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Option Pricing Under Incompleteness and Stochastic Volatility

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  • Norbert Hofmann
  • Eckhard Platen
  • Martin Schweizer

Abstract

We consider a very general diffusion model for asset prices which allows the description of stochastic and past-dependent volatilities. Since this model typically yields an incomplete market, we show that for the purpose of pricing options, a small investor should use the minimal equivalent martingale measure associated to the underlying stock price process. Then we present stochastic numerical methods permitting the explicit computation of option prices and hedging strategies, and we illustrate our approach by specific examples. Copyright 1992 Blackwell Publishers.

Suggested Citation

  • Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
  • Handle: RePEc:bla:mathfi:v:2:y:1992:i:3:p:153-187
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    References listed on IDEAS

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