OPTIMALITY OF PAYOFFS IN LÉVY MODELS

Ernst August von Hammerstein (), Eva Lütkebohmert, Ludger Rüschendorf () and Viktor Wolf ()
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Ernst August von Hammerstein: Department of Quantitative Finance, University of Freiburg, Platz der Alten Synagoge, D-79098 Freiburg im Breisgau, Germany
Ludger Rüschendorf: Department of Mathematical Stochastics, University of Freiburg, Eckerstrasse 1, D-79104 Freiburg im Breisgau, Germany
Viktor Wolf: Department of Mathematical Stochastics, University of Freiburg, Eckerstrasse 1, D-79104 Freiburg im Breisgau, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 06, 1-46

Abstract: In this paper, we determine the lowest cost strategy for a given payoff in Lévy markets where the pricing is based on the Esscher martingale measure. In particular, we consider Lévy models where prices are driven by a normal inverse Gaussian (NIG)- or a variance Gamma (VG)-process. Explicit solutions for cost-efficient strategies are derived for a variety of vanilla options, spreads, and forwards. Applications to real financial market data show that the cost savings associated with these strategies can be quite substantial. The empirical findings are supplemented by a result that relates the magnitude of these savings to the strength of the market trend. Moreover, we consider the problem of hedging efficient claims, derive explicit formulas for the deltas of efficient calls and puts and apply the results to German stock market data. Using the time-varying payoff profile of efficient options, we further develop alternative delta hedging strategies for vanilla calls and puts. We find that the latter can provide a more accurate way of replicating the final payoff compared to their classical counterparts.

Keywords: Cost-efficient strategies; optimal payoffs; Lévy model; Esscher transform; delta hedging (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024914500411

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