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Optimality Of Payoffs In Lévy Models

Author

Listed:
  • ERNST AUGUST VON HAMMERSTEIN

    (Department of Quantitative Finance, University of Freiburg, Platz der Alten Synagoge, D-79098 Freiburg im Breisgau, Germany)

  • EVA LÜTKEBOHMERT

    (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)

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.

Suggested Citation

  • Ernst August Von Hammerstein & Eva Lütkebohmert & Ludger Rüschendorf & Viktor Wolf, 2014. "Optimality Of Payoffs In Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(06), pages 1-46.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:06:n:s0219024914500411
    DOI: 10.1142/S0219024914500411
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    Cited by:

    1. Carole Bernard & Junsen Tang, 2016. "Simplified Hedge For Path-Dependent Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-32, November.
    2. Jonathan Ansari & Ludger Rüschendorf, 2018. "Ordering Results for Risk Bounds and Cost-efficient Payoffs in Partially Specified Risk Factor Models," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 817-838, September.

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