Adaptive Multilevel Splitting: First Application to Rare Event Derivative Pricing

Battle Count: 88

Primarily relevant to derivatives pricing desks, structured products, and insurance-linked securities rather than high-frequency trading. Directly applicable to pricing deep OTM binaries, barrier options, and parametric insurance products. The 200x speedup in rare event regimes makes previously intractable pricing feasible, enabling tighter spreads and better market-making for illiquid derivatives. Less relevant for standard liquid option pricing where closed-form or standard MC suffices.

The AMS algorithm itself is conceptually straightforward (sort, kill, clone, resimulate, update weight). However, correct implementation requires careful handling of: (1) first crossing times for cloning, (2) randomised selection to preserve exchangeability and unbiasedness, (3) proper SDE discretization (Euler, Milstein, Andersen QE for Heston), (4) importance function design per payoff type. The provided Rcpp package significantly reduces implementation burden. Theoretical understanding of unbiasedness conditions (D subset of super-level set) is important for correct application.

Open-source R package 'amsSim' available on CRAN with full C++ implementation via Rcpp. GitHub repository provided. Detailed algorithm pseudocode (Algorithm 1), specific parameter settings (sigma=0.2, rho=-0.5, kappa=2.0, theta=0.04, psi=0.3, V0=0.04), hardware specifications (MacBook Pro M2 Pro, 16GB RAM), and all numerical results reported in tables. 50 independent runs averaged over 5 seeds x 10 simulations.