Journal of Real Estate Finance and Economics, 28:2/3, 109±121, 2004
# 2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
Effects of Noise on Optimal Exercise Decisions:
The Case of Risky Debt Secured by Renewable
PAUL D. CHILDS
Carol Martin Gatton College of Business and Economics, University of Kentucky, Lexington, KY 40506±0034
STEVEN H. OTT
Belk College of Business Administration, University of North Carolina at Charlotte, Charlotte,
TIMOTHY J. RIDDIOUGH
School of Business, University of Wisconsin±Madison, Madison, WI 53705
This paper considers the valuation and default exercise policy of risky coupon debt that is secured by a lease-
encumbered noisy real asset. For parameter values used in our analysis, asset value noise is shown to reduce the
value of waiting to default. Moreover, the borrower is shown to delay default exercise until the noisy signal of
asset value is far into-the-money. This latter ®nding provides an information-based explanation for the apparent
under-exercise of the mortgage default option that has been observed in the literature. An implication of this
®nding is that, if the claimholder recognizes that noise exists, but the empiricistÐwho is trying to compare
observed exercise policy with that predicted by a noiseless model of asset pricesÐdoes not, a ``sub-optimal''
exercise policy may be inferred when in fact the policy is rational given the information available. This
explanation is consistent with evidence from mortgage default studies as to why the observed default exercise
boundary is lower than that predicted by standard theoretical option-based models.
Key Words: noise, real options, debt contacting, leases
Real assets often exhibit unique locational, physical, and contractual-relational
characteristics that make their payoffs dif®cult to replicate using combinations of other
real or ®nancial assets. This heterogeneity is largely why real estate assets trade in
decentralized markets, with attendant search and matchmaking costs (see, for example,
Wheaton, 1990; Williams, 1993). Infrequent decentralized trading and the lack of a
continuously available benchmark create noise in real asset markets, implying that precise
asset values are unobservable.
In this paper we apply the theory developed in Childs et al. (2001, 2002b) for valuing