Semi-Closed-Form Pricing of Vulnerable Geometric Asian Options Under a Three-Factor Stochastic Volatility Jump-Diffusion Model with Stochastic Interest Rates

This paper develops a semi-closed-form pricing framework for vulnerable geometric Asian options under a three-factor stochastic volatility jump-diffusion model with stochastic interest rates. To the best of our knowledge, this is the new framework to simultaneously accommodate common and idiosyncratic volatility, co-jumps, stochastic rates, and counterparty default risk in a 2D-FFT setting. The theoretical contribution is threefold: (i) a fully flexible correlation structure among asset returns, volatility factors, and the short rate; (ii) a default intensity jump component correlated with asset jumps; and (iii) a two-dimensional fast Fourier transform (2D-FFT) algorithm that computes prices and all Greeks in a single execution. Numerical results demonstrate speedup factors of 22.6 to 114.2 over Monte Carlo simulation at comparable accuracy (APE below 0.02%), with near-constant time scaling for portfolios of up to 4096 options. Degeneracy tests confirm the framework correctly recovers known closed-form solutions and published benchmarks. The proposed method provides a computationally efficient pricing tool for real-time risk management of credit-risk-embedded derivatives.