Quantile Hedging in a Semi-Static Market with Model Uncertainty
28 Pages Posted: 21 Aug 2014 Last revised: 25 Sep 2017
Date Written: July 15, 2015
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the investor minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile hedging to a randomized composite hypothesis test, an arbitrage-free discretization of the market is proposed as an approximation. The discretized market has a dominating measure, which guarantees the existence of the optimal hedging strategy and enables numerical calculation of the quantile hedging price by applying the generalized Neyman-Pearson Lemma. Finally, the performance in the original market of the approximating hedging strategy and the convergence of the approximating quantile hedging price are analyzed.
Keywords: Quantile hedging, Model Uncertainty, Semi-static Hedging, Neyman-Pearson Lemma
JEL Classification: G11, G12, G13, D81
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