Approximation of CVaR minimization for hedging under exponential-Levy models

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:326

Article

Salhi, Khaled¹ 

[1] Univ Lorraine, Inst Elie Cartan de Lorraine, UMR 7502, F-54506 Vandoeuvre Les Nancy, France

关键词: Conditional Value-at-Risk;    Exponential-Levy models;    Incomplete market;    Neyman-Pearson lemma;    Esscher martingale measure;    Fast Fourier transform;   

DOI  :  10.1016/j.cam.2017.05.005

来源: Elsevier

【 摘 要 】

In this paper, we study the hedging problem based on the CVaR in incomplete markets. As the superhedging is quite expensive in terms of initial capital, we construct a self-financing strategy that minimizes the CVaR of hedging risk under a budget constraint on the initial capital. In incomplete markets, no explicit solution can be provided. To approximate the problem, we apply the Neyman-Pearson lemma approach with a specific equivalent martingale measure. Afterwards, we explicit the solution for call options hedging under the exponential-Levy class of price models. This approach leads to an efficient and easy to implement method using the fast Fourier transform. We illustrate numerical results for the Merton model. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free