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.
Highlights
Cliquet option based contracts constitute a customized subclass of equity indexed annuities
We investigate the pricing of cliquet options in a geometric Meixner model
We investigate the distributional properties of the corresponding Meixner–Lévy process under P related to the Radon–Nikodym function h(z) given in (3.18)
Summary
Cliquet option based contracts constitute a customized subclass of equity indexed annuities. The underlying options commonly are of monthly sum cap style paying a credited yield based on the sum of monthly-capped rates associated with some reference stock index In this regard, cliquet type investments belong to the class of path-dependent exotic options. The aim of the present paper is to provide analytical pricing formulas for globallyfloored locally-capped cliquet options with multiple resetting times where the underlying reference stock index is driven by a pure-jump time-homogeneous Meixner– Lévy process. In this setup, we derive cliquet option price formulas under two different approaches: once by using the distribution function of the driving Meixner–Lévy process and once by applying Fourier transform techniques (as proposed in [8]).
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