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

Author

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  • Farzad Alavi Fard

    (School of Business, The University of Sydney, Sydney, NSW 2006, Australia)

  • Firmin Doko Tchatoka

    (School of Economics, The University of Adelaide, Adelaide, SA 5005, Australia)

  • Sivagowry Sriananthakumar

    (School of Economics, Finance and Marketing, RMIT University, Melbourne, VIC 3000, Australia)

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.

Suggested Citation

  • Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2021. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," JRFM, MDPI, vol. 14(3), pages 1-19, February.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:3:p:97-:d:507723
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    More about this item

    Keywords

    generalised jump; kernel biased; asymptotic hedging error; esscher transform; maximum entropy density; value-at-risk; expected shortfall;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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