What is stratified sampling and when should I use it in option pricing?

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AcadiFi · Accepted Answer

Stratified sampling divides the sampling space into strata and allocates samples proportionally or optimally across them, ensuring tail regions get representation. Instead of drawing N uniform U(0,1) values and inverting to get Z, you divide [0,1] into K equal strata, draw N/K from each stratum (typically at deterministic midpoints plus noise), and invert. This eliminates clustering and empty regions that hurt raw Monte Carlo. For a deep out-of-the-money call on Greenhaven Pharma strike $145 when spot is $120 (15% OTM), raw MC might have few paths reaching in-the-money. Stratified sampling forces uniform coverage across quantiles, including the right tail where payoff happens. Variance reduction: 50-95% depending on payoff shape. Latin Hypercube Sampling extends stratification to multiple dimensions by stratifying each dimension independently and randomly permuting across strata. Useful for basket options with 10+ underlyings where full grid stratification is infeasible. Stratification combines well with antithetic and control variates for compounding variance reduction. ```mermaid graph LR A[Raw MC
clustered] --> B[Stratified
uniform coverage] B --> C[Invert to Z] C --> D[Better tail
sampling] ```

What is stratified sampling and when should I use it in option pricing?

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