Discussion Papers, Department of Finance and Management Science, Norwegian School of Economics (NHH)
No 2005/9:
On the Consistency of the Lucas Pricing Formula
Knut K. Aase ()
Abstract: In order to find the real market value of an asset in an
exchange economy, one would typically apply the formula appearing in Lucas
(1978), developed in a discrete time framework. This theory has also been
extended to continuous time models, in which case the same pricing formula
has been universally applied. While the discrete time theory is rather
transparent, there has been some confusion regarding the continuous time
analogue. In particular, the continuous time pricing formula must contain a
certain type of a square covariance term that does not readily follow from
the discrete time formulation. As a result, this term has sometimes been
missing in situations where it should have been included. In this paper we
reformulate the discrete time theory in such a way that this covariance
term does not come as a mystery in the continuous time version. It is
shown, e.g., that this term is of importance also in the equivalent
martingale measure approach to pricing. In most real life situations
dividends are paid out in lump sums, not in rates. This leads to a
discontinuous model, and adding a continuous time framework, it appears
that our framework is a most natural one in finance.
Keywords: Exchange economy; state price deflator; discrete time; continuous time; equivalent martingale measure; the Gordon growth model; (follow links to similar papers)
JEL-Codes: G00; (follow links to similar papers)
19 pages, November 30, 2005
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