![]() ![]() ![]() (The difference between American and Bermudan options is that early exercise can occur at any time prior to expiration with an American option but only on a discrete number of dates for the the Bermudan option. Most real options situations can be modeled as American or Bermudan options because they possess early exercise features. This insight allows managers to use option pricing techniques and dynamic programming in valuing real assets and business decisions. Researchers noticed that the future decisions of a company could be conceptualized as call and put options much like the options that trade on financial exchanges.įor instance in the mine example below, at each decision date the operator has an option to abandon the project (if abandonment hasn’t already occurred), as well as options to change the operating mode of the project from open to close or closed to open depending upon the current state. Real options grew out of academic research in valuing financial options. Real options are models of managerial flexibility, which can be defined as the value created by the future decisions that managers possess in response to both economic and non-economic uncertainties. For an alternative approach to extending LSM to real options models, see section VIII of Sick & Gamba (2010), which includes a nice and simple example.īefore I discuss the model’s details, let’s do a brief review of real options and discuss several methods used for solving them. Since there are several ways to extend the LSM algorithm to multi-state switching options, the LSM variant that I use is from Cortazar et al (2008) (CGU) which also solves the B&S mine valuation model. The example in this post is a natural resource investment, specifically the mine valuation model from a classic real options paper, Brennan & Schwartz (1985) (henceforth “B&S”). This is an exciting area of finance as it has the potential to greatly improve business decision making. In future posts I plan on reconstructing several more examples including presenting a real estate case study. For a more extensive list see Nadarajah, Margot, & Secomandi (2017). Within the real options framework it has been applied to valuing pharmaceutical R&D, gas storage facilities, and renewable energy just to name a few. However the algorithm is very general and highly adaptable to many real options situations. This algorithm was introduced in an influential paper for the valuation of American style options, Longstaff & Schartz (2001). So I thought I would post a basic real options model that is solved using an approximate dynamic programming technique called Least Squares Monte Carlo simulation (LSM). Additionally advances in both algorithms and computing power allow the use of simulation to solve real options problems without the use of any sophisticated mathematics. With the rise of data science, and businesses becoming more comfortable with quantitative approaches to decision making, I suspect that real options analysis will become a standard technique in the financial analyst’s arsenal. They dedicated their book to “The Future” as they foretell of a time when real options analysis is the dominant paradigm for investment valuation and capital budgeting. ![]() The classic academic text on real options is Dixit & Pindyck (1994). 1.Many finance academics have long touted the superiority of the real options valuation approach for capital investment analysis over the traditional discounted cash flow method. The option value is then the expected value of the maximum of the difference between the two discounted distributions or zero. The method captures the real option value by discounting the distribution of operating profits at R, the market risk rate, and discounting the distribution of the discretionary investment at r, risk-free rate, before the expected payoff is calculated. The mathematical equation for the DM Method is shown below. 1 Typical project cash flow with uncertainty ![]()
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