public double GetTheta(double S, double X, double q, double r,
double sigma, double t, EPutCall PutCall)
{
double t_sqrt = Math.Sqrt(t);
double sigma2 = sigma * sigma;
double d1 = (Math.Log(S / X) + (r - q + sigma2 * 0.5) * t) / (t_sqrt * sigma);
double d2 = d1 - t_sqrt * sigma;
double part1 = S * sigma * Math.Exp(-q * t) * n(d1) / 2.0 / t_sqrt;
double part2 = -q *S *Math.Exp(-q *t);
double part3 = r * X * Math.Exp(-r * t);
switch (PutCall)
{
case EPutCall.Call:
return(-part1 - part2 * N(d1) - part3 * N(d2));
case EPutCall.Put:
return(-part1 + part2 * N(-d1) + part3 * N(-d2));
default:
return(0.0);
}
}
public double GetGamma(double S, double X, double q, double r,
double sigma, double t, EPutCall PutCall)
{
double t_sqrt = Math.Sqrt(t);
double sigma2 = sigma * sigma;
double d1 = (Math.Log(S / X) + (r - q + sigma2 * 0.5) * t) / (t_sqrt * sigma);
return(Math.Exp(-q * t) * n(d1) / S / t_sqrt / sigma);
}
public static double MC(double S, double X, double t, double s, double r, EPutCall PutCall, int n)
{
double num1 = (r - 0.5 * s * s) * t;
double num2 = s * Math.Sqrt(t);
double num3 = 0.0;
for (int index = 0; index < n; ++index)
{
num3 += FinMath.Payoff(S * Math.Exp(num1 + num2 * Random.Gaus()), X, PutCall);
}
return(FinMath.PV4(num3 / (double)n, r, t));
}
public static double BM(double S, double X, double t, double s, double r, EPutCall PutCall, int n)
{
double F = 0.0;
double x1 = u(t, s, n);
double x2 = d(t, s, n);
double p = FinMath.p(t, s, n, r);
for (int m = 0; m <= n; ++m)
{
F += Binom(m, n, p) * Payoff(S * Pow(x1, m) * Pow(x2, n - m), X, PutCall);
}
return(PV4(F, r, t));
}
public static double BM(double S, double X, double t, double s, double r, EPutCall PutCall, int n)
{
double F = 0.0;
double x1 = FinMath.u(t, s, n);
double x2 = FinMath.d(t, s, n);
double p = FinMath.p(t, s, n, r);
for (int m = 0; m <= n; ++m)
{
F += FinMath.Binom(m, n, p) * FinMath.Payoff(S * Math.Pow(x1, (double)m) * Math.Pow(x2, (double)(n - m)), X, PutCall);
}
return(FinMath.PV4(F, r, t));
}
private double Payoff(double S, double X, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return(Call(S, X));
case EPutCall.Put:
return(Put(S, X));
default:
return(0.0);
}
}
public static double Theta(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return(-S *n(d1(S, X, t, s, r)) * s / (2.0 * Sqrt(t)) - r * X * Exp(-r * t) * N(d2(S, X, t, s, r)));
case EPutCall.Put:
return(-S *n(d1(S, X, t, s, r)) * s / (2.0 * Sqrt(t)) + r * X * Exp(-r * t) * N(-d2(S, X, t, s, r)));
default:
return(0.0);
}
}
public static double BS(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return(S * N(d1(S, X, t, s, r)) - X * Exp(-r * t) * N(d2(S, X, t, s, r)));
case EPutCall.Put:
return(-S *N(-d1(S, X, t, s, r)) + X * Exp(-r * t) * N(-d2(S, X, t, s, r)));
default:
return(0.0);
}
}
public static double Delta(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return(FinMath.N(FinMath.d1(S, X, t, s, r)));
case EPutCall.Put:
return(FinMath.N(FinMath.d1(S, X, t, s, r)) - 1.0);
default:
return(0.0);
}
}
public static double Payoff(double s, double x, EPutCall putcall)
{
switch (putcall)
{
case EPutCall.Call:
return(Call(s, x));
case EPutCall.Put:
return(Put(s, x));
default:
return(0.0);
}
}
