Numerical stability of a hybrid method for pricing options

Maya Briani (1) , Lucia Caramellino (2) , Giulia Terenzi (3) , Antonino Zanette (4)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
2 Dipartimento di Matematica [Rome]
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
4 MATHRISK - Mathematical Risk Handling

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.

Mots clés: Stochastic volatility; Jump-diffusion process; European and American options; Tree methods; Finite-difference; Numerical stability

Domaines: Probabilités [math.PR]

Maya Briani, Lucia Caramellino, Giulia Terenzi, Antonino Zanette. Numerical stability of a hybrid method for pricing options. International Journal of Theoretical and Applied Finance, 2019, pp.1950036. ⟨10.1142/S0219024919500365⟩. ⟨hal-02380723⟩