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On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility |
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| Authors: | Elisa Alòs Jorge A León Josep Vives |
| Institution: | (1) Dpt. d’Economia i Empresa, Universitat Pompeu Fabra, c/Ramon Trias Fargas, 25–27, 08005 Barcelona, Spain;(2) Control Automático, CINVESTAV-IPN, Apartado Postal 14-740, 07000 México, D.F., Mexico;(3) Dpt. de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain;(4) Dpt. Probabilitat, Lògica i Estadística, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain |
| 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. 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. |
| Keywords: | Black-Scholes formula Derivative operator It?’ s formula for the Skorohod integral Jump-diffusion stochastic volatility model |
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