public static double Payoff(double S, double X, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return(FinMath.Call(S, X));
case EPutCall.Put:
return(FinMath.Put(S, X));
default:
return(0.0);
}
}
public static double Theta(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return(-S *FinMath.n(FinMath.d1(S, X, t, s, r)) * s / (2.0 * Math.Sqrt(t)) - r * X * Math.Exp(-r * t) * FinMath.N(FinMath.d2(S, X, t, s, r)));
case EPutCall.Put:
return(-S *FinMath.n(FinMath.d1(S, X, t, s, r)) * s / (2.0 * Math.Sqrt(t)) + r * X * Math.Exp(-r * t) * FinMath.N(-FinMath.d2(S, X, t, s, r)));
default:
return(0.0);
}
}
public static double Rho(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return(X * t * Math.Exp(-r * t) * FinMath.N(FinMath.d2(S, X, t, s, r)));
case EPutCall.Put:
return(-X *t *Math.Exp(-r *t) * FinMath.N(-FinMath.d2(S, X, t, s, r)));
default:
return(0.0);
}
}
/// <summary>
/// Constructor that takes all parameters used for calculatin option value using binomial tree
/// </summary>
/// <param name="assetPriceParam"></param>
/// <param name="strikeParam"></param>
/// <param name="timeStepParam"></param>
/// <param name="volatilityParam"></param>
/// <param name="riskFreeRateParam"></param>
/// <param name="putCallParam"></param>
/// <param name="optionStyleParam"></param>
/// <param name="stepsParam"></param>
public BinomialTree(
double assetPriceParam,
double strikeParam,
double timeStepParam,
double volatilityParam,
double riskFreeRateParam,
EPutCall putCallParam,
int stepsParam)
{
assetPrice = assetPriceParam;
strike = strikeParam;
volatility = volatilityParam;
timeStep = timeStepParam;
riskFreeRate = riskFreeRateParam;
putCall = putCallParam;
steps = stepsParam;
}
public double GetDelta(double S, double X, double q, double r,
double sigma, double t, EPutCall PutCall)
{
double t_sqrt = Math.Sqrt(t);
double sigma2 = sigma * sigma;
double d1 = (Math.Log(S / X) + (r - q + sigma2 * 0.5) * t) / (t_sqrt * sigma);
switch (PutCall)
{
case EPutCall.Call:
return(Math.Exp(-q * t) * N(d1));
case EPutCall.Put:
return(-Math.Exp(-q * t) * N(-d1));
default:
return(0.0);
}
}
public double GetOptionValue(double S, double X, double q, double r,
double sigma, double t, EPutCall PutCall)
{
double t_sqrt = Math.Sqrt(t);
double sigma2 = sigma * sigma;
double d1 = (Math.Log(S / X) + (r - q + sigma2 * 0.5) * t) / (t_sqrt * sigma);
double d2 = d1 - t_sqrt * sigma;
switch (PutCall)
{
case EPutCall.Call:
return(S * Math.Exp(-q * t) * N(d1) - X * Math.Exp(-r * t) * N(d2));
case EPutCall.Put:
return(-S *Math.Exp(-q *t) * N(-d1) + X * Math.Exp(-r * t) * N(-d2));
default:
return(0.0);
}
}
public double GetImpliedVol(double S, double X, double q, double r, double optionPrice,
double t, EPutCall PutCall, double accuracy, int maxIterations)
{
if (optionPrice < 0.99 * (S - X * Math.Exp(-r * t)))
{
return(0.0);
}
double t_sqrt = Math.Sqrt(t);
double sigma = optionPrice / S / 0.398 / t_sqrt;
for (int i = 0; i < maxIterations; i++)
{
double price = GetOptionValue(S, X, q, r, sigma, t, PutCall);
double diff = optionPrice - price;
if (Math.Abs(diff) < accuracy)
{
return(sigma);
}
double vega = GetVega(S, X, q, r, sigma, t, PutCall);
sigma = sigma + diff / vega;
}
return(sigma);
}
public static double MC(double S, double X, double t, double s, double r, EPutCall PutCall, int n)
{
