# Using variance reduction on only some models

I am pricing options with some copula based models using Monte Carlo simulation. I was looking up some easily implementable variance reduction methods and decided on antithetic variates. However, antithetic variates can only be applied to symmetric copula families. My question is is it ok to use variance reduction methods on the symmetric copula models and not on the asymmetric copula models and compare the results? My intuition says yes, I'm not doing anything to change the expectation of the results. Thanks!

• You can always "compare results"! So maybe you can clarify your question. And why can you use antithetic variates only for symmetric copulas (which you define how exactly?) It seems to me symmetry is applied to margins in antithetic variates ($F^{-1}(u)$ vs $F^{-1}(1 - u)$). And if the variates are negatively correlated you will have variance reduction of the sample mean. – g g Apr 14 at 19:52
• Thanks for your response! By compare results, I just meant compare the price outputs. I guess it sounds sort of weird because the answer ended up being obvious haha. I just wanted to make sure there wasn't something I was missing. Also, antithetic variates can't be used for asymmetric copulas because the density at u is different from 1-u. – Jason Apr 14 at 21:10