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RFS Advance Access originally published online on May 15, 2006
Review of Financial Studies 2007 20(2):359-390; 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.

Options and Bubbles

Steven L. Heston
University of Maryland

Mark Loewenstein
University of Maryland

Gregory A. Willard
University of Maryland

Address correspondence to Steve Heston, Robert H. Smith School of Business, Van Munching Hall, University of Maryland, College Park, MD 20742, or e-mail: sheston{at}rhsmith.umd.edu.


  Abstract

The Black-Scholes-Merton option valuation method involves deriving and solving a partial differential equation (PDE). But this method can generate multiple values for an option. We provide new solutions for the Cox-Ingersoll-Ross (CIR) term structure model, the constant elasticity of variance (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. (JEL G12 and G13)


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