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RFS Advance Access published online on May 15, 2006
Review of Financial Studies, doi:10.1093/rfs/hhl005
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© The Author 2006. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Article

Options and Bubbles

Steven L. Heston 1 *, Mark Loewenstein 1, and Gregory A. Willard 1
1 University of Maryland

* To whom correspondence should be addressed.
Steven L. Heston, E-mail: sheston{at}rhsmith.umd.edu


  Abstract

The Black-Scholes-Merton option valuation method involves deriving and solving a PDE. But this method can generate multiple values for an option. We provide new solutions for the CIR term structure model, the CEV model, and the Heston stochastic volatility model. Multiple solutions reflect asset pricing bubbles, dominated investments, and (possibly infeasible) arbitrages. We provide conditions to rule out bubbles on underlying prices. If they are not satisfied, put-call parity might not hold, American calls have no optimal exercise policy, and lookback calls have infinite value. We clarify a longstanding conjecture of Cox, Ingersoll, and Ross (1985).


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