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Parameter risk in the Black and Scholes model

Author

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  • Henrard Marc

    (Bank for International Settlements)

Abstract

We study parameter or estimation risk in the hedging of options. We suppose that the world is such that the price of an asset follows a stochastic differential equation. The only unknown is the (future) volatility of the asset. Options are priced and hedged according to the Black and Scholes formula. We describe the distribution of the profit and loss of the hedging activity when the volatility of the underlying is misestimated. A financial interpretation of the results is provided. Analytical bounds and numerical results for call, put, and portfolios complete our description.

Suggested Citation

  • Henrard Marc, 2003. "Parameter risk in the Black and Scholes model," Risk and Insurance 0310002, EconWPA.
  • Handle: RePEc:wpa:wuwpri:0310002
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    File URL: http://econwpa.repec.org/eps/ri/papers/0310/0310002.pdf
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    Keywords

    Black and Scholes model; option; parameter risk; profit distribution;

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