Simulation of stochastic volatility models via operator splitting schemes

Battle Count: 66

Highly relevant for quantitative trading desks that price and hedge derivatives under stochastic volatility models. The operator splitting schemes offer significant computational speedups (potentially hundreds of times faster than Fourier inversion methods) while maintaining second-order accuracy. This is particularly valuable for real-time pricing of path dependent options, VIX derivatives, and portfolio risk calculations. The ease of implementation and versatility across multiple SV model families make it practical for production trading systems. However, it is primarily a pricing/simulation tool rather than a direct trading signal generator.

Moderate complexity. The operator splitting framework is conceptually straightforward and avoids the most challenging aspects of existing methods (Fourier inversion, root-finding, moment matching, acceptance-rejection sampling). The main implementation tasks are: (1) exact CIR process simulation (well-documented via Alfonsi 2015), (2) BDLP increment simulation for BN-S models, (3) matrix operations for the lifted Heston model (matrix exponential, inverse). The paper provides explicit formulas for all steps. No sophisticated numerical libraries beyond standard random number generation and basic linear algebra are required.

The paper provides detailed mathematical derivations, explicit algorithmic steps (Propositions 1-4), parameter settings for all numerical experiments, and references to specific algorithms (Alfonsi 2015 for CIR simulation). Benchmark values are cited from prior literature. However, no code repository or supplementary computational materials are provided. The methodology is fully specified analytically, making reimplementation feasible for experts in the field.