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Cliquet option pricing with Meixner processes
Volume 5, Issue 1 (2018), pp. 81–97
Markus Hess  

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https://doi.org/10.15559/18-VMSTA96
Pub. online: 12 February 2018      Type: Research Article      Open accessOpen Access

Received
27 September 2017
Revised
2 January 2018
Accepted
21 January 2018
Published
12 February 2018

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.

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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

MSC2010
60G51 (primary) 60H10 (primary) 60H30 (primary) 91B30 (secondary) 91B70 (secondary)

JEL
G22 D52

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