Discount Factors Ex Post and Ex Ante, and Discounted Utility Anomalies II
15 Pages Posted: 14 Jan 2009
Date Written: January 12, 2009
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
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