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On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

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Abstract

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be a diffusion or a Markov process, as the examples in Sect. 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

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Authors and Affiliations

  1. Dpt. d’Economia i Empresa, Universitat Pompeu Fabra, c/Ramon Trias Fargas, 25–27, 08005, Barcelona, Spain

    Elisa Alòs

  2. Control Automático, CINVESTAV-IPN, Apartado Postal 14-740, 07000, México, D.F., Mexico

    Jorge A. León

  3. Dpt. de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra (Barcelona), Spain

    Josep Vives

  4. Dpt. Probabilitat, Lògica i Estadística, Universitat de Barcelona, Gran Via, 585, 08007, Barcelona, Spain

    Josep Vives

Authors
  1. Elisa Alòs
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  2. Jorge A. León
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  3. Josep Vives
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Corresponding author

Correspondence to Elisa Alòs.

Additional information

E. Alòs’ research is supported by grants MEC FEDER MTM 2006 06427 and SEJ2006-13537.

J.A. León’s research is partially supported by the CONACyT grant 45684-F.

J. Vives’ research is supported by grant MEC FEDER MTM 2006 06427.

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Alòs, E., León, J.A. & Vives, J. On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility. Finance Stoch 11, 571–589 (2007). https://doi.org/10.1007/s00780-007-0049-1

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  • DOI: https://doi.org/10.1007/s00780-007-0049-1

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