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Asymptotic Expansion for a Black–Scholes Model with Small Noise Stochastic Jump-Diffusion Interest Rate

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Geometry and Invariance in Stochastic Dynamics (RTISD19 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 378))

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Abstract

In the present paper we study the asymptotic expansion for a Black–Scholes model with small noise stochastic jump-diffusion interest rate. In particular, we consider the case when the small perturbation is due to a general, but small, noise of Lévy type. Moreover, we provide explicit expressions for the involved expansion coefficients as well as accurate estimates on the remainders.

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Acknowledgements

The authors would like to thank the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) for the financial support that has funded the present research within the project called Set-valued and optimal transportation theory methods to model financial markets with transaction costs both in deterministic and stochastic frameworks.

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Strada le Grazie, 15, 37134, Verona, Italy

    Francesco Cordoni & Luca Di Persio

Authors
  1. Francesco Cordoni
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  2. Luca Di Persio
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Corresponding author

Correspondence to Luca Di Persio .

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Editors and Affiliations

  1. Department of Mathematics, Università degli Studi di Milano, Milan, Italy

    Stefania Ugolini

  2. Department of Mathematics, Università degli Studi di Milano, Milan, Italy

    Marco Fuhrman

  3. Department of Economics, Università degli Studi dell'Insubria, Varese, Italy

    Elisa Mastrogiacomo

  4. Department of Agricultural and Environmental Sciences, Università degli Studi di Milano, Milan, Italy

    Paola Morando

  5. Mathematic and Informatic Department, Bergische Universität Wuppertal, Wuppertal, Germany

    Barbara Rüdiger

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Cordoni, F., Di Persio, L. (2021). Asymptotic Expansion for a Black–Scholes Model with Small Noise Stochastic Jump-Diffusion Interest Rate. In: Ugolini, S., Fuhrman, M., Mastrogiacomo, E., Morando, P., Rüdiger, B. (eds) Geometry and Invariance in Stochastic Dynamics. RTISD19 2019. Springer Proceedings in Mathematics & Statistics, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-030-87432-2_3

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