Efficient Importance Sampling under Heston Model: Short Maturity and Deep Out-of-the-Money Options

Battle Count: 132

The paper is primarily relevant to derivatives pricing and risk management rather than direct trading strategy development. It provides efficient Monte Carlo methods for pricing exotic/path-dependent options under stochastic volatility, which is critical for market-making in derivatives, hedging, and portfolio valuation. The variance reduction of 2-3 orders of magnitude makes previously intractable simulations feasible. However, it does not directly address trading signals, execution, or alpha generation.

Implementation requires: (1) Simulating the Heston model with proper discretization (Milstein for variance to preserve positivity), (2) Computing the state-dependent drift h_t = -h_bar/rho_bar * sqrt(V_t) at each time step, (3) Evaluating the Radon-Nikodym derivative (likelihood ratio) along each path, (4) Solving Riccati ODEs for parameter calibration, (5) Understanding the slow mean-reversion scaling for deep OTM regime. The theoretical framework involves Girsanov theorem, large deviation principles, and affine model structure. The numerical implementation itself is moderate, but the theoretical understanding and parameter selection require significant expertise.

The paper provides specific model parameters (S0, K, v0, theta, kappa, sigma, rho, r) and simulation details (M=2^18 paths, Milstein scheme) for numerical experiments. However, no code repository is provided. The theoretical derivations are complete with appendices containing full Riccati equation solutions. Reproduction requires implementing Girsanov transformations, affine Heston simulation, and the specific drift adjustment.