Stochastic Volatility, Jumps, and Rates: A Unified Framework for Option Pricing and Term-Structure Simulation

Battle Count: 81

The paper is primarily focused on model calibration and pricing accuracy rather than trading strategy development. However, the findings are directly relevant to quantitative trading desks that price equity options, manage volatility risk, and assess interest rate exposure. The conclusion that continuous stochastic volatility dominates short-term pricing while stochastic rates matter beyond one year has practical implications for model selection in trading systems. The calibration stability results support robust model implementation.

Implementation requires expertise in stochastic calculus, Fourier transform methods, numerical optimization (Differential Evolution + L-BFGS-B), Monte Carlo simulation, and term structure modeling. The multi-model pipeline (Heston → Bates → CIR) with sequential calibration adds complexity. However, the mathematical formulations are well-established in the literature, and standard libraries exist for FFT pricing and CIR bond formulas. The two-stage optimization and Feller condition enforcement add practical implementation challenges.

The paper provides detailed parameter tables, calibration procedures, and model specifications. However, the dataset is referenced as a course file (MScFE 622 GWP1 Option Data.xlsx) without a public link. No code repository is provided. The methodology is well-documented with specific optimization algorithms (Differential Evolution, L-BFGS-B) and integration limits (u_max=200), but exact implementation details (software, random seeds) are not fully specified.