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.

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. In [

The aim of the present paper is to provide analytical pricing formulas for globally-floored 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 [

The paper is organized as follows: In Section

Let

A real-valued, càdlàg, pure-jump, time-homogeneous Lévy process

Let

Recall that we worked under the risk-neutral probability measure

In this section, we present a generalized structure preserving measure change from the risk-neutral to the physical probability measure. Recall that the measure change proposed above only affects the skewness parameter

In the sequel, we investigate the distributional properties of the corresponding Meixner–Lévy process under

This section is devoted to the pricing of cliquet options in the Meixner stock price model presented in Chapter

See the proof of Prop. 3.1 in [

In the subsequent sections, we derive explicit expressions for

Let us first apply a method involving probability distribution functions (cf. [

By similar arguments as in the proof of Prop. 3.2 in [

If we insert (

In accordance to Prop. 2.4 in [

As mentioned in Section

There is an alternative method to derive expressions for

The proof follows the same lines as the proof of Prop. 3.4 in [

Our argumentation in the proof of Proposition

Similar computations as in the proof of Prop. 3.5 in [

There is an alternative method involving (

The claimed representation immediately follows from Eq. (3.16) in [

Inspired by the Fourier transform techniques applied in the proof of Proposition

The proof of Theorem 3.7 in [

In this paper, we investigated the pricing of a monthly sum cap style cliquet option with underlying stock price modeled by a geometric pure-jump Meixner–Lévy process. In Section