Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model

• Main Authors: Farzad Alavi Fard, Firmin Doko Tchatoka, Sivagowry Sriananthakumar
• Format: Article
• Language: English
• Published: MDPI AG 2021-02-01
• Series: Journal of Risk and Financial Management
• Subjects: generalised jump; kernel biased; asymptotic hedging error; esscher transform; maximum entropy density; value-at-risk
• Online Access: https://www.mdpi.com/1911-8074/14/3/97
• ISSN: 1911-8066; 1911-8074

In this paper we propose a maximum entropy estimator for the asymptotic distribution of the hedging error for options. Perfect replication of financial derivatives is not possible, due to market incompleteness and discrete-time hedging. We derive the asymptotic hedging error for options under a generalised jump-diffusion model with kernel bias, which nests a number of very important processes in finance. We then obtain an estimation for the distribution of hedging error by maximising Shannon’s entropy subject to a set of moment constraints, which in turn yields the value-at-risk and expected shortfall of the hedging error. The significance of this approach lies in the fact that the maximum entropy estimator allows us to obtain a consistent estimate of the asymptotic distribution of hedging error, despite the non-normality of the underlying distribution of returns.