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Exact and approximated option pricing in a stochastic volatility jump-diffusion model

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Fernanda D’Ippoliti

    (University of Chieti-Pescara, Dipartimento di Scienze)

  • Enrico Moretto

    (University of Insubria, Facoltà di Economia)

  • Sara Pasquali

    (CNR-IMATI)

  • Barbara Trivellato

    (CNR-IMATI
    Polytechnic University of Turin)

Abstract

We propose a stochastic volatility jump-diffusion model for option pricing with contemporaneous jumps in both spot return and volatility dynamics. The model admits, in the spirit of Heston, a closed-form solution for European-style options. To evaluate more complex derivatives for which there is no explicit pricing expression, such as barrier options, a numerical methodology, based on an “exact algorithm” proposed by Broadie and Kaya, is applied. This technique is called exact as no discretisation of dynamics is required. We end up testing the goodness of our methodology using, as real data, prices and implied volatilities from the DJ Euro Stoxx 50 market and providing some numerical results for barrier options and their Greeks.

Suggested Citation

  • Fernanda D’Ippoliti & Enrico Moretto & Sara Pasquali & Barbara Trivellato, 2010. "Exact and approximated option pricing in a stochastic volatility jump-diffusion model," Springer Books, in: Marco Corazza & Claudio Pizzi (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 133-142, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-1481-7_14
    DOI: 10.1007/978-88-470-1481-7_14
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