Lecture 4

Lecture 4 - Black-Scholes approach to the valuation of real...

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Black-Scholes approach to the valuation of real options Differences between real and financial options , which are crucial for the Black-Scholes approach: 1. The underlying asset is not traded Option pricing theory is built on the premise that a replicating portfolio can be created using the underlying asset and riskless lending and borrowing. 2. The price of the asset may not follow a continuous process If there are no price jumps, as it is with most real options, the model will underestimate the value of deep out-of-the-money options. o One solution is to use a higher variance estimate to value deep out-of-the-money options and lower variance estimates for at-the-money or in-the-money options. o Another is to use an option pricing model that explicitly allows for price jumps, though the inputs to these models are often difficult to estimate. 3. The variance may change over the life of the option The assumption that option pricing models make, that the variance is known and does not change over the option lifetime, is not unreasonable when applied to listed short-term options on traded stocks. When option pricing theory is applied to long-term real options, there are problems with this assumption, since the variance is unlikely to remain constant over extended periods of time and may in fact be difficult to estimate in the first place. 4. Exercise is not instantaneous The option pricing models are based upon the premise that the exercise of an option is instantaneous. This assumption may be difficult to justify with real options, where exercise may require the building of a plant or the construction of an oil rig, actions which are unlikely to happen in an instant. The fact that exercise takes time also implies that the true life of a real option is often less than the stated life. Valuing Natural Resource Options/ Firms Input Estimation Process 1. Value of Available Reserves of the Resource Expert estimates (Geologists for oil. .); The present value of the after-tax cash flows from the resource are then estimated. 2. Cost of Developing Reserve
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Lecture 4 - Black-Scholes approach to the valuation of real...

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