IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2512.15071.html

Arbitrage-Free Pricing with Diffusion-Dependent Jumps

Author

Listed:
  • Hamza Virk
  • Yihren Wu
  • Majnu John

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 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.

Suggested Citation

  • Hamza Virk & Yihren Wu & Majnu John, 2025. "Arbitrage-Free Pricing with Diffusion-Dependent Jumps," Papers 2512.15071, arXiv.org.
    • Handle: RePEc:arx:papers:2512.15071
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2512.15071
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shin-Yun Wang & Ming-Che Chuang & Shih-Kuei Lin & So-De Shyu, 2021. "Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index," Review of Quantitative Finance and Accounting, Springer, vol. 56(1), pages 25-51, January.
    2. Michael C. Fu & Bingqing Li & Guozhen Li & Rongwen Wu, 2017. "Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions," Management Science, INFORMS, vol. 63(11), pages 3961-3977, November.
    3. Melenberg, B. & Werker, B.J.M., 1996. "On the Pricing of Options in Incomplete Markets," Discussion Paper 1996-19, Tilburg University, Center for Economic Research.
    4. El-Khatib, Youssef & Goutte, Stephane & Makumbe, Zororo S. & Vives, Josep, 2023. "A hybrid stochastic volatility model in a Lévy market," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 220-235.
    5. Carbonneau, Alexandre, 2021. "Deep hedging of long-term financial derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 327-340.
    6. Carolyn W. Chang, 1995. "A No-Arbitrage Martingale Analysis For Jump-Diffusion Valuation," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(3), pages 351-381, September.
    7. Leisen, Dietmar P. J., 1999. "The random-time binomial model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1355-1386, September.
    8. repec:dau:papers:123456789/5374 is not listed on IDEAS
    9. Melenberg, B. & Werker, B.J.M., 1996. "On the Pricing of Options in Incomplete Markets," Other publications TiSEM 3531d5d5-d0a6-4d54-9d8a-9, Tilburg University, School of Economics and Management.
    10. S H Martzoukos, 2009. "Real R&D options and optimal activation of two-dimensional random controls," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(6), pages 843-858, June.
    11. Paul McCloud, 2020. "Expectation and Price in Incomplete Markets," Papers 2006.16703, arXiv.org.
    12. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    13. Pakorn Aschakulporn & Jin E. Zhang, 2022. "Bakshi, Kapadia, and Madan (2003) risk-neutral moment estimators: A Gram–Charlier density approach," Review of Derivatives Research, Springer, vol. 25(3), pages 233-281, October.
    14. René Carmona, 2022. "The influence of economic research on financial mathematics: Evidence from the last 25 years," Finance and Stochastics, Springer, vol. 26(1), pages 85-101, January.
    15. Jacques Pézier & Johanna Scheller, 2011. "A Comprehensive Evaluation of Portfolio Insurance Strategies," ICMA Centre Discussion Papers in Finance icma-dp2011-15, Henley Business School, University of Reading.
    16. Pakorn Aschakulporn & Jin E. Zhang, 2022. "Bakshi, Kapadia, and Madan (2003) risk‐neutral moment estimators: An affine jump‐diffusion approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 365-388, March.
    17. Gerald H. L. Cheang & Carl Chiarella & Andrew Ziogas, 2013. "The representation of American options prices under stochastic volatility and jump-diffusion dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 241-253, January.
    18. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.
    19. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    20. Marcelo F. Perillo, 2021. "Valuación de Títulos de Deuda Indexados al Comportamiento de un Índice Accionario: Un Modelo sin Riesgo de Crédito," CEMA Working Papers: Serie Documentos de Trabajo. 784, Universidad del CEMA.
    21. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2512.15071. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.