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Subsections

Hedge parameters



// file simulated_delta_call.cc
// author: Bernt A Oedegaard
// estimation of the partials when doing monte carlo

#include <cmath>     // standard mathematical functions
#include "random.h"   // definition of random number generator
#include <algorithm>   // define the max() function

double option_price_delta_call_european_simulated( double S, 
					   double X, 
					   double r,
					   double sigma, 
					   double time,
					   int no_sims)
   // estimate the price using two different S values
{
    double sigma_sqr = sigma * sigma;
    double R = (r - 0.5 * sigma_sqr)*time;
    double SD = sigma * sqrt(time);
    double sum_payoffs = 0.0;
    double sum_payoffs_2 = 0.0;
    double q = S*0.01; 
    for (int n=1; n<=no_sims; n++) {
	double Z = random_normal();

	double S_T  = S* exp(R + SD * Z);
	sum_payoffs += max(0.0, S_T-X);

	double S_T_2 = (S+q)* exp(R + SD * Z);
	sum_payoffs_2 += max(0.0, S_T_2-X);
    };
    double c = exp(-r*time) * ( sum_payoffs/no_sims); 
    double c2 = exp(-r*time) * ( sum_payoffs_2/no_sims); 
    return (c2-c)/q;
};


Further Reading

Boyle (1977)


next up previous contents index
Next: Approximations Up: Simulation Previous: Simulating the sample path.   Contents   Index
Bernt Arne Odegaard
1999-09-09