文档介绍：Chapter 28 Real Options
1
An Alternative to the NPV Rule for Capital Investments
Define stochastic processes for the key underlying variables and use risk-neutral valuation
This approach (known as the real options approach) is likely to do a better job at valuing growth options, abandonment options, etc than NPV
2
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
The Problem with using NPV to Value Options
Consider the example from Chapter 10
Suppose that the expected return required by investors in the real world on the stock is 16%. What discount rate should we use to value an option with strike price $21?
Stock Price = $22
Stock price = $20
Stock Price=$18
3
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Correct Discount Rates are Counter-Intuitive
Correct discount rate for a call option is %
Correct discount rate for a put option is –%
4
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
General Approach to Valuation
We can value any asset dependent on a variable q by
Reducing the expected growth rate of q by ls where l is the market price of q-risk and s is the volatility of q
Assuming that all investors are risk-neutral
5
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Extension to Many Underlying Variables
When there are several underlying variable qi we reduce the growth rate of each one by its market price of risk times its volatility and then behave as though the world is risk-neutral
Note that the variables do not have to be prices of traded securities
6
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Estimating the Market Price of Risk (equation , page 665)
7
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Schwartz and Moon Have Applied the Real Options Approach to Valuing
They estimated stochastic processes for pany’s sales revenue and its revenue