# Antithetic Variable Technique in Matlab

Matlab → Simulations → Monte Carlo → Antithetic Variable Technique

In antithetic variable technique for variance reduction, the stock price path is constructed in the usual manner with positive $\varepsilon$ and payoff is calculated. Then another path with negative $\varepsilon$, that is $-\varepsilon$, is constructed, and payoff is calculated again. Finally, average of these two payoffs is calculated, that is

$f=\frac{f_1+f_2}{2}$

The following Matlab code calculates European-style standard call option price using antithetic variable technique for variance reduction in the Monte Carlo simulation method.

Monte Carlo using antithetic variable technique in Matlab
function call=AntitheticTechnique(s0,k,r,v,t,n) st1=s0*exp((r-1/2*v^2)*t+v*randn(n,1)*sqrt(t)); st2=s0*exp((r-1/2*v^2)*t+v*(-randn(n,1))*sqrt(t)); payoff1=max(st1-k,0); payoff2=max(st2-k,0); payoff=0.5*(payoff1+payoff2); call=exp(-r*t)*mean(payoff) stderr=std(payoff)/sqrt(n) CI=[call-1.96*stderr,call+1.96*stderr]

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