The β-Meixner model

We propose to approximate the Meixner model by a member of the β-family introduced by Kuznetsov (2010) in [2]. The advantage of the approximation is the semi-explicit   formulae for the running extrema under the β-family processes which enables us to produce more efficient algorithms for pricing path dependent options through the Wiener–Hopf factors. We will explore the performance of the approximation both in an equity framework and in the credit risk setting, where we use the approximation to calibrate a surface of credit default swaps. The paper follows the approach of the study made by Schoutens and Damme (2010) in [1], where the aim was to approximate the variance gamma. We will contextualize the results by Schoutens and Damme (2010) in [1] and the ones here with respect to the approach taken by Jeannin and Pistorius (2010) in [15]. An asymptotic expression for the rate of convergence of the approximation is derived.