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Exact Pricing With Stochastic Volatility And Jumps

  • 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)

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.

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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 13 (2010)
Issue (Month): 06 ()
Pages: 901-929

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Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:06:p:901-929
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