private Greeks fnGreeks()
{
double dIv;
bool isCall = OptionQuote.Option.OpType == AOption.EOpType.Call;
DateTime dtTradeDate = Date.Decode(OptionQuote.TradeDate);
DateTime dtExpDate = Date.Decode(OptionQuote.Option.ExpDate);
double dT = Convert.ToDouble(OptionQuote.Option.TimeToExp(dtTradeDate, dtExpDate));
double dRfr = fnRiskFreeRate(dtTradeDate, dtExpDate);
int implVolNewton = BlackSholes.ImplVol_Newton(
Convert.ToDouble(OptionQuote.Mid),
Convert.ToDouble(OptionQuote.UnderPx),
Convert.ToDouble(OptionQuote.Option.Strike),
dT,
dRfr,
0,
isCall,
out dIv);
if (implVolNewton != 0) return null;
double dTheoPx;
var gg = new Greeks();
int nRet =
BlackSholes.BlackSholesCals(
Convert.ToDouble(OptionQuote.UnderPx),
Convert.ToDouble(OptionQuote.Option.Strike),
dT,
dRfr,
0,
isCall,
dIv,
out dTheoPx,
gg);
return nRet != 0 ? null : gg;
}
public static int BlackSholesCals(double dUnderPx, double dStrike, double dT, double dR, double dQ, bool isCall,
double dSigma,out double dPx,Greeks greeks)
{
const double dEps = 10e-6;
dPx = double.NaN;
if( (dStrike < dEps) || (dSigma < dEps) || (dT < dEps) ) return 2;/* Check if any of the the input arguments are too small */
var dExpQt = Math.Exp(-dQ * dT);
var dExpRt = Math.Exp(-dR * dT);
var d1 = Math.Log(dUnderPx / dStrike) + (dR - dQ + (dSigma * dSigma / 2.0)) * dT;
d1 = d1/(dSigma*Math.Sqrt(dT));
var d2 = d1-dSigma*Math.Sqrt(dT);
if (isCall) dPx = dUnderPx * dExpQt * CumNormDistrib(d1) - dStrike * dExpRt * CumNormDistrib(d2);
else dPx = -dUnderPx * dExpQt * CumNormDistrib(-d1) + dStrike * dExpRt * CumNormDistrib(-d2);
if (greeks!=null)
{
double dPnd = Math.Exp(-d1 * d1 / 2.0) / Math.Sqrt(2.0 * Pi);
if (isCall)
{
greeks.Delta = (CumNormDistrib(d1)) * dExpQt; /* delta */
greeks.Theta = -dUnderPx * dExpQt * dPnd * dSigma / (2.0 * Math.Sqrt(dT))
+ dQ * dUnderPx * CumNormDistrib(d1) * dExpQt - dR * dStrike * dExpRt * CumNormDistrib(d2); /* theta */
greeks.Rho = dStrike * dT * dExpRt * CumNormDistrib(d2); /* rho */
}
else
{
greeks.Delta = (CumNormDistrib(d1) - 1.0) * dExpQt; /* delta */
greeks.Theta = -dUnderPx * dExpQt * dPnd * dSigma / (2.0 * Math.Sqrt(dT)) -
dQ * dUnderPx * CumNormDistrib(-d1) * dExpQt + dR * dStrike * dExpRt * CumNormDistrib(-d2); /* theta */
greeks.Rho = -dStrike * dT * dExpRt * CumNormDistrib(-d2); /* rho */
}
greeks.Gamma = dPnd * dExpQt / (dUnderPx * dSigma * Math.Sqrt(dT)); /* gamma */
greeks.Vega = dUnderPx * dExpQt * Math.Sqrt(dT) * dPnd; /* vega */
greeks.IV = dSigma;
}
return 0;
}
public static int ImplVol(double dPx, double dUnderPx, double dStrike, double dT, double dR, double dQ, bool isCall,
double dSigMin,
out double dImplVol)
{
const int nMaxIter = 50;
const double dEps = 10e-6;
dImplVol = double.NaN;
double dTmp = isCall ? Math.Max(dUnderPx*Math.Exp(-dQ*dT)-dStrike*Math.Exp(-dR*dT),0) :
Math.Max(dStrike*Math.Exp(-dR*dT)-dUnderPx*Math.Exp(-dQ*dT),0);
if(Math.Abs(dPx-dTmp)<=Math.Sqrt(dEps)) return 3;
double dSig = dSigMin; /* initial estimate */
double dSig1 = double.NaN;
bool bDone=false;
var greeks = new Greeks();
for(var i =0;i<nMaxIter&&(!bDone);++i)
{
double dVal;
if(BlackSholesCals(dUnderPx, dStrike, dT, dR, dQ, isCall, dSig, out dVal, greeks)!= 0) return 1;
dSig1 = dSig - (dVal - dPx)/greeks.Vega; /* compute the new estimate of sigma using Newton’s method */
if (dEps > Math.Abs((dSig1 - dSig)/dSig1)) bDone=true; /* check whether the specified accuracy has been reached */
dSig = dSig1; /* up date sigma */
}
dImplVol = dSig1; /* return the estimate for sigma */
return !bDone ? 3 : 0;
}
public static int ImplVol_Newton(double dPx, double dUnderPx, double dStrike, double dT, double dR, double dQ, bool isCall,out double dImplVol)
{
const int nMaxIter = 10000;
const double dEps = 10e-6;
dImplVol = Math.Sqrt(Math.Abs(Math.Log(dUnderPx / dStrike) + dR * dT) * 2 / dT);
var greeks = new Greeks();
double dTryPx;
if (BlackSholesCals(dUnderPx, dStrike, dT, dR, dQ, isCall, dImplVol, out dTryPx, greeks) != 0) return 1;
double dMinDiff = Math.Abs(dPx - dTryPx);
var bDone = false;
for (var i = 0; i < nMaxIter; ++i)
{
if (Math.Abs(dPx - dTryPx) < dEps || Math.Abs(dPx - dTryPx) > dMinDiff)
{
bDone = true;
break;
}
dImplVol = dImplVol - (dTryPx - dPx) / greeks.Vega;
if (BlackSholesCals(dUnderPx, dStrike, dT, dR, dQ, isCall, dImplVol, out dTryPx, greeks) != 0) return 1;
dMinDiff = Math.Abs(dPx - dTryPx);
}
return !bDone ? 3 : 0;
}
