acca p4课件、真题及其他chp

1、Chapter 6Application of option pricing theory in investment decisionsStudy guideOption pricing theory:The five principal drivers of option valueAssumptions, structure, application and limitations of Black-Scholes modelApplication of option pricing theory in investment decisions:Real options within a

2、 projectUsing B-S model to value real options within a projectBasic concepts of optionA option is a contract that gives the holder the option to enter into a transactionCall (put) option: buyer of it acquires the right to buy (sell) the underlyingeither at a specific time in the future (European opt

3、ion) or within a specific future period (American option) at a price that is agreed (exercise/ striking price) when the contract is issued.Premium is the price paid by the option buyer (long position) to the seller (short position).Profiles of call options at expirationLong call Value of call option

4、: CT = Max ST-X,0Profit from the purchase : profit = CT C0Short callThe value of the call option for a seller is exactly the opposite of the value of the call option for the buyerProfit from short position: profit = C0 CTProfiles of put options at expirationLong put Value of put option: PT = Max X-S

5、T,0Profit from the purchase: profit = PT P0Short putThe value of the put option for a seller is exactly the opposite of the value of the put option for the buyerProfit from short position: profit = P0 PTProfit or loss at expirationXST0-cP&LXST0 cP&LXST0-pP&LXST0pP&LLong callLong putShort callShort p

6、utSTSTSTSTDeterminants of option valuesFive primary factors affecting the value and price of an option:Exercise price: Pe Price of the underlying: PaVolatility of the underlying: Time to expiration: tInterest rate: rThe five factors will affect the value of an option in directions of:PaPetrcallputDe

7、terminants of option valuesIntrinsic and time valueIntrinsic value is the value of the option if exercised now:If the intrinsic value is positive, the option is in the money (ITM)If the intrinsic value is zero, the option is at the money (ATM)If the intrinsic value is negative, the option is out of

8、the money (OTM)The difference between the market price of an option and its intrinsic value is the time value of the option.Call option: intrinsic value= Pa - PePut option: intrinsic value= Pe - Pa Black-Scholes option pricing modelAssumptions (p221):Lognormality: asset prices is lognormal, price ch

9、anges are normally distributedPerfect market: no taxes, no transaction costs, perfect security divisibility, no restrictions on short sellingConstant interest rates: over the option lifeConstant price volatility: over the option lifeTradability of asset: there is a market for the underlying asset an

10、d it can be tradedStock pays no dividends or interests over the options lifeB-S formulaValue of a European call option:Value of European put option:Value of American call option: the same as the value of an equivalent European optionNo exact analytic formula for the value for American put optionPa +

11、 P = Pee-rt + CP = C - Pa + Pee-rt P214 Q&A+2009-12-3(a)收益StX0卖权+收益St0股票=收益StX0组合AX（a）卖权+股票收益StX0买权+收益StX0债券 =收益StX0组合BX（b）买权+债券Real optionsAn option exists when the decision-maker has the right, but not the obligation, to take a particular action.Financial options relate to intangibles such as exch

12、ange rates or interest ratesReal options relate to tangibles, is the actual choices that a business can make in relation to investment opportunities.For a real option to exist, there must be uncertainty in terms of future cash flows and management must have the flexibility to respond to the uncertai

13、nty as it evolves.Limitations of NPV ruleDoes not explicitly deal with uncertainty when valuing the project; use of a single discount rate does not allow for the many sources of uncertainty surround the project.Fails to consider the extent of managements flexibility to respond to uncertainties surro

14、und the project.Real optionsReal options embedded in projects:Option to delay: a firm can has rights to delay taking a project or product until later (2011-6-4)A call option: underlying is the present value; exercise price is the investmentOption to expand: firms invest in projects which allow them

15、to make further investments in the future or enter new market (P220 Q&A; 2012-6-1(c)A call option: underlying is the present value; exercising price is the additional investmentOption to abandon: firms may have the option to cease a project during its life. (P219 Q&A)A put option: underlying is the

16、present value of remaining cash flows; exercise price is the liquidation valueOption to redeploy: the firm can use its productive assets for activities other than the original oneA call option: underlying is the present value of new project; exercise price is the switching costsApplication of B-S mo

17、del to value real optionP219-220 Q&ADetermine the real option is a call or put optionDetermine the input variables used in B-S model, especially Pa and PeUse the option pricing model (for call or put) right When making investment decisions, the value of real option should be added to the traditional

18、 project NPV to get total NPV. *2012/6-1(c); 2011/6-4; 2007/12-3Implication of real option valuationThe company does not actually receive the value of real optionIts inclusion in the NPV calculation takes into account the uncertainty of project, and the time before the company has to make the decisi

19、onwith the real option, the company can reduce the uncertainty surrounding the projectLimitations of B-S modelLimitations of B-S model2007-12-3(c)Limitations of B-S model in valuing real optionThere are certain differences between the application of the B-S model to financial options and real option

20、sSince the underlying asset is not tradedThe main practical problem is the estimation of volatilityImplication of real options for capital budgetingReal options provide a more accurate estimate of a projects valueShifts the focus away from trying to predict the future “perfectly” to identifying what

21、 can be done about responding to uncertainty.Promotes a discipline that extends over the entire life of the projectGives the decision-makers the ability to identify the optimal level of flexibility by providing estimates of the value of increased flexibilitybut this great accuracy comes at a costAna

22、lysis of real options is much more complex and requires greater investment in time and effort.KaplanFor quoted underlying assets, its mid-price is usually used for option pricingVolatility= STD DEV. of price change annuallyDiscount factor using continuous rate is DF=e-rtThe value of European and US

23、call options on shares not paying dividends before expiration are equalWhen dividends are payable before expiration date, Pa es Pa-PV(div.)Conventional investment appraisal techniques typically undervalue flexibility within projects with high uncertainty.Examiners article(2009/11): Application of op

24、tion pricing to valuation of firmsBSM provides a general framework for company valuation and helps in those situations where conventional techniques cannot be used, or where they do not fully reflect the risks involved.The price of a firm pays for its shares in a limited liability company represents

25、 the premium on a call option written by the lenders on the underlying assets of the business. Examiners article(2009/11): Application of option pricing to valuation of firmsExaminers article(2009/11): Application of option pricing to valuation of firmsExaminers article(2009/11): Application of opti

26、on pricing to valuation of firmsThe value of underlying assetWhere the assets of a firm are actively traded and easily liquidated then their current market value should be used, such as in the case of a bankIn the case of other companies, value in use will normally be based on the PV of the future c

27、ash flows that the firms assets are expected to generate over their useful lives.Examiners article(2009/11): Application of option pricing to valuation of firmsThe volatility of assetsIs the most difficult variable to estimate One approach implies the asset value and the volatility from the BSMAnoth

28、er approach is to project and simulate the expected future cash flows of the business.Examiners article(2009/11): Application of option pricing to valuation of firmsThe effective exercise priceEstimate the average term to maturity of the companys outstanding long-term debt;Estimate the average coupo

29、n rate;Use the current yield on the companys debt to estimate the market value of a notional bond;Estimate the repayment value of an equivalent bond where no interest is paid.Examiners article(2009/11): Application of option pricing to valuation of firmsAfter achieving good estimates of the input va

30、riables, the next task is to bring it all together in the BSM.Example of Northern Rock*2010-6-2(bcd)Examiners article(2009/11): Application of option pricing to valuation of firmsThe equity of a business can still have substantial positive value even though the balance sheet shows a nil balance on a fair value basis,Because the presence of limited liability protects the investors from loss, and they hav