static void Main(string[] args)
{
// Reproduces Table 2 in Medvedev and Scaillet (2010) for American puts
// under the Black Scholes model
// Option settings
double S = 40.0;
double r = 0.0488;
double q = 0.00;
// Medvedev-Scaillet put option settings
MSset mssettings = new MSset();
mssettings.r = r;
mssettings.q = q;
// Trinomial tree settings
int N = 500;
string PutCall = "P";
string EuroAmer = "A";
// Table 2 settings
double[] sigma = new double[9] {
0.2, 0.2, 0.2, 0.3, 0.3, 0.3, 0.4, 0.4, 0.4
};
double[] T = new double[9] {
1.0 / 12.0, 1.0 / 3.0, 7.0 / 12.0, 1.0 / 12.0, 1.0 / 3.0, 7.0 / 12.0, 1.0 / 12.0, 1.0 / 3.0, 7.0 / 12.0
};
double[,] BSPut = new double[3, 9]; // Black-Scholes
double[,] MSPut = new double[3, 9]; // Medvedev-Scaillet
double[,] BTPut = new double[3, 9]; // Trinomial tree
double SumError = 0.0;
// Settings for the Bisection Method
int MaxIter = 20000;
double tol = 1e-20;
double dt = 1e-10;
double b = 3.0;
// Find the tree and M-S prices
BlackScholesPrice BS = new BlackScholesPrice();
MSPrice MS = new MSPrice();
TrinomialPrice TP = new TrinomialPrice();
double[] K = new double[3] {
35.0, 40.0, 45.0
};
for (int k = 0; k <= 2; k++)
{
for (int i = 0; i <= 8; i++)
{
// Black Scholes European put
BSPut[k, i] = BS.BlackScholes(S, K[k], T[i], r, q, sigma[i], "P");
// Medvedev Scaillet American Put
MSPut[k, i] = MS.MSPriceBS(S, K[k], T[i], sigma[i], r, q, MaxIter, tol, b, dt);
// Trinomial Tree American put
BTPut[k, i] = TP.TrinomialTree(S, K[k], r, q, T[i], sigma[i], N, PutCall, EuroAmer);
SumError += Math.Abs(MSPut[k, i] - BTPut[k, i]);
}
}
// Output the results for K = 35, 40, 45
Console.WriteLine(" ");
Console.WriteLine(" Table 2 of Medvedev and Scaillet (2010)");
Console.WriteLine("----------------------------------------------------------------------------");
Console.WriteLine(" sigma = 0.2 sigma = 0.3 sigma = 0.4");
Console.WriteLine(" --------------------- --------------------- ---------------------");
Console.WriteLine("K = 35 T=1/12 T=1/3 T=7/12 T=1/12 T=1/3 T=7/12 T=1/12 T=1/3 T=7/12 ");
Console.WriteLine("----------------------------------------------------------------------------");
for (int k = 0; k <= 2; k++)
{
Console.WriteLine("EuroPut {0,6:F3} {1,6:F3} {2,6:F3} {3,8:F3} {4,6:F3} {5,6:F3} {6,8:F3} {7,6:F3} {8,7:F3}",
BSPut[k, 0], BSPut[k, 1], BSPut[k, 2], BSPut[k, 3], BSPut[k, 4], BSPut[k, 5], BSPut[k, 6], BSPut[k, 7], BSPut[k, 8]);
Console.WriteLine("MSPut {0,6:F3} {1,6:F3} {2,6:F3} {3,8:F3} {4,6:F3} {5,6:F3} {6,8:F3} {7,6:F3} {8,7:F3}",
MSPut[k, 0], MSPut[k, 1], MSPut[k, 2], MSPut[k, 3], MSPut[k, 4], MSPut[k, 5], MSPut[k, 6], MSPut[k, 7], MSPut[k, 8]);
Console.WriteLine("TreePut {0,6:F3} {1,6:F3} {2,6:F3} {3,8:F3} {4,6:F3} {5,6:F3} {6,8:F3} {7,6:F3} {8,7:F3}",
BTPut[k, 0], BTPut[k, 1], BTPut[k, 2], BTPut[k, 3], BTPut[k, 4], BTPut[k, 5], BTPut[k, 6], BTPut[k, 7], BTPut[k, 8]);
Console.WriteLine("----------------------------------------------------------------------------");
}
Console.WriteLine("EuroPut = Black-Scholes closed form European put price");
Console.WriteLine("MSPut = Fifth-order MS (2001) American put expansion");
Console.WriteLine("TreePut = Trinomial tree American put with {0} steps", N);
Console.WriteLine("Sum of absolute errors {0,8:F5}", SumError);
Console.WriteLine("----------------------------------------------------------------------------");
Console.WriteLine(" ");
}
// Derivative of the MS approximation
public double MSPutBSdiff(double y, MSset mssettings, double dy)
{
MSPrice MS = new MSPrice();
return((MS.MSPutBS(y + dy, mssettings) - MS.MSPutBS(y - dy, mssettings)) / 2.0 / dy);
}