double num1 = (r - 0.5 * s * s) * t;
double num2 = s * Math.Sqrt(t);
double num3 = 0.0;
for (int index = 0; index < n; ++index)
num3 += FinMath.Payoff(S * Math.Exp(num1 + num2 * Random.Gaus()), X, PutCall);
return FinMath.PV4(num3 / (double)n, r, t);
}
public static double Parity(double P, double S, double X, double t, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return P - (S - X * Math.Exp(-r * t));
case EPutCall.Put:
return P + (S - X * Math.Exp(-r * t));
default:
return 0.0;
}
}
public static double BM(double S, double X, double t, double s, double r, EPutCall PutCall, int n)
{
double F = 0.0;
double x1 = FinMath.u(t, s, n);
double x2 = FinMath.d(t, s, n);
double p = FinMath.p(t, s, n, r);
for (int m = 0; m <= n; ++m)
F += FinMath.Binom(m, n, p) * FinMath.Payoff(S * Math.Pow(x1, (double)m) * Math.Pow(x2, (double)(n - m)), X, PutCall);
return FinMath.PV4(F, r, t);
}
public static double BM(double S, double X, double t, double s, double r, EPutCall PutCall)
{
return(BM(S, X, t, s, r, PutCall, 100));
}
public static double Payoff(double S, double X, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return FinMath.Call(S, X);
case EPutCall.Put:
return FinMath.Put(S, X);
default:
return 0.0;
}
}
public static double Payoff(double s, double x, EPutCall putcall)
{
switch (putcall)
{
case EPutCall.Call:
return Call(s, x);
case EPutCall.Put:
return Put(s, x);
default:
return 0.0;
}
}
public static double Theta(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return -S * n(d1(S, X, t, s, r)) * s / (2.0 * Sqrt(t)) - r * X * Exp(-r * t) * N(d2(S, X, t, s, r));
case EPutCall.Put:
return -S * n(d1(S, X, t, s, r)) * s / (2.0 * Sqrt(t)) + r * X * Exp(-r * t) * N(-d2(S, X, t, s, r));
default:
return 0.0;
}
}
public static double BS(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return S * N(d1(S, X, t, s, r)) - X * Exp(-r * t) * N(d2(S, X, t, s, r));
case EPutCall.Put:
return -S * N(-d1(S, X, t, s, r)) + X * Exp(-r * t) * N(-d2(S, X, t, s, r));
default:
return 0.0;
}
}
public static double Parity(double P, double S, double X, double t, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return(P - (S - X * Math.Exp(-r * t)));
case EPutCall.Put:
return(P + (S - X * Math.Exp(-r * t)));
default:
return(0.0);
}
}
public static double Theta(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return -S * FinMath.n(FinMath.d1(S, X, t, s, r)) * s / (2.0 * Math.Sqrt(t)) - r * X * Math.Exp(-r * t) * FinMath.N(FinMath.d2(S, X, t, s, r));
case EPutCall.Put:
return -S * FinMath.n(FinMath.d1(S, X, t, s, r)) * s / (2.0 * Math.Sqrt(t)) + r * X * Math.Exp(-r * t) * FinMath.N(-FinMath.d2(S, X, t, s, r));
default:
return 0.0;
}
}
public static double ImpliedVolatility(double S, double X, double t, double r, double P, EOptionType OptionType, EPutCall PutCall, EOptionPrice Method, int n, double Eps)
{
double num1 = 0.0;
double num2 = 10.0;
double num3 = 0.0;
double s = 0.0;
while (Math.Abs(num2 - num1) > Eps)
{
s = num1 + (num2 - num1) / 2.0;
switch (Method)
{
case EOptionPrice.BlackScholes:
num3 = FinMath.BS(S, X, t, s, r, PutCall);
break;
case EOptionPrice.Binomial:
num3 = FinMath.BM(S, X, t, s, r, PutCall, n);
break;
case EOptionPrice.MonteCarlo:
num3 = FinMath.MC(S, X, t, s, r, PutCall, n);
break;
}
if (num3 > P)
