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Numerical Stability Of A Hybrid Method For Pricing Options

Author

Listed:
  • 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)

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.

Suggested Citation

  • Maya Briani & Lucia Caramellino & Giulia Terenzi & Antonino Zanette, 2019. "Numerical Stability Of A Hybrid Method For Pricing Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-46, November.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:07:n:s0219024919500365
    DOI: 10.1142/S0219024919500365
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    References listed on IDEAS

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    Cited by:

    1. Ludovic Gouden`ege & Andrea Molent & Xiao Wei & Antonino Zanette, 2024. "Enhancing Valuation of Variable Annuities in L\'evy Models with Stochastic Interest Rate," Papers 2404.07658, arXiv.org.
    2. Ascione, Giacomo & Mehrdoust, Farshid & Orlando, Giuseppe & Samimi, Oldouz, 2023. "Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework," Applied Mathematics and Computation, Elsevier, vol. 446(C).

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