Academic journal article Real Estate Economics

Optimal Valuation of Claims on Noisy Real Assets: Theory and an Application

Academic journal article Real Estate Economics

Optimal Valuation of Claims on Noisy Real Assets: Theory and an Application

Article excerpt

A theory for valuing claims on noisy real assets is developed and applied. Central to the theory is determination of the dynamics for the best estimate of real asset value. The dynamics of the value estimate are shown to differ from the dynamics of the true asset value only in the arrival rate of information. The rate of information arrival in the value estimate can be faster or slower than information arrival in the true asset value, which can lead to unexpected outcomes in the valuation and exercise of options on noisy real assets. The theory we develop is illustrated through an application. An imperfectly competitive market for real estate development is examined, in which agents compete over the timing of lead investment. Information spillover and free-rider incentives are shown to cause significant delay in lead investment. Delay together with a competitive response once lead investment has occurred explain observed patterns of development in gentrified urban land markets and multistage development proje cts.

**********

We develop a theory for valuing claims that are contingent on noisy real asset values. This is an important topic--options on noisy real assets are ubiquitous and have substantial economic value. Examples of noisy contingent claims in a real estate setting include the valuation and exercise of proprietary development options in untested local real estate markets, strategic interaction among developers when investment outcomes are a public good, the exercise of leasing options, and the exercise of default options on debt that is securitized by real property. Other applications include the general process of research and development and the valuation of corporate assets such as mines, factories, and human capital.

We directly extend Childs, Ott and Riddiough (2002) (hereafter COR) by developing a theory for valuing claims on noisy assets when noise is mean-reverting. A major difference between the two papers is the role of time and information.

COR show how to optimally value a noisy real asset using current and historical information. In contrast, contingent-claims pricing is explicitly forward-looking. Agents form expectations as to future asset values and calculate a variance around those expected values. Contingent-claim valuation of noisy real assets thus requires a shift from a historical (ex post) perspective to a forward-looking (ex ante) perspective that explicitly depends on rational expectations.

The central result of this paper is the determination of forward-looking dynamics for the time-filtered value, which is the best estimate of the true asset value when true values are observed with noise. (1) These dynamics are shown to be identical to those associated with the true asset value, except that the variance rate of the time-filtered value depends crucially on the rate of time change in the variance of the estimation error (we call the estimation error the residual variance). The variance rate of the time-filtered value-which is a measure of the instantaneous rate of information arrival-may be higher or lower than the variance rate of the true asset value.

We show that revealed variance, which is the total variance of the time-filtered value as measured over a specified time interval, is bounded from above by the total information in the system. Revealed variance differs from the upper bound by the residual variance, and may equal or even exceed total variance associated with the true asset value.

Futures and options values that are contingent on noisy real asset values follow directly from the time-filtered value dynamics. A noisy asset's forward value is simply its expected value conditioned on the current value estimate. The value and exercise policy for an option on a noisy real asset are shown to depend critically on the revealed variance. Option value may exceed, equal, or be less than the full information option value depending on the arrival rate of information. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.