public double K; // strike
public EuropeanOptionParams(OptionPayoff type, double t, double k)
{
if (type != OptionPayoff.Call && type != OptionPayoff.Put)
{
throw new InvalidOperationException("Invalid type for European option");
}
Type = type;
T = t;
K = k;
}
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>
///
/// </summary>
/// <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 Price(double spot, double strike, double time, double rate, double dividend, double sigma, OptionPayoff payoff, bool isAmerican = true, int time_steps = 1024)
{
double r = rate;
double q = dividend;
double S = spot;
double K = strike;
int n = time_steps; //number of time steps
double dt = time / n;
double df = Exp(-r * dt);
double up = Exp(sigma * Sqrt(dt));
double up2 = up * up; //up/dn ratio
double dn = 1d / up;
double p_up = df * (up * Exp((r - q) * dt) - 1d) / (up2 - 1d);
//double p_up = (up * Exp(- q* dt) - df) / (up2 - 1d);
double p_dn = df - p_up;
if (p_up < 0 || p_dn < 0)
{
//number of steps needs to be increased to keep dt below the following threshold,
//we are not going to do this inside the function - since it is computationaly costly,
//dt < sigma^2 /(r - q)^2
return(Double.NaN);
}
double[] v = new double[n + 1]; //option values
double[] p = new double[n + 1]; //underlying asset prices
p[0] = S * Pow(up, -n);
for (int i = 1; i <= n; i++)
{
p[i] = up2 * p[i - 1]; //compute terminal distribution of prices, (there might be some error accumulation)
}
// options values at expiration
for (int i = 0; i <= n; i++)
{
v[i] = payoff(p[i], K);
}
for (int j = n - 1; j >= 0; j--)
{
for (int i = 0; i <= j; i++)
{
v[i] = p_up * v[i + 1] + p_dn * v[i];
p[i] = dn * p[i + 1];
if (isAmerican)
{
v[i] = Max(v[i], payoff(p[i], K));
}
}
}
return(v[0]);
}
