public double IV(OptionContractType optionType, double S, double K, double T, double r, double q, double optionMarketPrice)
{
Func <double, double> f = sigma => Premium(optionType, S, K, T, sigma, r, q) - optionMarketPrice;
Func <double, double> df = sigma => Vega(S, K, T, sigma, r, q);
return(RobustNewtonRaphson.FindRoot(f, df, lowerBound: 0, upperBound: 100, accuracy: 0.001));
}
/// <summary>
/// Computes theta.
/// </summary>
/// <param name="optionType">call or put</param>
/// <param name="S">Underlying price</param>
/// <param name="K">Strike price</param>
/// <param name="T">Time to expiration in % of year</param>
/// <param name="sigma">Volatility</param>
/// <param name="r">continuously compounded risk-free interest rate</param>
/// <param name="q">continuously compounded dividend yield</param>
/// <returns></returns>
public double Theta(OptionContractType optionType, double S, double K, double T, double sigma, double r, double q)
{
double d1 = D1(S, K, T, sigma, r, q);
double d2 = D2(T, sigma, d1);
switch (optionType)
{
case OptionContractType.Call:
{
double theta = -Math.Exp(-q * T) * (S * Normal.PDF(0, 1, d1) * sigma) / (2.0 * Math.Sqrt(T))
- (r * K * Math.Exp(-r * T) * Normal.CDF(0, 1, d2))
+ q * S * Math.Exp(-q * T) * Normal.CDF(0, 1, d1);
return(theta / 365);
}
case OptionContractType.Put:
{
double theta = -Math.Exp(-q * T) * (S * Normal.PDF(0, 1, d1) * sigma) / (2.0 * Math.Sqrt(T))
+ (r * K * Math.Exp(-r * T) * Normal.PDF(0, 1, -d2))
- q * S * Math.Exp(-q * T) * Normal.CDF(0, 1, -d1);
return(theta / 365);
}
default:
throw new NotSupportedException();
}
}
/// <summary>
/// Computes delta.
/// </summary>
/// <param name="optionType">call or put</param>
/// <param name="S">Underlying price</param>
/// <param name="K">Strike price</param>
/// <param name="T">Time to expiration in % of year</param>
/// <param name="sigma">Volatility</param>
/// <param name="r">continuously compounded risk-free interest rate</param>
/// <param name="q">continuously compounded dividend yield</param>
/// <returns></returns>
public double Delta(OptionContractType optionType, double S, double K, double T, double sigma, double r, double q)
{
double d1 = D1(S, K, T, sigma, r, q);
switch (optionType)
{
case OptionContractType.Call:
return(Math.Exp(-r * T) * Normal.CDF(0, 1, d1));
case OptionContractType.Put:
return(-Math.Exp(-r * T) * Normal.CDF(0, 1, -d1));
default:
throw new NotSupportedException();
}
}
/// <summary>
/// Computes theoretical price.
/// </summary>
/// <param name="optionType">call or put</param>
/// <param name="S">Underlying price</param>
/// <param name="K">Strike price</param>
/// <param name="T">Time to expiration in % of year</param>
/// <param name="sigma">Volatility</param>
/// <param name="r">continuously compounded risk-free interest rate</param>
/// <param name="q">continuously compounded dividend yield</param>
/// <returns></returns>
public double Premium(OptionContractType optionType, double S, double K, double T, double sigma, double r, double q)
{
double d1 = D1(S, K, T, sigma, r, q);
double d2 = D2(T, sigma, d1);
switch (optionType)
{
case OptionContractType.Call:
return(S * Math.Exp(-q * T) * Normal.CDF(0, 1, d1) - K * Math.Exp(-r * T) * Normal.CDF(0, 1, d2));
case OptionContractType.Put:
return(K * Math.Exp(-r * T) * Normal.CDF(0, 1, -d2) - S * Math.Exp(-q * T) * Normal.CDF(0, 1, -d1));
default:
throw new NotSupportedException(" Option Type Error 1 " + optionType + "Type does not exist!");
}
}
