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A Note on the Suboptimality of Path-Dependent Pay-Offs in Levy Markets


  • Steven Vanduffel
  • Andrew Chernih
  • Matheusz Maj
  • Wim Schoutens


Cox and Leland used techniques from the field of stochastic control theory to show that, in the particular case of a Brownian motion for the asset log-returns, risk-averse decision makers with a fixed investment horizon prefer path-independent pay-offs over path-dependent pay-offs. In this note we provide a novel and simple proof for the Cox and Leland result and we will extend it to general Levy markets where pricing is based on the Esscher transform (exponential tilting). It is also shown that, in these markets, optimal path-independent pay-offs are increasing with the underlying final asset value. We provide examples that allow explicit verification of our theoretical findings and also show that the inefficiency cost of path-dependent pay-offs can be significant. Our results indicate that path-dependent investment pay-offs, the use of which is widespread in financial markets, do not offer good value from the investor's point of view.

Suggested Citation

  • Steven Vanduffel & Andrew Chernih & Matheusz Maj & Wim Schoutens, 2009. "A Note on the Suboptimality of Path-Dependent Pay-Offs in Levy Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(4), pages 315-330.
  • Handle: RePEc:taf:apmtfi:v:16:y:2009:i:4:p:315-330
    DOI: 10.1080/13504860802639360

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    Cited by:

    1. Fajardo, José & Corcuera, José Manuel & Menouken Pamen, Olivier, 2016. "On the optimal investment," MPRA Paper 71901, University Library of Munich, Germany.
    2. Rüschendorf Ludger & Wolf Viktor, 2015. "Cost-efficiency in multivariate Lévy models," Dependence Modeling, De Gruyter Open, vol. 3(1), pages 1-16, April.
    3. Martin Wallmeier, 2011. "Beyond payoff diagrams: how to present risk and return characteristics of structured products," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 25(3), pages 313-338, September.

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    Path-dependent pay-offs; Levy markets;


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