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Sep 7

Variance reduction by antithetic variable

Posted by abiao at 15:36 | Code » Matlab | Comments(0) | Reads(15338)
Had a small party with friends yesterday and drank until 5 o'clock in the morning, hangover is still here after 6 hours sleep. All feasts must come to an end, we have to accept this fact, going to leave soon the country i have stayed over one year, leave friends accompanying me when i was sad and joyful, specially a girl i favor.

Back to code, Whenever we price a derivative via Monte Carlo simulation, for instance use Gaussian variates to simulate Brownian motion by constructing sample paths of standard Wiener processes, we can make use of the fact that for any one drawn path its mirror image has equal probability. In other words, if a single evaluation driven by a Gaussian variate vector draw zi is given by vi = v(zi), we also use vvi = v(−zi), which is called antithetic sampling and widely used for variance reduction because of its simplicity to add to your code.

Run the sample code to check the variance reduction effect if you wish http://www.ma.ic.ac.uk/~becherer/Course07MS15/antitheticexample.m.

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