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Exploding hedging errors for digital options

Author

Listed:
  • Christoph Gallus

    (Deutsche Bank AG, Equities, Global Equity Derivatives, D-60325 Frankfurt am Main, Germany Manuscript)

Abstract

In the complete market model of geometric Brownian motion, all kinds of exotic options can be priced and hedged perfectly using a delta hedging strategy which duplicates the option's payoff. If trading takes place in a frictionless market, this delta hedging strategy is said to eliminate the option writer's risk completely. It will be shown that for certain contingent claims, for example digital options, the hedge can fail completely if the underlying risky asset does not follow the assumed geometric Brownian motion. Indeed, the hedging error may diverge and delta hedging can actually increase the risk of the option writer.

Suggested Citation

  • Christoph Gallus, 1999. "Exploding hedging errors for digital options," Finance and Stochastics, Springer, vol. 3(2), pages 187-201.
    • Handle: RePEc:spr:finsto:v:3:y:1999:i:2:p:187-201
    Note: received: October 1996; final version received: February 1998
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    Citations

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    Cited by:

    1. Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.
    2. Meyer, Thomas O., 2003. "Calculation and comparison of delta-neutral and multiple-Greek dynamic hedge returns inclusive of market frictions," International Review of Economics & Finance, Elsevier, vol. 12(2), pages 207-235.
    3. Augusto Blanc-Blocquel & Luis Ortiz-Gracia & Rodolfo Oviedo, 2023. "Hedging At-the-money Digital Options Near Maturity," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.
    4. Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.

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