public static double NumericalGreeks(OptionPriceDelegate price, enOptionGreeks greek, double underlying, double strike, double time, double rate, double dividend, double sigma)
{
const double dx = 1e-3; //shifts to compute numeric greeks
double value = Double.NaN;
double q = dividend;
double S = underlying;
double K = strike;
double t = time;
double r = rate;
double ds = System.Math.Max(dx, S * dx);
switch (greek)
{
case enOptionGreeks.Price:
value = price(S, K, time, r, q, sigma);
break;
case enOptionGreeks.Delta:
value = (price(S + ds, K, t, r, q, sigma) - price(S - ds, K, t, r, q, sigma)) / (2 * ds);
break;
case enOptionGreeks.Gamma:
value = (price(S + ds, K, t, r, q, sigma) + price(S - ds, K, t, r, q, sigma) - 2 * price(S, K, t, r, q, sigma)) / (ds * ds);
break;
case enOptionGreeks.Vega:
double sigma_up = sigma + dx;
double sigma_dn = System.Math.Max(1e-12, sigma - dx);
value = (price(S, K, t, r, q, sigma_up) - price(S, K, t, r, q, sigma_dn)) / (sigma_up - sigma_dn);
break;
case enOptionGreeks.Vomma:
value = (price(S, K, t, r, q, sigma + dx) + price(S, K, t, r, q, sigma - dx) - 2 * price(S, K, t, r, q, sigma)) / (dx * dx);;
break;
case enOptionGreeks.Rho:
value = (price(S, K, t, r + dx, q, sigma) - price(S, K, t, r - dx, q, sigma)) / (2 * dx);
break;
case enOptionGreeks.Theta:
double dt = System.Math.Min(dx, t);
value = (price(S, K, t - dt, r, q, sigma) - price(S, K, t, r, q, sigma)) / (dt);
break;
case enOptionGreeks.Vanna:
value = (price(S + dx, K, t, r, q, sigma + dx) - price(S + dx, K, t, r, q, sigma - dx) - price(S - dx, K, t, r, q, sigma + dx) + price(S - dx, K, t, r, q, sigma - dx)) / (4 * dx * dx);
break;
}
return(value);
}
public static double Greeks(enOptionGreeks greek, double spot, double strike, double time, double rate, double dividend, double sigma, bool isCall)
{
double value = Double.NaN;
//TODO: redo using reflection
switch (greek)
{
case enOptionGreeks.Price:
value = Price(spot, strike, time, rate, dividend, sigma, isCall);
break;
case enOptionGreeks.Delta:
value = Delta(spot, strike, time, rate, dividend, sigma, isCall);
break;
case enOptionGreeks.Gamma:
value = Gamma(spot, strike, time, rate, dividend, sigma);
break;
case enOptionGreeks.Vega:
value = Vega(spot, strike, time, rate, dividend, sigma);
break;
case enOptionGreeks.Vomma:
value = Vomma(spot, strike, time, rate, dividend, sigma);
break;
case enOptionGreeks.Vanna:
value = Vanna(spot, strike, time, rate, dividend, sigma);
break;
case enOptionGreeks.Rho:
value = Rho(spot, strike, time, rate, dividend, sigma, isCall);
break;
case enOptionGreeks.Theta:
value = Theta(spot, strike, time, rate, dividend, sigma, isCall);
break;
case enOptionGreeks.Charm:
value = Charm(spot, strike, time, rate, dividend, sigma, isCall);
break;
case enOptionGreeks.Epsilon:
value = Epsilon(spot, strike, time, rate, dividend, sigma, isCall);
break;
}
return(value);
}
public static double Greeks(enOptionGreeks greek, double spot, double strike, double time, double rate, double dividend, double sigma, bool isCall, int time_steps)
{
Binomial.OptionPayoff payoff;
if (isCall)
{
payoff = (price, K) => Max(0d, price - K);
}
else
{
payoff = (price, K) => Max(0d, K - price);
}
return(Binomial.Greeks(greek, spot, strike, time, rate, dividend, sigma, payoff, true, time_steps));
}
public static double Greeks(enOptionGreeks greek, double spot, double strike, double time, double rate, double dividend, double sigma, OptionPayoff payoff, bool isAmerican, int time_steps)
{
double value = Double.NaN;
if (greek == enOptionGreeks.Price)
{
value = Price(spot, strike, time, rate, dividend, sigma, payoff, isAmerican, time_steps);
}
else
{
Utils.OptionPriceDelegate price_function = delegate(double S, double K, double t, double r, double q, double v) {
return(Binomial.Price(S, K, t, r, q, v, payoff, isAmerican, time_steps));
};
value = Utils.NumericalGreeks(price_function, greek, spot, strike, time, rate, dividend, sigma);
}
return(value);
}
/// <summary>
/// Compute finite difference greeks
/// </summary>
/// <param name="greek"></param>
/// <param name="spot"></param>
/// <param name="strike"></param>
/// <param name="time"></param>
/// <param name="rate"></param>
/// <param name="dividend"></param>
/// <param name="sigma"></param>
/// <param name="isCall"></param>
/// <returns></returns>
public static double Greeks(enOptionGreeks greek, double spot, double strike, double time, double rate, double dividend, double sigma, bool isCall)
{
double value = Double.NaN;
if (greek == enOptionGreeks.Price)
{
value = Price(spot, strike, time, rate, dividend, sigma, isCall);
}
else
{
Utils.OptionPriceDelegate price_function = delegate(double S, double K, double t, double r, double q, double v) {
return(BjerksundStensland.Price(S, K, t, r, q, v, isCall));
};
value = Utils.NumericalGreeks(price_function, greek, spot, strike, time, rate, dividend, sigma);
}
return(value);
}
public static double Greeks(enOptionGreeks greek, double forward, double strike, double time, double rate, double sigma, bool isCall)
{
double value = Double.NaN;
//TODO: redo using reflection
switch (greek)
{
case enOptionGreeks.Price:
value = Price(forward, strike, time, rate, sigma, isCall);
break;
case enOptionGreeks.Delta:
value = Delta(forward, strike, time, rate, sigma, isCall);
break;
case enOptionGreeks.Gamma:
value = Gamma(forward, strike, time, rate, sigma);
break;
case enOptionGreeks.Vega:
value = Vega(forward, strike, time, rate, sigma);
break;
case enOptionGreeks.Vomma:
value = Vomma(forward, strike, time, rate, sigma);
break;
case enOptionGreeks.Vanna:
value = Vanna(forward, strike, time, rate, sigma);
break;
case enOptionGreeks.Rho:
value = Rho(forward, strike, time, rate, sigma, isCall);
break;
case enOptionGreeks.Theta:
value = Theta(forward, strike, time, rate, sigma, isCall);
break;
}
return(value);
}
