Variance Reduction Techniques in Simulation › Practical Considerations and Guidelines

Selecting and implementing variance reduction techniques requires balancing theoretical benefits against practical constraints. This section provides guidance for you.

The best variance reduction technique depends on the problem structure:

• Antithetic variates work best for monotonic payoff functions. They are simple to implement and add minimal computational overhead. Use them as a default first step.

• Control variates excel when you have access to related quantities with known expectations. The underlying asset price is a natural control for many options. More sophisticated controls (delta-based, basket components) provide larger reductions but require more computation.

• Stratified sampling is most effective for low-dimensional problems where the payoff varies significantly across the input space. LHS extends this to moderate dimensions.

A practical approach is to layer techniques:

1. Start with antithetic variates (easy, low overhead)
2. Add a simple control variate (underlying asset price)
3. Consider stratified sampling for path-independent options
4. For exotic options, explore delta-based or more sophisticated controls

Always estimate your variance reduction factor empirically. The theoretical formulas depend on correlations that may differ from expectations. Run a pilot study with a subset of simulations to estimate the improvement before committing to a full production run.