(System.Math.Exp(-q * _tau) * temp);
}
/// <summary>
/// Gets the price.
/// </summary>
/// <returns></returns>
public double GetPrice()
{
double fwd = EquityAnalytics.GetForwardCCLin365(_spot, _tau, _dividendDays, _dividendAmounts, _rateDays, _rateAmounts);
double r = EquityAnalytics.GetRateCCLin365(0, _tau, _rateDays, _rateAmounts);
double q = EquityAnalytics.GetYieldCCLin365(_spot, 0, _tau, _dividendDays, _dividendAmounts, _rateDays, _rateAmounts);
double df = EquityAnalytics.GetDFCCLin365(0, _tau, _rateDays, _rateAmounts);
double flatSkewPrice = df * FlatSkewPrice(fwd, r, q);
double[] res = OptionAnalytics.OptWithGreeks(true, fwd, _strike, _volatility, _tau);
double callVega = res[3];
double price;
if (_isCall)
{
price = flatSkewPrice - _skew * df * callVega;
}
else
{
price = flatSkewPrice + _skew * df * callVega;
}
return(price);
}
/// <summary>
/// Gets the theta.
/// </summary>
/// <returns></returns>
public double GetTheta()
{
double q = EquityAnalytics.GetYieldCCLin365(_spot, 0, _tau, _divdays, _divamts, _rtdays, _rtamts);
double fwd = EquityAnalytics.GetForwardCCLin365(_spot, _tau, _divdays, _divamts, _rtdays, _rtamts);
double d1 = (System.Math.Log(fwd / _strike) + _vol * _vol * _tau / 2) / _vol / System.Math.Sqrt(_tau);
double rate = EquityAnalytics.GetRateCCLin365(0, _tau, _rtdays, _rtamts);
double d2 = d1 - _vol * System.Math.Sqrt(_tau);
double rhs1 = -System.Math.Exp(-q * _tau) * _spot * _nd.ProbabilityDensity(d1) * _vol / 2 / System.Math.Sqrt(_tau);
double rhs3 = 0;
if (_isCall)
{
double rhs2 = -rate *_strike *System.Math.Exp(-rate *_tau) * _nd.CumulativeDistribution(d2);
//rhs3 = q * _spot * System.Math.Exp(-q * _tau) * _nd.CumulativeDistribution(d1);
return((rhs1 + rhs2 + rhs3) / 365.0);
}
else
{
double rhs2 = rate * _strike * System.Math.Exp(-rate * _tau) * _nd.CumulativeDistribution(-d2);
//rhs3 = -q * _spot * System.Math.Exp(-q * _tau) * _nd.CumulativeDistribution(-d1);
return((rhs1 + rhs2 + rhs3) / 365.0);
}
}
//compute Sstar for the BC's
/// <summary>
/// Computes the disc div.
/// </summary>
/// <param name="tTemp">The t temp.</param>
/// <param name="T">The T.</param>
/// <param name="ratedays">The ratedays.</param>
/// <param name="rateamts">The rateamts.</param>
/// <param name="divdays">The divdays.</param>
/// <param name="divamts">The divamts.</param>
/// <returns></returns>
private double ComputeDiscDiv(double tTemp, double T, int[] ratedays, double[] rateamts, int[] divdays, double[] divamts)
{
return(EquityAnalytics.GetPVDivsCCLin365(tTemp, T, divdays, divamts, ratedays, rateamts));
}
/// <summary>
/// Gets the AT MFWD.
