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# Real Options

In previous chapters, I restricted my discussion to the explicit valuation of financial options. In practice, the concept of optionality is something one faces daily in both a personal and business capacity. As such, it is important and interesting to see if one can use ideas discussed in the earlier chapters to value such options or decisions. Before discussing how to do this, I will first illustrate some practical examples of real options.

Real options[1] are options couched as decisions that one can optimize on. Examples of this include decisions to abandon a project, expand on an investment, scale down an operation, defer an investment, or cancel a project.[2] Although this has been the traditional definition of a real option, for the purpose of this book I will use the term real options in a broader context so as to also include the ability to quantify the value of a choice. More precisely, in addition to the above, I will use the term real options to also include the quantification of choices associated with operations management, optimal allocation, decision making under uncertainty, amongst others. As such, additional examples of real options include:

■ Deciding when to turn on and off power generating units (e.g., hydroelectric stations, fossil units, coal plants, nuclear stations) so to optimize profits.

■ Operating a gas storage facility in a manner to optimize storage facilities and manage the supply and demand for storage space as gas prices fluctuate and gas producers move between pumping out their stored gas and storing more gas.

■ Pricing airline seats to maximize the profitability associated with a flight route while taking into consideration the costs associated with the operation of that flight.

■ Valuing a company by taking into consideration its revenue, operating costs, debts, employee options, pension plans.

■ Shutting down a mine production facility due to a drop in commodity prices, taking into consideration the cost of layoffs and restarting the mine.

■ Determining the number of phone operators to be hired to ensure that incoming calls are not lost due to long waiting times.

■ Quantifying consumer behavior as it relates to the timing of optimally lapsing (or surrendering) an insurance policy or any other investment products.

Given the above backdrop, it is easy to realize how prevalent real options are in one's daily life. To add more color to the subject of real options, I next discuss two nontraditional applications of real options. While the first concerns the quantification of rational policyholder behavior when deciding when to optimally surrender a GMAB rider, the second relates to the quantification of the value associated with the hiring of servers so as to simultaneously minimize the waiting time in a queue and the cost of operating the queue.

• [1] After the publication of the seminal paper by Black and Scholes in 1973, the term real options was coined by Myers in 1977 to discuss the use of quantitative methods to value corporate liabilities.
• [2] See Hull (2012).

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