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Options and Bubbles

Steven L. Heston; Mark Loewenstein; Gregory A. Willard

University of Maryland, College Park

Review of Financial Studies 2007

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)

DOI
10.1093/rfs/hhl005
Volume
20 (2)
Pages
359-390
Language
en
Export
BibTeX
Sources
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