Cliquet option pricing with Meixner processes

TL;DR

This paper develops semi-analytic pricing formulas for cliquet options within a pure-jump Meixner-Lévy process model, utilizing Fourier techniques and measure changes to handle the distribution complexities.

Contribution

It introduces a novel approach to pricing cliquet options using Meixner processes, including a customized measure change that preserves the distribution.

Findings

Derived semi-analytic pricing formulas for cliquet options.

Applied Fourier transform techniques to Meixner-Lévy processes.

Proposed a measure change preserving Meixner distribution.

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--L\'{e}vy 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--L\'{e}vy 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--L\'{e}vy processes. We also propose a customized measure change preserving the Meixner distribution of any Meixner process.