Comparing Option Pricing Models With Uneven Variance Reduction

Summary

The document asks whether Monte Carlo option-pricing results from different copula models can be compared when antithetic variates are used only for symmetric copula families. The concern is that the variance-reduction technique may not be applicable to asymmetric families, while still allowing the same expected value to be estimated.

The key distinction is between changing an estimator’s variance and changing its expectation. Antithetic variates pair simulations designed to reduce sampling noise; when correctly applied, they should preserve the target expectation. Thus, applying the method to only some models need not bias the comparison, but estimates will have different precision. A fair comparison should account for that uncertainty, for example by reporting standard errors or confidence intervals. The document poses the question but provides no answer, experiment, or details about the copulas and payoff, so whether the method is valid for a particular implementation remains unverified.

Key ideas

• Antithetic variates are described as applicable only to symmetric copula families in the stated setup.
• A variance-reduction method can change sampling precision without changing the target expectation when correctly implemented.
• Using variance reduction for only some models may leave point estimates comparable while their uncertainty differs.
• Model comparisons should account for different estimator precision.
• The document offers no tested result or implementation details to establish validity for a specific pricing setup.

Tags

# Using variance reduction on only some models


# 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!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.