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Pricing by Arbitrage Under Arbitrary Information
Author(s) -
Babbs Simon H.,
Selby Michael J. P.
Publication year - 1998
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00050
Subject(s) - arbitrage , economics , financial economics , rational pricing , risk arbitrage , index arbitrage , arbitrage pricing theory , econometrics , fixed income arbitrage , law of one price , statistical arbitrage , capital asset pricing model , monetary economics , price level , mid price
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.