public static double CalculateImplVolatility(double S, double T, double K, double r,
double OptionPrice, bool CallOption, double x0)
//CallOption is set to 'true' if the given option price is a call option, and to 'false' if it is a put option
{
Func <double, double> CalculateOptionPrice; //Assign the function to a method for call/put price calculation
if (CallOption == true) //If the option price is that of a call option
{
CalculateOptionPrice
= (sigma) => BlackScholesFormula.CalculateCallOptionPrice(S, T, K, sigma, r) - OptionPrice;
}
else if (CallOption == false) //If the option price is that of a put option
{
CalculateOptionPrice
= (sigma) => BlackScholesFormula.CalculatePutOptionPrice(S, T, K, sigma, r) - OptionPrice;
}
else
{
throw new ArgumentOutOfRangeException("CallOption is TRUE if price is a call option price," +
"and FALSE if put option price");
}
//Find the roots of the function by passing it to the NewtonSolver
double maxError = 1e-5;
int maxIter = 10000;
double ImplVolatility = NewtonSolver.Solver(CalculateOptionPrice, null, x0, maxError, maxIter);
return(ImplVolatility);
}
public static void Main()
{
//Use the given parameter values to test the implemented classes
double S = 100;
double K = 100;
double[] T = { 1, 1, 1, 10, 1 };
double[] sigma = { 0.1, 0.1, 0.2, 0.1, 0.1 };
double[] r = { 0.05, 0, 0.05, 0.05, 0.05 };
Func <double, double> putPayoff = (S0) => Math.Max(K - S0, 0);
Func <double, double> callPayoff = (S0) => Math.Max(S0 - K, 0);
uint N = 200;
uint M = 100;
//For calculating the implied volatility
// double CallPrice = 10;
// double PutPrice = 3;
double call; //Exact call option price using the Black-Scholes formula
double put; //Exact put option price
// double MCcall; //Monte Carlo estimate of the call option
// double MCput; //MC estimate of the put option
double FDcall, FDput;
//Calculate the option prices both using the formula and the estimate for each set of parameters
for (int i = 0; i < 5; i++)
{
// call = BlackScholesFormula.CalculateCallOptionPrice (S, T[i], K, sigma[i], r[i]);
put = BlackScholesFormula.CalculatePutOptionPrice(S, T[i], K, sigma[i], r[i]);
// BSFiniteDifferenceSolver CallSolver = new BSFiniteDifferenceSolver(T[i],callPayoff,r[i],sigma[i],5*K,N,M);
BSFiniteDifferenceSolver PutSolver = new BSFiniteDifferenceSolver(T[i], putPayoff, r[i], sigma[i], 5 * K, N, M);
// FDcall = CallSolver.Price(S);
FDput = PutSolver.Price(S);
// MCcall = BSMonteCarlo.CalculateCallOptionPrice (S, T[i], K[i], sigma[i], r[i]);
// MCput = BSMonteCarlo.CalculatePutOptionPrice (S, T[i], K[i], sigma[i], r[i]);
Console.Write("Put: {0} FD Estimate: {1}\n", put, FDput);
}
//Now compute the implied volatilities for given call and put prices
// double Volatility1 = BSImpliedVolatility.CalculateImplVolatility (S, T[0], K[0], r[0], CallPrice, true, 0.5);
// double Volatility2 = BSImpliedVolatility.CalculateImplVolatility (S, T[0], K[0], r[0], PutPrice, false, 0.5);
// Console.Write ("Implied volatility: {0}\nImplied volatility: {1}\n", Volatility1, Volatility2);
Console.ReadKey();
}
public static void Main()
{
// Use the given parameter values to test the implemented class
double r = 0.05;
double sigma = 0.1;
double K = 100;
double T = 1;
double S0 = 100;
double error;
Func <double, double> putPayoff = (S) => Math.Max(K - S, 0); // = g(x), the payoff function
uint N = 200; // Number of timesteps
uint M = 100; // Number of space partitions
int numberCalculations = 1;
// Get the exact value using the Black-Scholes formula
double putPrice = BlackScholesFormula.CalculatePutOptionPrice(S0, T, K, sigma, r);
// Use finite difference estimation to approximate the option price and compare it to the exact value
/*
* for (int i = 0; i < numberCalculations; i++, M*=2)
* {
* BSFiniteDifferenceSolver solver =
* new BSFiniteDifferenceSolver (T, putPayoff, r, sigma, 5*K, N, M);
*
* error = Math.Abs (putPrice - solver.Price (S0));
* Console.WriteLine ("Space partitions: {0}, time steps: {1}, error: {2}", M, N, error);
* }
* Console.WriteLine();
*/
N = 10;
M = 1600;
for (int i = 0; i < numberCalculations; i++, N *= 2)
{
BSFiniteDifferenceSolver solver =
new BSFiniteDifferenceSolver(T, putPayoff, r, sigma, 5 * K, N, M);
error = Math.Abs(putPrice - solver.Price(S0));
Console.WriteLine("Space partitions: {0}, time steps: {1}, error: {2}", M, N, error);
}
Console.ReadKey();
}