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Is the gamma risk of options insurable?

Author

Listed:
  • Egli, Daniel
  • Blum, Peter
  • Dacorogna, Michel M
  • Müller, Ulrich A

Abstract

In this article we analyze the risk associated with hedging written call options. We introduce a way to isolate the gamma risk from other risk types and present its loss distribution, which has heavy tails. Moving to an insurance point of view, we define a loss ratio that we find to be well behaved with a slightly negative correlation to traditional lines of insurance business, offering diversification opportunities. The tails of the loss distribution are shown to be much fatter than those of the underlying stock returns. We also show that badly estimated volatility, in the Black-Scholes model, leads to considerably biased values for the replicating portfolio. Operational risk is defined as caused by imperfect delta hedging and is found to be limited in today's markets where the autocorrelation of stock returns is small.

Suggested Citation

  • Egli, Daniel & Blum, Peter & Dacorogna, Michel M & Müller, Ulrich A, 2005. "Is the gamma risk of options insurable?," MPRA Paper 8564, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:8564
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    References listed on IDEAS

    as
    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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    More about this item

    Keywords

    Option; Insurance; Risk;
    All these keywords.

    JEL classification:

    • G19 - Financial Economics - - General Financial Markets - - - Other
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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