Arbitrage-Free Pricing with Diffusion-Dependent Jumps
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911324015951872 |
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| author | Virk, Hamza Wu, Yihren John, Majnu |
| author_facet | Virk, Hamza Wu, Yihren John, Majnu |
| contents | 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 parameters 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arbitrage-Free Pricing with Diffusion-Dependent Jumps Virk, Hamza Wu, Yihren John, Majnu Mathematical Finance 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 parameters 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. |
| title | Arbitrage-Free Pricing with Diffusion-Dependent Jumps |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2512.15071 |