Hermite Expansion of Transition Densities and European Option Prices for Multivariate Diffusions with Jumps

65 Pages Posted: 2 Jul 2019 Last revised: 15 Dec 2020

See all articles by Xiangwei Wan

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management

Nian Yang

Nanjing University - Department of Finance and Insurance

Date Written: December 15, 2020

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, Irreducible diffusions, Transition densities, European option pricing, Stochastic volatility models

JEL Classification: C13, C32, G13, C63

Suggested Citation

Wan, Xiangwei and Yang, Nian, Hermite Expansion of Transition Densities and European Option Prices for Multivariate Diffusions with Jumps (December 15, 2020). Available at SSRN: https://ssrn.com/abstract=3413376 or http://dx.doi.org/10.2139/ssrn.3413376

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management ( email )

No.1954 Huashan Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200030
China
+86-21-52301570 (Phone)

HOME PAGE: http://sites.google.com/view/wanxiangwei/research

Nian Yang (Contact Author)

Nanjing University - Department of Finance and Insurance ( email )

Nanjing
China

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