Hermite expansion of transition densities and European option prices for multivariate diffusions with jumps

Xiangwei Wan and Nian Yang

Journal of Economic Dynamics and Control, 2021, vol. 125, issue C

Abstract: This paper shows that a small-time Hermite expansion is feasible for multivariate diffusions. By introducing an innovative quasi-Lamperti transform, which unitizes the diffusion matrix at the initial time, we derive explicit recursive formulas for the expansion coefficients of transition densities and European option prices for multivariate diffusions with jumps in return. These immediately available explicit formulas, particularly for the irreducbile, nonaffine, time-inhomogeneous model with different types of jump-size distribution, is new to the literature. The explicit formulas can lead to real-time derivatives pricing and hedging as well as model calibration. Extensive numerical experiments illustrate the accuracy and effectiveness of our approach.

Keywords: Hermite expansion; Transition density; European option price; Stochastic volatility models; Jumps (search for similar items in EconPapers)
JEL-codes: C13 C32 C63 G13 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:125:y:2021:i:c:s016518892100018x

DOI: 10.1016/j.jedc.2021.104083

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