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

Farzad Alavi Fard, Firmin Doko Tchatoka and Sivagowry Sriananthakumar
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Farzad Alavi Fard: School of Business, The University of Sydney, Sydney, NSW 2006, Australia
Sivagowry Sriananthakumar: School of Economics, Finance and Marketing, RMIT University, Melbourne, VIC 3000, Australia

JRFM, 2021, vol. 14, issue 3, 1-19

Abstract: 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.

Keywords: generalised jump; kernel biased; asymptotic hedging error; esscher transform; maximum entropy density; value-at-risk; expected shortfall (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2021
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Working Paper: Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model (2015)
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