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Wasserstein distance estimates for jump-diffusion processes

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  • Breton, Jean-Christophe
  • Privault, Nicolas

Abstract

We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (Itô) process with jumps (Xt)t∈[0,T] and a jump-diffusion process (Xt∗)t∈[0,T]. Our bounds are expressed using the stochastic characteristics of (Xt)t∈[0,T] and the jump-diffusion coefficients of (Xt∗)t∈[0,T] evaluated in Xt, and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and Lp integrability results for the flow of stochastic differential equations with jumps, without relying on the Stein equation.

Suggested Citation

  • Breton, Jean-Christophe & Privault, Nicolas, 2024. "Wasserstein distance estimates for jump-diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:spapps:v:172:y:2024:i:c:s0304414924000401
    DOI: 10.1016/j.spa.2024.104334
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    References listed on IDEAS

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    1. Erik Ekström & Johan Tysk, 2007. "Properties Of Option Prices In Models With Jumps," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 381-397, July.
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    3. Jean-Christophe Breton & Nicolas Privault, 2008. "Bounds On Option Prices In Point Process Diffusion Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 597-610.
    4. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    5. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    6. Francis Hirsch & Marc Yor, 2014. "Comparing Brownian Stochastic Integrals for the Convex Order," Springer Optimization and Its Applications, in: Volodymyr Korolyuk & Nikolaos Limnios & Yuliya Mishura & Lyudmyla Sakhno & Georgiy Shevchenko (ed.), Modern Stochastics and Applications, edition 127, pages 3-19, Springer.
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