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Option Pricing in ARCH-type Models

Author

Listed:
  • Jan Kallsen
  • Murad S. Taqqu

Abstract

ARCH models have become popular for modeling financial time series. They seem, at first, however, to be incompatible with the option pricing approach of Black, Scholes, Merton et al., because they are discrete-time models and possess too much variability. We show that completeness of the market holds for a broad class of ARCH-type models defined in a suitable continuous-time fashion. As an example we focus on the GARCH(1,1)-M model and obtain, through our method, the same pricing formula as Duan, who applied equilibrium-type arguments. Copyright Blackwell Publishers 1998.

Suggested Citation

  • Jan Kallsen & Murad S. Taqqu, 1998. "Option Pricing in ARCH-type Models," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 13-26.
  • Handle: RePEc:bla:mathfi:v:8:y:1998:i:1:p:13-26
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