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
2 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: Incomplete Market; Neyman Pearson Lemma; Conditional Value-at-Risk; Exponential-Lévy models; Esscher Martingale Measure; Fast Fourier Transform

Domaines: Mathématiques [math]

Madalina Deaconu, Antoine Lejay, Khaled Salhi. Approximation of CVaR minimization for hedging under exponential-Lévy models. Journal of Computational and Applied Mathematics, 2017, 326, pp.171-182. ⟨10.1016/j.cam.2017.05.005⟩. ⟨hal-01461215⟩