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Haug_example_p270.cpp
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Haug_example_p270.cpp
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// Haug_example_p270.cpp : Defines the entry point for the console application.
//
#include "stdafx.h"
#include <vector>
#include "SABRvol.h"
#include "findAlpha.h"
#include "oFmt.h"
#include "alphaSABR.h"
#include "Black76.h"
double** createMatrix(unsigned int rows, unsigned int cols) {
double ** matrix;
matrix = (double **)calloc(cols, sizeof(double *));
for (unsigned int i = 0; i < cols; i++)
matrix[i] = (double *)calloc(cols, sizeof(double));
return matrix;
}
int main()
{
// Example from page 270 of Espen Haug's (aka The Collector) excellent book
// By Fabrice Douglas Rouah ( for matlab )
// Converted to C/C++ by Nicholas Ferguson
// Added Black-76 put, call and put call parity.
// Required inputs
double F = 100; // Futures price
double T = 0.5; // Maturity in years
double b = 0.999; // beta SABR parameter
double v = 0.5; // vol - of - vol SABR parameter
double ATMvol = 0.30; // Market ATM volatility
double r = .02; // for Black 76 only.
// Define the strikes and correlation levels
std::vector<double> K = { 70, 80, 90, 100, 110, 120, 130 };
// Correlation levels are simply incremented by .25 about a mean of zero?
std::vector<double> rho = { -0.75, -0.50 ,-0.25, 0.00, 0.25, 0.50, 0.75 };
// Find the length of each vector
int I = rho.size();
int J = K.size();
// data structures.
double** Vol = createMatrix(I, J);
double** alpha = createMatrix(I, J);
double** blackP = createMatrix(I, J);
double** blackC = createMatrix(I, J);
double** parity = createMatrix(I, J);
// Find the SABR volatilities for each strike / correlation combination
// SABRVolatility is from VB code from Haug's book
// SABRVol is from matlab code from Fabrice Douglas Rouah website.
// We can run either and get same result.
for (int i = 0; i < I; ++i){
for (int j = 0; j < J; ++j){
alpha[i][j] = findAlpha(F, K[j], T, ATMvol, b, rho[i], v);
//Vol[i][j] = SABRVolatility(F, K[j], T, alpha[i][j], b, v, rho[i]);
Vol[i][j] = SABRvol(alpha[i][j], b, rho[i], v, F, K[j], T);
blackP[i][j] = Black76(F, K[j], T, Vol[i][j], r, "Put");
blackC[i][j] = Black76(F, K[j], T, Vol[i][j], r, "Call");
parity[i][j] = diffInPutCallParity(blackC[i][j], blackP[i][j], F, K[j], r, T);
Vol[i][j] *= 100; // to make ouput %. This format agrees with Haug's example.
}}
std::cout << "SABR Black-76 Equivalent Volatilies (%)" << std::endl << std::endl;
print_2Dmatrix2(Vol,K, rho);
std::cout << std::endl;
std::cout << "Alpha Parameter Values" << std::endl << std::endl;
print_2Dmatrix2(alpha, K, rho);
std::cout << std::endl;
std::cout << "Black-76 Put Prices r:" << r << std::endl << std::endl;
print_2Dmatrix2(blackP, K, rho);
std::cout << std::endl;
std::cout << "Black-76 Call Prices r:" << r << std::endl << std::endl;
print_2Dmatrix2(blackC, K, rho);
std::cout << std::endl;
std::cout << "diff in Black-76 Put Call Parity Eqn: (C-P) - (F-K)exp(-rT) r:" << r << " F: " << F << " T:" << T << std::endl << std::endl;
print_2Dmatrix2(parity, K, rho);
return 0;
}