Discount Factors Ex Post and Ex Ante, and Discounted Utility Anomalies II

15 Pages Posted: 14 Jan 2009

See all articles by Svetlana Boyarchenko

Svetlana Boyarchenko

University of Texas at Austin - Department of Economics

Sergei Levendorskii

Calico Science Consulting

Date Written: January 12, 2009

Abstract

Using the real options approach, we show that discounted utility anomalies result from the optimizing behavior of an individual with standard preferences, who perceives the utility from consumption in the future as uncertain, and believes that she can wait. The fair price (or compensation) that the individual agrees to pay (or accept) is the expected value of utility of the future gain (or loss) multiplied by certain non-exponential discount factors ex ante. These factors are different for gains and losses. After the decision of exchange had been made, valuation ex post reduces to calculation of the standard expected present value. The formulas for the discount factors are derived in a discrete time model, where the individual believes that she can wait for one period, and in a continuous time model, where the individual believes that she can wait for an infinitesimally small time interval. In the discrete time model, a simple backward induction argument is used. The proofs in the continuous time model are based on the general formula for the gap between the early exercise boundary and strike, at expiry, for American call and put options. In the first variant of the paper, the formulas for the discount factors were derived assuming that the individual believes that she can wait till infinity.

Keywords: hyperbolic discounting, bid-ask asymmetry, gain-loss asymmetries

JEL Classification: C91, C93, D81, D91, G12

Suggested Citation

Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., Discount Factors Ex Post and Ex Ante, and Discounted Utility Anomalies II (January 12, 2009). Available at SSRN: https://ssrn.com/abstract=1326708 or http://dx.doi.org/10.2139/ssrn.1326708

Svetlana I. Boyarchenko

University of Texas at Austin - Department of Economics ( email )

Austin, TX 78712
United States

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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