/// </summary>
/// <param name="ratedays">The ratedays.</param>
/// <param name="rateamts">The rateamts.</param>
/// <param name="divdays">The divdays.</param>
/// <param name="divamts">The divamts.</param>
/// <param name="t">The t.</param>
/// <returns></returns>
public double GetATMfwd(int[] ratedays, double[] rateamts, int[] divdays, double[] divamts, double t)
{
return(EquityAnalytics.GetForwardCCLin365(_spot, t, divdays, divamts, ratedays, rateamts));
}
public double[] GetPriceAndGreeks()
{
double[] greeks = new double[3];
double[] res = new double[4];
_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) < -0.001 * _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, divdays, divamts);
//compute the real time and backward time tau
tTemp -= dt;
tau = _T - tTemp;
//compute the increment forward rate
_domR = EquityAnalytics.GetRateCCLin365(tTemp, tTemp + dt, ratedays, rateamts);
_forR = 0.0;
//compute the forward rate from real time tTemp to expiry for the BC'c
double domRbc = EquityAnalytics.GetRateCCLin365(tTemp, _T, ratedays, rateamts);
//compute discounted dividends for the bc's
double DiscDiv = ComputeDiscDiv(tTemp, _T, ratedays, rateamts, divdays, divamts);
//save the value at the spot for use in theta calcuation
int nKeyInt = (int)((System.Math.Log(_spot) - _xl) / _dx);
double fracInt = (System.Math.Log(_spot) - _x[nKeyInt]) / (_x[nKeyInt + 1] - _x[nKeyInt]);
tempInt = _v[nKeyInt] * (1.0 - fracInt) + _v[nKeyInt + 1] * fracInt;
//get the fwd
_lnfwd = System.Math.Log(GetATMfwd(ratedays, rateamts, divdays, divamts, 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, System.Math.Exp(_x[0]), domRbc, DiscDiv);
_v[_steps - 1] = MakeUpperBC(tau, System.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, System.Math.Exp(_x[0]), domRbc, DiscDiv);
_v[_steps - 1] = MakeUpperBC(tau, System.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)((System.Math.Log(_spot) - _xl) / _dx);
double frac = (System.Math.Log(_spot) - _x[nKey]) / (_x[nKey + 1] - _x[nKey]);
double temp = _v[nKey] * (1.0 - frac) + _v[nKey + 1] * frac;
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] = System.Math.Exp(_x[nKey - 1]);
a[1, 1] = System.Math.Exp(_x[nKey]);
a[2, 1] = System.Math.Exp(_x[nKey + 1]);
a[3, 1] = System.Math.Exp(_x[nKey + 2]);
a[0, 2] = System.Math.Exp(_x[nKey - 1]) * System.Math.Exp(_x[nKey - 1]);
a[1, 2] = System.Math.Exp(_x[nKey]) * System.Math.Exp(_x[nKey]);
a[2, 2] = System.Math.Exp(_x[nKey + 1]) * System.Math.Exp(_x[nKey + 1]);
a[3, 2] = System.Math.Exp(_x[nKey + 2]) * System.Math.Exp(_x[nKey + 2]);
a[0, 3] = System.Math.Exp(_x[nKey - 1]) * System.Math.Exp(_x[nKey - 1]) * System.Math.Exp(_x[nKey - 1]);
a[1, 3] = System.Math.Exp(_x[nKey]) * System.Math.Exp(_x[nKey]) * System.Math.Exp(_x[nKey]);
a[2, 3] = System.Math.Exp(_x[nKey + 1]) * System.Math.Exp(_x[nKey + 1]) * System.Math.Exp(_x[nKey + 1]);
a[3, 3] = System.Math.Exp(_x[nKey + 2]) * System.Math.Exp(_x[nKey + 2]) * System.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);
*/
res[0] = temp;
res[1] = greeks[0];
res[2] = greeks[1];
res[3] = greeks[2];
return(res);
}
/// <summary>
/// PVs the divs.
/// </summary>
/// <param name="yearFraction1">The year fraction1.</param>
/// <param name="yearFraction2">The year fraction2.</param>
/// <returns></returns>
private double PVDivs(double yearFraction1, double yearFraction2)
{
double res = EquityAnalytics.GetPVDivsCCLin365(yearFraction1, yearFraction2, _divDays, _divAmts, _rateDays, _rateAmts);
return(res);
}
/// <summary>
/// Gets the yield.
/// </summary>
/// <param name="yearFraction">The year fraction.</param>
/// <returns></returns>
private double GetYield(double yearFraction)
{
return(EquityAnalytics.GetYieldCCLin365(_spot, 0, yearFraction, _divDays, _divAmts, _rateDays, _rateAmts));
}
