Almost-Exact Simulation Scheme for Heston-type Models: Bermudan and American Option Pricing

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Highly relevant for quantitative finance practitioners dealing with exotic option pricing, particularly Bermudan and American options under stochastic volatility models. The AES scheme provides a computationally efficient alternative to Euler discretization, reducing simulation time and memory requirements. Directly applicable to derivatives desks, risk management, and algorithmic trading strategies involving options. However, it is primarily a pricing methodology rather than a trading strategy.

Moderate complexity. The AES scheme itself is elegant and simple (sampling from non-central chi-square distribution and computing closed-form coefficients). However, implementing the full Bermudan/American option pricing pipeline requires: (1) Monte Carlo path simulation, (2) Least Squares Monte Carlo regression for continuation values, (3) proper handling of exercise dates, and (4) sufficient number of paths (1,000,000 used). The double Heston extension adds complexity with Cholesky decomposition and two variance processes. Python implementation is feasible using numpy.random.noncentral_chisquare.

The paper provides detailed algorithms (Algorithm 1 and 2 in Appendix A) for implementing the AES scheme for both Heston and Double Heston models. Parameter sets are explicitly given. Python implementation using numpy.random library is mentioned. Hardware specifications are provided. However, no code repository is linked.