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A Note on Delta Hedging in Markets with Jumps

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  • Aleksandar Mijatovi\'c
  • Mikhail Urusov
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    Abstract

    Modelling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black--Merton--Scholes model where it perfectly replicates contingent claims. From the theoretical viewpoint, there is no reason for this to hold in models with jumps. However in practice the delta-hedging strategy is widely used and its potential shortcoming in models with jumps is disregarded since such models are typically incomplete and hence most contingent claims are non-attainable. In this note we investigate a complete model with jumps where the delta-hedging strategy is well-defined for regular payoff functions and is uniquely determined via the risk-neutral measure. In this setting we give examples of (admissible) delta-hedging strategies with bounded discounted value processes, which nevertheless fail to replicate the respective bounded contingent claims. This demonstrates that the deficiency of the delta-hedging strategy in the presence of jumps is not due to the incompleteness of the model but is inherent in the discontinuity of the trajectories.

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    File URL: http://arxiv.org/pdf/1103.4965
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1103.4965.

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    Date of creation: Mar 2011
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    Handle: RePEc:arx:papers:1103.4965

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