Finance and Stochastics

, Volume 11, Issue 4, pp 571–589 | Cite as

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

  • Elisa Alòs
  • Jorge A. León
  • Josep Vives


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.


Black-Scholes formula Derivative operator Itô’s formula for the Skorohod integral Jump-diffusion stochastic volatility model 


G12 G13 

Mathematics Subject Classification (2000)

91B28 91B70 60H07 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dpt. d’Economia i EmpresaUniversitat Pompeu FabraBarcelonaSpain
  2. 2.Control AutomáticoCINVESTAV-IPNMéxicoMexico
  3. 3.Dpt. de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain
  4. 4.Dpt. Probabilitat, Lògica i EstadísticaUniversitat de BarcelonaBarcelonaSpain

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