num2 = s;
else
num1 = s;
}
return s;
}
public static double MC(double S, double X, double t, double s, double r, EPutCall PutCall)
{
return FinMath.MC(S, X, t, s, r, PutCall, 100000);
}
public static double BM(double S, double X, double t, double s, double r, EPutCall PutCall, int n)
{
double F = 0.0;
double x1 = u(t, s, n);
double x2 = d(t, s, n);
double p = FinMath.p(t, s, n, r);
for (int m = 0; m <= n; ++m)
F += Binom(m, n, p) * Payoff(S * Pow(x1, m) * Pow(x2, n - m), X, PutCall);
return PV4(F, r, t);
}
public static double Parity(double p, double s, double x, double t, double r, EPutCall putcall)
{
switch (putcall)
{
case EPutCall.Call:
return(p - (s - x * Exp(-r * t)));
case EPutCall.Put:
return(p + (s - x * Exp(-r * t)));
default:
return(0.0);
}
}
public static double MC(double S, double X, double t, double s, double r, EPutCall PutCall)
{
return(FinMath.MC(S, X, t, s, r, PutCall, 100000));
}
public static double Parity(double p, double s, double x, double t, double r, EPutCall putcall)
{
switch (putcall)
{
case EPutCall.Call:
return p - (s - x * Exp(-r * t));
case EPutCall.Put:
return p + (s - x * Exp(-r * t));
default:
return 0.0;
}
}
public static double Delta(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return FinMath.N(FinMath.d1(S, X, t, s, r));
case EPutCall.Put:
return FinMath.N(FinMath.d1(S, X, t, s, r)) - 1.0;
default:
return 0.0;
}
}
public static double ImpliedVolatility(double S, double X, double t, double r, double P, EOptionType OptionType, EPutCall PutCall, EOptionPrice Method, int n, double Eps)
{
double num1 = 0.0;
double num2 = 10.0;
double num3 = 0.0;
double s = 0.0;
while (Math.Abs(num2 - num1) > Eps)
{
s = num1 + (num2 - num1) / 2.0;
switch (Method)
{
case EOptionPrice.BlackScholes:
num3 = FinMath.BS(S, X, t, s, r, PutCall);
break;
case EOptionPrice.Binomial:
num3 = FinMath.BM(S, X, t, s, r, PutCall, n);
break;
case EOptionPrice.MonteCarlo:
num3 = FinMath.MC(S, X, t, s, r, PutCall, n);
break;
}
if (num3 > P)
{
num2 = s;
}
else
{
num1 = s;
}
}
return(s);
}
public static double Rho(double S, double X, double t, double s, double r, EPutCall PutCall)
{
switch (PutCall)
{
case EPutCall.Call:
return X * t * Math.Exp(-r * t) * FinMath.N(FinMath.d2(S, X, t, s, r));
case EPutCall.Put:
return -X * t * Math.Exp(-r * t) * FinMath.N(-FinMath.d2(S, X, t, s, r));
default:
return 0.0;
}
}
public static double ImpliedVolatility(double S, double X, double t, double r, double P, EOptionType OptionType, EPutCall PutCall, EOptionPrice Method)
{
int n = 0;
switch (Method)
{
case EOptionPrice.Binomial:
n = 100;
break;
case EOptionPrice.MonteCarlo:
n = 100000;
break;
}
double Eps = 0.001;
return(FinMath.ImpliedVolatility(S, X, t, r, P, OptionType, PutCall, Method, n, Eps));
}
public static double ImpliedVolatility(double S, double X, double t, double r, double P, EOptionType OptionType, EPutCall PutCall, EOptionPrice Method)
{
int n = 0;
switch (Method)
{
case EOptionPrice.Binomial:
n = 100;
break;
case EOptionPrice.MonteCarlo:
n = 100000;
break;
}
double Eps = 0.001;
return FinMath.ImpliedVolatility(S, X, t, r, P, OptionType, PutCall, Method, n, Eps);
}
public static double BM(double S, double X, double t, double s, double r, EPutCall PutCall)
{
return BM(S, X, t, s, r, PutCall, 100);
}