🤖 AI Summary
This study proposes a unified model integrating the Heston stochastic volatility, Bates jump-diffusion, and Cox-Ingersoll-Ross (CIR) stochastic interest rate frameworks to jointly address mid- to short-term equity option pricing and interest rate risk assessment. The model calibrates volatility and jump parameters using Lewis’s Fourier inversion and the Carr-Madan FFT method, while the CIR component is calibrated to Euribor data to generate economically plausible forward rate paths. Empirical results indicate that jump effects are negligible within 60 days, with stochastic volatility dominating short-term pricing dynamics, whereas stochastic interest rates exert a significant influence on valuations beyond one year. The model exhibits stable parameter estimates and produces forward rate trajectories consistent with economic intuition, thereby confirming the robustness of the standard Heston/Bates framework for mid- to short-term option pricing.
📝 Abstract
This study develops an integrated stochastic modeling framework for pricing short and medium-maturity equity options and assessing interest-rate risk using the Heston (1993), Bates (1996), and CIR (1985) models. We calibrate the Heston model using both the Lewis (2001) Fourier inversion and the Carr-Madan (1999) FFT approach, finding near-identical parameter sets, which is consistent with the calibration stability reported in recent studies such as Agazzotti et al. (2025). Extending the model to Bates shows that jump intensities converge to values effectively equal to zero for 60-day maturities, echoing empirical findings that jumps contribute marginally to short-term smile fitting. We further compare our calibration approach with the joint volatility-surface and variance-term-structure framework proposed by Yoo (2025), confirming that standard Heston/Bates calibration remains robust for the maturities considered. Finally, we calibrate the CIR short-rate model to the Euribor term structure, generating positive and economically consistent forward-rate scenarios in line with recent stochastic-rate option-pricing research by Jeon and Kim (2025). Overall, our results show that continuous stochastic volatility dominates near-term pricing dynamics, while stochastic interest rates materially influence valuations beyond one year.