期权期货及其衍生品第34弹.ppt
Chapter 34Real Options,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,1,An Alternative to the NPV Rule for Capital Investments,Define stochastic processes for the key underlying variables and use risk-neutral valuationThis approach(known as the real options approach)is likely to do a better job at valuing growth options,abandonment options,etc than NPV,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,2,The Problem with using NPV to Value Options,Consider the example from Chapter 12:risk-free rate=12%;strike price=$21 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?,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,3,Correct Discount Rates are Counter-Intuitive,Correct discount rate for a call option is 42.6%Correct discount rate for a put option is 52.5%,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,4,General Approach to Valuation,We can value any asset dependent on a variable q byReducing 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,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,5,Extension to Many Underlying Variables,When there are several underlying variables 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-neutralNote that the variables do not have to be prices of traded securities,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,6,Estimating the Market Price of Risk Using CAPM(equation 34.2,page 740),Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,7,Types of Options,AbandonmentExpansionContractionOption to deferOption to extend life,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,8,Example of Application of Real Options Approach to Valuing A at end of 1999(Business Snapshot 34.1;Schwartz and Moon),Estimate stochastic processes for the companys sales revenue and its average growth rate.Estimated the market price of risk and other key parameters(cost of goods sold as a percent of sales,variable expenses as a percent of sales,fixed expenses,etc.)Use Monte Carlo simulation to generate different scenarios in a risk-neutral world.The stock price is the average of the present values of the net cash flows discounted at the risk-free rate.,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,9,Example(page 746),A company has to decide whether to invest$15 million to obtain 6 million units of a commodity at the rate of 2 million units per year for three years.The fixed operating costs are$6 million per year and the variable costs are$17 per unit.The spot price of the commodity is$20 per unit and 1,2,and 3-year futures prices are$22,$23,and$24,respectively.The risk-free rate is 10%per annum for all maturities.,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,10,The Process for the Commodity Price,We assume that this is d ln(S)=q(t)aln(S)dt+s dzwhere a=0.1 and s=0.2We build a tree as in Chapter 33,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,11,The Tree of Commodity Prices(Figure 34.1),Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,12,Valuation of Base Project;Fig 34.2,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,13,Valuation of Option to Abandon;Fig 34.3(No Salvage Value;No Further Payments),Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,14,Value of Expansion Option;Fig 34.4(Company Can Increase Scale of Project by 20%for$2 million),Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,15,
