Real Options in Theory and Practice

By Graeme Guthrie | Go to book overview

3
Valuing Single-period Cash Flows

This chapter introduces the valuation approach that is used throughout the remainder of the book. By the time we have finished working through its contents we will be able to estimate the market value of a risky cash flow that will be received after one period of time elapses. In the next chapter we see how to use this approach to value a stream of cash flows that will be received in many future periods. Then, in Chapter 5, we modify the approach so that we can simultaneously calculate the market value and identify policies that maximize the market value. For now, though, we focus on the simplest case of valuing a cash flow to be received one period in the future.

We start by using the binomial tree introduced in Section 2.2, together with the so-called law of one price, to reduce the problem of valuing an arbitrary cash flow to the problem of valuing a particular asset known as the spanning asset. Thus, no matter what cash flow we need to value, we must start by valuing the spanning asset. In Section 3.2 we see how to calculate its market value when the state variable is the price of a traded asset, while Section 3.3 shows an alternative approach that is available when forward or futures contracts on the state variable are traded. Section 3.4 shows a different approach, which can be used even when the state variable is not the price of a traded asset. The valuation approach is summarized in Section 3.5.


3.1 ARBITRAGE-FREE ASSET PRICES

Our valuation problem is expressed using the modeling framework introduced in Chapter 2. That is, a state variable currently takes the value X and, after one period has elapsed, will equal either Xu or Xd. We may be interested in estimating the

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