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Hedging Large Portfolios of Options in Discrete Time

Author

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  • B. Peeters
  • C. L. Dert
  • A. Lucas

Abstract

The problem studied is that of hedging a portfolio of options in discrete time where underlying security prices are driven by a combination of idiosyncratic and systematic risk factors. It is shown that despite the market incompleteness introduced by the discrete time assumption, large portfolios of options have a unique price and can be hedged without risk. The nature of the hedge portfolio in the limit of large portfolio size is substantially different from its continuous time counterpart. Instead of linearly hedging the total risk of each option separately, the correct portfolio hedge in discrete time eliminates linear as well as second and higher order exposures to the systematic risk factors only. The idiosyncratic risks need not be hedged, but disappear through diversification. Hedging portfolios of options in discrete time thus entails a trade-off between dynamic and cross-sectional hedging errors. Some computations are provided on the outcome of this trade-off in a discrete-time Black-Scholes world.

Suggested Citation

  • B. Peeters & C. L. Dert & A. Lucas, 2008. "Hedging Large Portfolios of Options in Discrete Time," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(3), pages 251-275.
  • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:3:p:251-275
    DOI: 10.1080/13504860701718471
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    Keywords

    Option hedging; discrete time; preference free valuation; hedging errors; cross-sectional hedging; static hedging; JEL Codes: G13; G12;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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