FinMath.ImpliedVolatility (Double, Double, Double, Double, Double, EOptionType, EPutCall, EOptionPrice, Int32, Double) Method
Parameters
- S
- double
spot price of underlying asset
- X
- double
option exercise (strike) price
- t
- double
time till exercise (fraction of year, f.ex. 0.5 for six months)
- r
- double
risk-free interst rate (continuous, decimal, f.ex. 0.1 for 10%)
- P
- double
option price (premium)
- OptionType
- EOptionType
Option type
- PutCall
- EPutCall
Put or call
- Method
- EOptionPrice
- n
- int
number of binomial periods or number of Monte Carlo price trajectories
- Eps
- double
error tolerance
Return Value
double
Bisectional
double S = 35.0; // spot price
double X = 35.0; // strike price
double t = 1.0; // time to expiration (one year)
double s = 0.2; // volatility (annualized standard deviation of asset log returns) (20%)
double r = 0.1; // risk-free interest rate (10%)
double P = TFinMath.BS(S,X,t,s,r, EOptionType.kCall);
double BSV = TFinMath.ImpliedVolatility(S,X,t,r,P,EOptionType.kCall,EOptionPrice.kBlackScholes);
double BMV = TFinMath.ImpliedVolatility(S,X,t,r,P,EOptionType.kCall,EOptionPrice.kBinomial);
double MCV = TFinMath.ImpliedVolatility(S,X,t,r,P,EOptionType.kCall,EOptionPrice.kMonteCarlo);
Console.WriteLine();
Console.WriteLine("Spot price = {0:F2}", S);
Console.WriteLine("Strike price = {0:F2}", X);
Console.WriteLine("Time to expiration = {0:F2}", t);
Console.WriteLine("Volatility = {0:F2}", s);
Console.WriteLine("Interest rate = {0:F2}", r);
Console.WriteLine();
Console.WriteLine("Implied BS = {0:F2}", BSV);
Console.WriteLine("Implied BM = {0:F2}", BMV);
Console.WriteLine("Implied MC = {0:F2}", MCV);
Console.WriteLine();
Console.WriteLine("Black-Scholes = {0:F2}", P);
Console.WriteLine("Binomial = {0:F2}", TFinMath.BM(S,X,t,s,r,EOptionType.kCall,100));
Console.WriteLine("Monte Carlo = {0:F2}", TFinMath.MC(S,X,t,s,r,EOptionType.kCall));
Console.WriteLine();
Console.WriteLine("Delta = {0:F2}", TFinMath.Delta(S,X,t,s,r,EOptionType.kCall));
Console.WriteLine("Gamma = {0:F2}", TFinMath.Gamma(S,X,t,s,r));
Console.WriteLine("Theta = {0:F2}", TFinMath.Theta(S,X,t,s,r,EOptionType.kCall));
Console.WriteLine("Vega = {0:F2}", TFinMath.Vega (S,X,t,s,r));
Console.WriteLine("Rho = {0:F2}", TFinMath.Rho (S,X,t,s,r,EOptionType.kCall));