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A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility


  • Elisa Alòs


  • Jorge A. León
  • Monique Pontier
  • Josep Vives


In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

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  • Elisa Alòs & Jorge A. León & Monique Pontier & Josep Vives, 2008. "A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility," Economics Working Papers 1081, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:1081

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    References listed on IDEAS

    1. Mendonca, Sandro & Pereira, Tiago Santos & Godinho, Manuel Mira, 2004. "Trademarks as an indicator of innovation and industrial change," Research Policy, Elsevier, vol. 33(9), pages 1385-1404, November.
    2. Rebecca Henderson, 1993. "Underinvestment and Incompetence as Responses to Radical Innovation: Evidence from the Photolithographic Alignment Equipment Industry," RAND Journal of Economics, The RAND Corporation, vol. 24(2), pages 248-270, Summer.
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    More about this item


    Hull and White formula; Malliavin calculus; Ito’s formula for the Skorohod integral; jumpdiffusion stochastic volatility models;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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