What problem does it solve? Crude Monte Carlo simulation is too slow and imprecise for rare-event estimation and tail-risk contracts, often requiring millions of samples to produce usable confidence intervals. This Skill applies variance reduction techniques that achieve 100-10,000x efficiency gains over naive sampling. ## Core Features & Use Cases - Importance Sampling for Rare Events: Tilts the sampling distribution to oversample extreme outcomes (e.g., market crashes), then corrects with likelihood ratios for unbiased estimates. - Antithetic Variates: Pairs each random draw Z with -Z to exploit symmetry in monotone payoffs, cutting variance at zero computational cost. - Stratified Sampling: Partitions the probability space into strata and samples within each for uniform coverage of the outcome distribution. - Control Variates: Uses closed-form Black-Scholes digital prices to correct stochastic volatility simulation estimates. - Use Case: Pricing a binary contract on a 20% S&P drop in one week where crude Monte Carlo at 100K samples yields zero hits; importance sampling produces a stable estimate with measurable standard error. ## Quick Start Ask the agent to estimate the probability of a 20% market crash in one week using importance sampling with 100,000 paths and compare it against crude Monte Carlo.
