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.

D'Ippoliti, F., Moretto, E., Pasquali, S., & Trivellato, B. (2010). Exact and approximated option pricing in a stochastic volatility jump-diffusion model. In Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp.133-142). Milano : Springer [10.1007/978-88-470-1481-7_14].

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

Moretto, Enrico;
2010

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.
Si
paper
Scientifica
Barrier option pricing; Rejection sampling; Stochastic volatility jump-diffusion models;
English
International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance, MAF 2008 - 26 March 2008 through 28 March 2008
978-88-470-1480-0
D'Ippoliti, F., Moretto, E., Pasquali, S., & Trivellato, B. (2010). Exact and approximated option pricing in a stochastic volatility jump-diffusion model. In Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp.133-142). Milano : Springer [10.1007/978-88-470-1481-7_14].
D'Ippoliti, F; Moretto, E; Pasquali, S; Trivellato, B
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/382314
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