Option Pricing under Stochastic Volatility and Jumps:A PIDE Framework with Empirical Evidence (opens in new tab)

We develop a partial integro-differential equation (PIDE) framework for option pricing under joint stochastic volatility and jump dynamics, and evaluate its empirical content using the S&P500 index option contracts across three maturities. The framework is derived from the infinitesimal generator of an affine L\'evy-type process and implemented via finite-difference discretization with FFT-based treatment of the nonlocal jump operator. Calibra...