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Complete Models with Stochastic Volatility

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  • David G. Hobson
  • L. C. G. Rogers

Abstract

The paper proposes an original class of models for the continuous-time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log-price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference-independent options prices. Copyright Blackwell Publishers 1998.

Suggested Citation

  • David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48.
  • Handle: RePEc:bla:mathfi:v:8:y:1998:i:1:p:27-48
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    References listed on IDEAS

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