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Pricing by Arbitrage Under Arbitrary Information

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  • Simon H. Babbs
  • Michael J. P. Selby

Abstract

A substantial applications literature on pricing by arbitrage has effectively restricted information to that arising solely from securities markets; return distributions are then governed solely by past prices. We reconsider pricing by arbitrage in markets rendered incomplete by arbitrary information, which, moreover, may influence required returns. We show that contingent claims depending solely on securities’ normalized price histories are priced by arbitrage if and only if all risk‐adjusted probabilities agree upon the law of primitive securities’ normalized prices. We show how existing diffusion‐based results can be preserved, and resolve an issue relating to Merton's (1973) stochastic interest rate model.

Suggested Citation

  • Simon H. Babbs & Michael J. P. Selby, 1998. "Pricing by Arbitrage Under Arbitrary Information," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 163-168, April.
    • Handle: RePEc:bla:mathfi:v:8:y:1998:i:2:p:163-168
    DOI: 10.1111/1467-9965.00050
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    Cited by:

    1. Foldes, Lucien, 2000. "Valuation and martingale properties of shadow prices: An exposition," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1641-1701, October.
    2. Carey, Alexander, 2010. "Higher-order volatility: time series," MPRA Paper 21087, University Library of Munich, Germany.

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