Approximation of CVaR minimization for hedging under exponential-Lévy models

Madalina Deaconu 1, 2 Antoine Lejay 1, 2 Khaled Salhi 1, 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : 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-Lévy 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.
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Submitted on : Tuesday, February 7, 2017 - 11:23:08 PM
Last modification on : Saturday, October 6, 2018 - 1:16:22 AM
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Madalina Deaconu, Antoine Lejay, Khaled Salhi. Approximation of CVaR minimization for hedging under exponential-Lévy models. Journal of Computational and Applied Mathematics, Elsevier, 2017, 326, pp.171-182. ⟨10.1016/j.cam.2017.05.005⟩. ⟨hal-01461215⟩

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