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Exact Pricing With Stochastic Volatility And Jumps

Author

Listed:
  • FERNANDA D'IPPOLITI

    (Università "G. D'Annunzio" di Chieti-Pescara, Viale Pindaro 87, Pescara, 65127, Italy)

  • ENRICO MORETTO

    (Università dell'Insubria, Via Monte Generoso 71, Varese, 21100, Italy)

  • SARA PASQUALI

    (CNR-IMATI, Via Bassini 15, Milano, 20133, Italy)

  • BARBARA TRIVELLATO

    (Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, 10129, Italy)

Abstract

A stochastic volatility jump-diffusion model for pricing derivatives with jumps in both spot return and volatility underlying dynamics is presented. This model admits, in the spirit of Heston, a closed-form solution for European-style options. The structure of the model is also suitable to explicitly obtain the fair delivery price for variance swaps. To evaluate derivatives whose value does not admit a closed-form expression, a methodology based on an "exact algorithm", in the sense that no discretization of equations is required, is developed and applied to barrier options. Goodness of pricing algorithm is tested using DJ Euro Stoxx 50 market data for European options. Finally, the algorithm is applied to compute prices and Greeks for barrier options and to determine the fair delivery prices for variance swaps.

Suggested Citation

  • Fernanda D'Ippoliti & Enrico Moretto & Sara Pasquali & Barbara Trivellato, 2010. "Exact Pricing With Stochastic Volatility And Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 901-929.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:06:n:s0219024910006042
    DOI: 10.1142/S0219024910006042
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    References listed on IDEAS

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    1. Gerald Cheang & Carl Chiarella & Andrew Ziogas, 2009. "An Analysis of American Options Under Heston Stochastic Volatility and Jump-Diffusion Dynamics," Research Paper Series 256, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Ulyah, Siti Maghfirotul & Lin, Xenos Chang-Shuo & Miao, Daniel Wei-Chung, 2018. "Pricing short-dated foreign equity options with a bivariate jump-diffusion model with correlated fat-tailed jumps," Finance Research Letters, Elsevier, vol. 24(C), pages 113-128.
    2. Rehez Ahlip & Laurence A. F. Park & Ante Prodan, 2017. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-30, March.

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