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Efficient hedging for a complete jump-diffusion model

Author

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  • Kirch, Michael
  • Krutchenko, R. N.
  • Melnikov, Aleksandr V.

Abstract

This paper is devoted to the problem of hedging contingent claims in the framework of a complete two-factor jump-diffusion model. In this context, it is well understood that every contingent claim can be hedged perfectly if one invests the unique arbitrage-free price. Based on the results of H. Föllmer and P. Leukert [4][ 5] in a general semimartingale setting, we determine the unique hedging strategies which minimize a suitably defined shortfall risk under a given cost constraint. We derive explicit formulas for this so-called efficient or quantile hedging strategy for a European call option. We then compare the performance of the optimal strategy for different degrees of the investor's risk-aversion.

Suggested Citation

  • Kirch, Michael & Krutchenko, R. N. & Melnikov, Aleksandr V., 2002. "Efficient hedging for a complete jump-diffusion model," SFB 373 Discussion Papers 2002,27, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200227
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    Keywords

    Efficient hedging; Quantile Hedging; jump-diffusion; martingale Measure;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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