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Unformatted text preview: the effect of time on the value of money; however, this is not immediately apparent in
the option pricing equations. In option theory, the time value of money is incorporated through the risk-free rate of return and by way of a “change of
probability” (Smith and McCardle, 1997, Baxter and Rennie, 1996 and Trigeorgis,
1996, all provide good explanations of this) (Galli et al., 1999).
The application of these methods to “real”, as opposed to financial options, dates back
to Myers (1977) and was popularised by Myers (1984) and Kester (1984) (see Mason
and Merton (1985) for an early review and Dixit and Pindyck (1994) for a survey of
the current state of the art). In this approach rather than determining project values
and optimal strategies using subjective probabilities and utilities, the analyst seeks
market-based valuations and policies that maximise these market values. In particular, the analyst looks for a portfolio of securities and a trading strategy that
exactly replicates the project’s cash flows in all future times and all future states. The
value of the project is then given by the current market price of this replicating
portfolio. The fundamental principal underlying this approach is the “no arbitrage”
principle or the so-called “law of one price”: two investments with the same payoffs
at all time and in all states – the project and the replicating portfolio must have the
The idea of investments as options is well illustrated in the decision to acquire and
exploit natural resources. The similarity of natural resources to stock market options
is obvious. Stock market options give the holder the right but not the obligation to
acquire or sell securities at a particular price (the strike price) within a specified
timeframe but there is not an obligation to do so. The owner of an undeveloped oil
well has the possibility of acquiring the proceeds from the oil well’s output but does
not have an obligation to do so and the company may defer selling the proceeds of the
asset’s output. Further, much as a stock pays dividends to its owner, the holder of
developed reserves receives production revenues (net of depletion). Table 5.9 lists the
important features of a call option on a stock (or, at least, all those necessary to enable
114 one to price it) and the corresponding aspects of the managerial option implicit in
holding an undeveloped reserve (Siegel et al., 1987).
Using this analogy, Brennan and Schwartz (1985) worked out a way to extend it to
valuing natural resource projects using Chilean copper mines to illustrate the
procedure. They reasoned that managerial flexibility should improve the value of the
project. They allowed for three options: production (when prices are high enough),
temporary shutdown (when they are lower) and permanent closure (when prices drop
too low for too long). Different costs were associated with changing from one
production option to another. They found the threshold copper prices at which it was
optimal to close a producing mine temporarily (Galli et al., 1999).
STOCK CALL OPTION
Current Stock Price
Time to expiration
Riskless rate of...
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This document was uploaded on 03/30/2014.
- Summer '14
- The Land