NUMERICAL STABILITY OF A HYBRID METHOD FOR PRICING OPTIONS

Maya Briani (), Lucia Caramellino, Giulia Terenzi () and Antonino Zanette ()
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Maya Briani: Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Rome, Italy
Lucia Caramellino: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy
Giulia Terenzi: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy
Antonino Zanette: Dipartimento di Scienze Economiche e Statistiche, Università di Udine, via Palladio 8, 33100 Udine, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 07, 1-46

Abstract: We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propose hybrid simulations for the model, following a binomial tree in the direction of both the volatility and the interest rate, and a space-continuous approximation for the underlying asset price process coming from a Euler–Maruyama type scheme. We test our numerical schemes by computing European and American option prices.

Keywords: Stochastic volatility; jump-diffusion process; European and American options; tree methods; finite-difference; numerical stability (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024919500365

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