Options and Bubbles

Posted: 17 Jul 2008

See all articles by Steven L. Heston

Steven L. Heston

University of Maryland - Department of Finance

Mark Loewenstein

University of Maryland - Robert H. Smith School of Business

Gregory A. Willard

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Date Written: March 2007

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 Classification: JEL G12 and G13

Suggested Citation

Heston, Steven L. and Loewenstein, Mark and Willard, Gregory A., Options and Bubbles (March 2007). The Review of Financial Studies, Vol. 20, Issue 2, pp. 359-390, 2007. Available at SSRN: https://ssrn.com/abstract=1161656 or http://dx.doi.org/10.1093/rfs/hhl005

Steven L. Heston

University of Maryland - Department of Finance ( email )

Robert H. Smith School of Business
Van Munching Hall
College Park, MD 20742
United States

Mark Loewenstein

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States

Gregory A. Willard

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States
617-253-2933 (Phone)
617-258-6855 (Fax)

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