Convolution-FFT for option pricing in the Heston model

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Highly relevant for quantitative trading desks that price and hedge options under stochastic volatility models. The Heston model is widely used in practice for equity and FX options. The CFFT method offers faster computation than Carr-Madan FFT (up to 2x speedup) with comparable accuracy, making it suitable for real-time pricing and calibration. The explicit error bounds provide theoretical guarantees absent in most existing FFT methods. However, the method is primarily for European vanilla options, limiting direct applicability to exotic derivatives without extension.

Moderate complexity. Requires: (1) implementing the differentiable characteristic function representation (Theorem 2.1), (2) setting up FFT grids in log-stock domain, (3) implementing damping and shifting transformations for boundary control, (4) handling the convolution via DFT with trapezoidal weights. The mathematical derivation is involved but the final formulas are explicit. The main practical challenges are choosing appropriate grid parameters (L, N, α) and implementing the shifting schemes correctly to avoid boundary artifacts.

The paper provides detailed analytical formulas, parameter settings (r=0.03, v=0.1, Λ=1, ρ=-0.8, κ=3, θ=0.1, σ=0.25, T=1, L=10, N=2000-8000), and complete proofs in the appendix. However, no code repository or implementation details (programming language, libraries) are provided. The method is fully analytical and reproducible from the formulas given, but practical implementation requires careful handling of FFT grids and boundary schemes.