Cliquet Option Pricing with Meixner Processes

Abstract

We investigate the pricing of cliquet options in a geometric Meixner model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a pure-jump Meixner-Lévy process yielding Meixner distributed log-returns. In this setting, we infer semi-analytic expressions for the cliquet option price by using the probability distribution function of the driving Meixner-Lévy process and by an application of Fourier transform techniques. In an introductory section, we compile various facts on the Meixner distribution and the related class of Meixner-Lévy processes. We also propose a customized measure change preserving the Meixner distribution of any Meixner process.

Keywords: Cliquet option pricing, path-dependent exotic option, equity indexed annuity, log-return of financial asset, Meixner distribution, Meixner-Lévy process, stochastic differential equation, probability measure change, characteristic function, Fourier transform

JEL Classification: G22, D52