public double CalcAvgMonteCaroError(int nForAverage, int N)
{
double callOptionPriceBS = BlackScholesFormula.CalculateCallOptionPrice(sigma, S, K, r, T);
double avgErr = 0;
for (int i = 0; i < nForAverage; ++i)
{
BlackScholesMonteCarlo mc = new BlackScholesMonteCarlo(sigma, r, N);
double mcPrice = mc.CalculateEuropeanCallOptionPrice(S, K, T);
avgErr += Math.Abs(mcPrice - callOptionPriceBS);
}
return(avgErr / nForAverage);
}
public static double CalculateImpliedVolCall(double C, double S, double K, double r, double T, double x0 = 0.5, double maxErr = 1e-6, int N = 10000)
{
if (C <= 0 || T <= 0 || K <= 0 || S <= 0 || maxErr <= 0 || N <= 0)
{
throw new System.ArgumentException("Need C > 0, T > 0, K > 0, S > 0, maxErr > 0, N > 0.");
}
Func <double, double> F = (x) => {
return(C - BlackScholesFormula.CalculateCallOptionPrice(x, S, K, r, T));
};
NewtonSolver s = new NewtonSolver(maxErr, N);
return(s.Solve(F, null, x0));
}
static void TestImpliedVol(double sigma = 0.1, //volatilty
double S = 100, //underlying price
double K = 100, //strike price
double r = 0.05, //risk free rate
double T = 1) //time to maturity in years
{
double CallOptionPrice = BlackScholesFormula.CalculateCallOptionPrice(sigma, S, K, r, T);
double PutOptionPrice = BlackScholesFormula.CalculatePutOptionPrice(sigma, S, K, r, T);
System.Console.WriteLine("Price of a call option using Black Scholes formula is: {0}", BlackScholesFormula.CalculateCallOptionPrice(sigma, S, K, r, T));
System.Console.WriteLine("Price of a put option using Black Scholes formula is: {0}", BlackScholesFormula.CalculatePutOptionPrice(sigma, S, K, r, T));
System.Console.WriteLine("Implied volatiliy of a call option given the price from Black Scholes is: {0}", BlackScholesImpliedVolEuropean.CalculateImpliedVolCall(10, S, K, r, T));
System.Console.WriteLine("Implied volatiliy of a put option given the price from Black Scholes is: {0}", BlackScholesImpliedVolEuropean.CalculateImpliedVolPut(3, S, K, r, T));
}
public static double CalculateImpliedVolPut(double P, double S, double K, double r, double T, double x0 = 0.5, double maxErr = 1e-6, int N = 10000)
{
if (P <= 0 || T <= 0 || K <= 0 || S <= 0 || maxErr <= 0 || N <= 0)
{
throw new System.ArgumentException("Need P > 0, T > 0, K > 0, S > 0, maxErr > 0, N > 0.");
}
double callPrice = BlackScholesFormula.GetCallFromPutPrice(S, K, r, T, P);
if (callPrice < 0)
{
throw new System.ArgumentException("Input arguments violate put/call parity.");
}
return(CalculateImpliedVolCall(callPrice, S, K, r, T, x0, maxErr, N));
}
public static void Main(string[] args)
{
// Model params
double r = 0.05;
double sigma = 0.1;
double K = 100;
double T = 1;
double S0 = 100;
BlackScholesFormula bsFormula = new BlackScholesFormula(new BlackScholesModelParams(r, sigma));
double bsPrice = bsFormula.PutPrice(new EuropeanCallPutParams(T, S0, K));
Func <double, double> putPayoff = (S) => Math.Max(K - S, 0);
BlackScholesFiniteDifferenceSolver solverFD =
new BlackScholesFiniteDifferenceSolver(T, putPayoff, r, sigma, 3 * K, 10, 10);
double bsPriceFD = solverFD.Price(100);
uint N, M;
int numberRefinments = 5;
// test convergence w.r.t. number of partitions of space interval
N = 200; M = 100;
for (int refinementIndex = 0; refinementIndex < numberRefinments; ++refinementIndex, M *= 2)
{
BlackScholesFiniteDifferenceSolver solverForThisLevelOfRefinement =
new BlackScholesFiniteDifferenceSolver(T, putPayoff, r, sigma, 5 * K, N, M);
double error = Math.Abs(bsPrice - solverForThisLevelOfRefinement.Price(S0));
Console.WriteLine("Space partitions: {0}, time steps: {1}, error: {2}", M, N, error);
}
// test convergence w.r.t. number of time steps
N = 10; M = 8001;
for (int refinementIndex = 0; refinementIndex < numberRefinments; ++refinementIndex, N *= 2)
{
BlackScholesFiniteDifferenceSolver solverForThisLevelOfRefinement =
new BlackScholesFiniteDifferenceSolver(T, putPayoff, r, sigma, 5 * K, N, M);
double error = Math.Abs(bsPrice - solverForThisLevelOfRefinement.Price(S0));
Console.WriteLine("Space partitions: {0}, time steps: {1}, error: {2}", M, N, error);
}
Console.WriteLine("Finished. Press any key.");
//Console.ReadKey ();
}
public static object DupireSsviEuropeanVanillaOptionPrice([ExcelArgument(Description = "the current risky asset price")] double S0,
[ExcelArgument(Description = "constant continuously compounded rate of return")] double riskFreeRate,
[ExcelArgument(Description = "parameter in theta(t) := alpha^2(e^(beta^2 t) - 1)")] double alpha,
[ExcelArgument(Description = "parameter in theta(t) := alpha^2(e^(beta^2 t) - 1)")] double beta,
[ExcelArgument(Description = "SSVI parameter")] double gamma,
[ExcelArgument(Description = "SSVI parameter")] double eta,
[ExcelArgument(Description = "SSVI parameter")] double rho,
[ExcelArgument(Description = "option maturity (time to expiry)")] double maturity,
[ExcelArgument(Description = "option strike")] double strike,
[ExcelArgument(Description = "option type, 'C' for call 'P' for put")] string type)
{
try
{
Ssvi SsviSurface = new Ssvi(alpha, beta, gamma, eta, rho);
double k = Math.Log(strike * Math.Exp(-riskFreeRate * maturity) / S0);
double sigmaBs = Math.Sqrt(SsviSurface.OmegaSsvi(maturity, k) / maturity);
if (type == "Call" || type == "call" || type == "C" || type == "c")
{
return(BlackScholesFormula.CalculateCallOptionPrice(sigmaBs, S0, k, riskFreeRate, maturity));
}
else if (type == "Put" || type == "put" || type == "P" || type == "p")
{
return(BlackScholesFormula.CalculatePutOptionPrice(sigmaBs, S0, k, riskFreeRate, maturity));
}
else
{
throw new ArgumentException("Input must be either Call, call, C, c, Put, put, P or p.");
}
}
catch (Exception e)
{
XLInterfaceBase.AddErrorMessage("DupireSsviEuropeanVanillaOptionPrice error: " + e.Message);
}
return(FunctionError);
}