Option Pricing under Stochastic Volatility and Jumps: A PIDE Framework with Empirical Evidence

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Highly relevant for quantitative trading desks involved in equity index derivatives. The paper provides a rigorous framework for pricing SPX options under realistic dynamics, with clear empirical decomposition showing that stochastic volatility (Heston) captures 39% improvement over Black-Scholes while jumps add marginal value in normal regimes. Directly applicable to: (1) option pricing and hedging, (2) volatility surface modeling for trading strategies, (3) tail-risk assessment and crash-risk pricing, (4) model selection for derivatives desks, (5) understanding when jump components become critical (crisis periods). The PIDE framework and numerical methods are directly implementable for real-time pricing systems.

High implementation complexity due to: (1) PIDE solver requiring Crank-Nicolson finite-difference discretization with mixed derivative stencils, (2) FFT-based convolution for nonlocal jump integral evaluation, (3) operator-splitting (Strang/IMEX) time-stepping schemes, (4) GMM calibration with differential evolution + Nelder-Mead optimization over 5-9 parameters, (5) multiple nested model specifications (BS, Heston, Heston+CGMY, SVJD), (6) implied volatility inversion via Newton-Raphson with bisection fallback, (7) Monte Carlo validation engine. Requires expertise in numerical PDE methods, Fourier analysis, optimization, and financial mathematics. However, the paper provides detailed algorithmic descriptions and validation benchmarks.

The paper provides detailed mathematical formulations, parameter estimates, and numerical method descriptions. However, no code repository is mentioned. The data (SPX options) is publicly available through standard sources. The GMM calibration procedure, PIDE solver, and FFT implementation are described in sufficient detail for replication, but specific implementation details (e.g., exact grid parameters, optimization settings) would require additional effort. Bootstrap and sensitivity analyses are reported, aiding verification.