Variance Reduction Techniques in Simulation › Limitations and Impact

Variance reduction techniques have transformed Monte Carlo simulation from a computationally expensive necessity into a practical tool for real-time pricing and risk management. However, these methods come with important limitations that you must understand.

The effectiveness of variance reduction varies dramatically with the problem structure. Antithetic variates provide consistent but moderate improvement for most options, but their benefit disappears for symmetric payoffs like straddles. Control variates can achieve spectacular variance reduction when strong controls exist, but finding good controls for exotic path-dependent derivatives requires insight into the problem structure; there is no automatic procedure that works universally. The delta-based control we implemented requires computing option deltas at each time step, which adds substantial computational cost and may not be worthwhile for simple European options where other methods suffice.

Stratified sampling faces the curse of dimensionality. For a single-asset European option, stratifying the terminal random variable works beautifully. But for a path-dependent option with 252 daily time steps, the effective dimension is far higher, and naive stratification becomes impractical. title="Latin Hypercube Sampling" helps but provides diminishing returns as dimension increases. For very high-dimensional problems, quasi-random sequences (which we'll explore in later chapters) may be more effective.

Another limitation is that combining techniques doesn't always multiply their benefits. The correlation structure that makes antithetic variates effective may already capture some of the information that a control variate would use, leading to overlap in variance reduction. The combined method is almost always better than either alone, but rarely twice as good.

Despite these limitations, variance reduction can make otherwise impractical calculations feasible. Real-time risk calculations become possible when variance reduction cuts required simulations by a factor of 100. Model calibration, which requires many option evaluations, becomes tractable. The techniques have enabled the pricing and risk management of exotic derivatives that would otherwise be computationally intractable.

Looking ahead, the finite difference methods covered in the next chapter provide an alternative approach for lower-dimensional problems, while exotic option pricing will require careful selection of variance reduction strategies tailored to specific payoff structures.