Maximum entropy evaluation of asymptotic hedging error under a generalised jump-diffusion model - Farzad Alavi Fard; Firmin Doko Tchatoka; Sivagowry Sriananthakumar (Journal of Risk and Financial Management, 2021)
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: C13; C51; G13; 330; expected shortfall; value-at-risk; asymptotic hedging error; esscher transform; generalised jump; kernel biased; maximum entropy density