Communications in Mathematical Finance

Optimal Option Pricing via Esscher Transforms with the Meixner Process

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• Abstract

  The Meixner process is a special type of Levy process. It originates from the theory of orthogonal polynomials and is related to the Meixner-Pollaczek polynomials by a martingale relation. In this paper, we apply instead the Meixner density function for option hedging. We make use of the decomposed Meixner and applied the Esscher transform to obtain the optimal option hedging strategy. We further obtain the option price by solving the parabolic partial differential equation which arises from the Meixner-OU process.