An Analytic COS Method for Compound Option Valuation

Battle Count: 81

The paper is primarily relevant to derivatives pricing and real options valuation rather than direct quantitative trading strategies. However, the compound option framework and jump-diffusion modeling are relevant for pricing exotic derivatives, structured products, and investment timing decisions. The computational efficiency improvements could benefit real-time pricing systems for compound options. The Q-Hawkes clustered jump model is relevant for understanding information arrival patterns in markets.

Implementation requires: (1) understanding of Fourier cosine expansions and characteristic functions, (2) derivation of closed-form trigonometric integral expressions (Appendices A and B), (3) numerical root-finding for exercise boundaries (Newton/Brent), (4) cumulant-based truncation interval construction, (5) backward recursion across multiple stages. The core algorithm is well-structured but requires careful handling of edge cases (ω_k = ν_n, boundary conditions). The Q-Hawkes characteristic function adds additional complexity.

The paper provides detailed closed-form formulas in Appendices A and B, specifies all model parameters for numerical experiments, and describes the algorithmic procedure step-by-step. However, no code repository is provided. The cumulant-based truncation interval construction and boundary-solving procedures are fully described. All characteristic functions for GBM, Merton, and Q-Hawkes models are given explicitly.