A Two-Method Solution to the Investment Timing Option
Henry Jacoby, December 1990Within the realm of derivative asset valuation, two types of methods are available for solving the investment timing option, each with a serious limitation for practical projects. Methods that use Monte Carlo simulation of risk-adjusted probability measures allow consideration of the complicated cash flow models typical of real projects, in the face of prespecified operating policies, but they do not provide an adequate way to determine what the optimal policy is. Formulation of the problem as an American option in the vein of Black-Scholes and Merton permits calculation of an optimal start policy, but only in situations with drastically simplified cash flow models.
The solution to this dilemma is the development of an approach which applies the two methods in tandem. The rights to explore and develop an oil field are used as an example, and Monte Carlo simulation is used to calculate the value of these rights as a function of start time and contemporaneous oil price. This payoff function is then input to a Black-Scholes-Merton option calculation. The resulting optimal start policy is then reinserted to the Monte Carlo model for further analysis of project and individual cash-flow magnitudes and risks. Also, possible bias because of numerical-analysis errors are checked by direct search of start policies in the vicinity of the calculated optimum.