
How To's  

Maximum Likelihood
Estimation of Mean Reverting Process (2/19/03) Mean reverting processes are frequently used in real option models. For instance, some commodity prices (or their logarithms) are believed to fluctuate around some value associated with marginal production costs. Fundamental parameter knowledge is perhaps the most meaningful channel for model calibration. Nevertheless, data base methods are often needed to validate a particular model. This note develops a maximumlikelihood (ML) methodology for parameter estimation of 1dimensional OrnsteinUhlenbeck (OR) mean reverting processes. Furthermore, the methodology ultimately relies on a onedimensional search which greatly facilitates estimation and easily accommodtes missing or unevenly spaced (timewise) observations. Discounting a mean reverting cash flow (6/26/02) Sometimes it is desirable to view a cash flow as fluctuating in a random manner around some set level or path. Such behavior can be conveniently modeled by a mean reverting process. A typical mean reverting model that can easily be implemented in a spreadsheet is the exponential OrnsteinUhlenbeck(OU) mean reverting process which we will discuss here. Using simulation to calculate the NPV of a project (5/31/02) Monte Carlo simulation is fast becoming the technology of choice for evaluating and analyzing assets, be it pure financial derivatives or investments in real assets. 
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