Jump-Diffusion dynamics and long-short term volatility: Evidence from option pricing

It is vital for option valuation to capture the variability of forward prices across different maturities. Based on the patterns of jumps and diffusion in stock prices, we propose a dynamic Jump-Diffusion factors model that decomposes volatility into jump and diffusion components. This model aims to capture the characteristics of jump and diffusion risks across different time horizons. We employ the sequential Bayesian learning method to learn asset pricing models and analyze the performance of different decompositions of volatility in elucidating stock price dynamics and option pricing. Based on this study, single-factor models fail to capture diffusion and jump risks simultaneously. Moreover, accounting for the cross-feedback effects between the jump and diffusion components is crucial for capturing the term structure of volatility. The dynamic Jump-Diffusion factors model is capable of capturing the evolution of both jump and diffusion risks and exhibits a more flexible term structure of conditional volatility compared to the Long-run and Short-run component model. The dynamic Jump-Diffusion factors model with cross-feedback effect outperforms the Long-run and Short-run component model in mitigating the upward-sloping term structure of option pricing errors. © 2024 Systems Engineering Society of China. All rights reserved.