ARBITRAGE-FREE PRICING WITH DIFFUSION-DEPENDENT JUMPS

Authors

Hamza A. Virk, Dept of Math., Hofstra University, Hempstead, NY 11549, USAFollow
Yihren Wu, Dept of Math., Hofstra University, Hempstead, NY 11549, USAFollow
Majnu John, Dept of Math., Hofstra University, Hempstead, NY 11549, USAFollow

Abstract

Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous one-sided models that create arbitrage opportunities, our framework includes upward and downward jumps triggered by both large upward and large downward diffusion increments. We derive the explicit no-arbitrage condition linking the physical drift to model pa- rameters and market risk premia by constructing an Equivalent Martingale Measure using Girsanov’s theorem and a normalized Esscher transform. This condition provides a rigorous foundation for arbitrage-free pricing in models with diffusion-dependent jumps.

Recommended Citation

Virk, Hamza A.; Wu, Yihren; and John, Majnu (2025) "ARBITRAGE-FREE PRICING WITH DIFFUSION-DEPENDENT JUMPS," Journal of Stochastic Analysis: Vol. 6: No. 3, Article 2.
DOI: 10.31390/josa.6.3.02
Available at: https://repository.lsu.edu/josa/vol6/iss3/2

DOI

10.31390/josa.6.3.02