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!