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: RMIT University
Sivagowry Sriananthakumar: RMIT University

No 2015-17, School of Economics and Public Policy Working Papers from University of Adelaide, School of Economics and Public Policy

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 biased, which nests a number of very important processes in finance. We then obtain an estimation for the distribution of hedging error by maximising ShannonÂ’s entropy subject to a set of moment constraints, which in turn yield 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: Generalized Jump; kernel biased; Asymptotic Hedging Error; Esscher Transform; Maximum Entropy Density; Value-at-Risk; Expected Shortfall (search for similar items in EconPapers)
JEL-codes: C13 C51 G13 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2015-09
New Economics Papers: this item is included in nep-ecm and nep-rmg
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Journal Article: Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model (2021)
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