期權(quán)管理知識(shí)講解-英文版

1、期權(quán)管理知識(shí)講解-英文版ReadingHBR Article: Stock options have had a very negative press of late and here we have Nobel prize winner Robert Merton and other high-profile academics discussing some of the issues and argue for stock options to be put on the balance sheet. This will actually come into force at the

2、start of 2005.Futures contracts are contracts which cost nothing to enter. This is because if you are in the long position you gain when the spot price of the underlying asset, S, rises, you also lose when the price goes down (and vice versa with the short position).An option is similar in many ways

3、 to a futures contract in that you have the right to buy (or sell) at a certain price in the future (this time it is called the exercise price). However, the principal difference is that you dont have the obligation to buy at this price you have the option as whether or not you choose to buy (or sel

4、l) at this price.Clearly you will have to pay some premium for this privilege. How much?Options: IntroductionWhy options?Options can again be used for three main purposes: hedging, speculating and arbitraging.An option enables you to hedge against adverse market movements (e.g. price of oil, price o

5、f corn, stock market value, interest rate changes) without, necessarily, limiting your potential gain should the market actually move in your favour.Just like with a futures contract an option enables you to leverage your position and hence make it easier to speculate on market movements.Again with

6、options as the financial instruments become more complex then there are more arbitrage opportunities to exploit.Options: definitionsAn option gives the holder of the option the right, but not the obligation to buy an economic good (usually called the underlying asset), at a specific point in time (t

7、he expiry date), for a specific price (the exercise price).The party who bought the option is said to be in the long position, the party who sold (or wrote) the option is said to be in the short position.A Call Option gives the holder of the option the right, but not the obligation, to buy the under

8、lying asset.A Put Option gives the holder of the option the right, but not the obligation, to sell the underlying asset.Options: TypesThere are two main types of options:European options: European options can only be exercised on the expiry date.American options: American options can be exercised at

9、 any time between the date of purchase and the expiry date.These names have no geographical significance, hence it is possible to buy American options on European options exchanges.Most traded options are American options, although we will start our discussion by assuming that all options are Europe

10、an.Options: ExampleConsider both call and put options on Microsoft shares, expiring on March 20, 2004. Both have exercise prices of $25 and each option enables the holder to buy or sell the Microsoft shares at this price. The current value of Microsoft shares is $27.03. Call options are currently pr

11、iced at $2.20 and put options at $0.13.Microsoft current option pricesOptions Product SpecificationsThe payoffs from these options for different values of the Microsoft shares are as follows: Options: exampleValue of Microsoft Shares on March 20 ($)Payoff to buyer of call option ($)Payoff to buyer o

12、f put option ($)1001515010200525003050351004015045200Options: exampleClearly is the value of a Microsoft share exceeds the exercise prices then the holder of the call option will exercise his right to exercise and make a profit of the share price less the exercise price. If it is less then he will n

13、ot, in this case the option expires worthless.In the case of the put option the if the Microsoft share price drops below the exercise price then she will exercise and receive the difference between these prices. If it is more then the option expires worthless.From this we note that options must alwa

14、ys have positive or zero value as the least they can ever be worth is zero.Options: leverageOptions on individual shares are actually 100 shares.Notice that if the value of Microsoft shares at expiry at $30 then the holder of the call option makes a profit of$500 $220 = $280or a return of 280/220 =

15、127%. If instead he would have spent this money on buying the shares then the return would have been only (30 27.03)/30 = 9.8%.This is an example of the leverage an investor can obtain from buying options rather than the underlying assets themselves.Notice however that is the share price is only $25

16、, then the investor has made returns of 100% (as the option expires worthless) compared to a loss of 7.5% from buying the shares.Payoff from a call optionIt is possible to depict the payoffs from this call option graphically:25Share price at expiryCalloption value at expiry (PAYOFF)Payoff from a put

17、 optionand also the put option:25Share price at expiryPutoption value at expiry (PAYOFF)Profit diagramsNotice that these graphs do not include the premium which has been paid for this option, if we include the amount paid then what we see is the following graphs:2525-$2.20-$0.13Profit from buying th

18、e Microsoft call option for $2.20Profit from buying the Microsoft put option for $0.13Writing (or selling) optionsWe have seen what happens when you buy call or put options. What about for the person who has sold (or written) these options?If you write a call option then it means that, first, you re

19、ceive the option premium. At the expiry of the option then you are obliged to sell the underlying asset at the exercise price if the holder wishes to buy it. In this case you lose out by the difference in the prices, if however, they dont exercise their option then you simply keep the premium. Note

20、that these transactions are zero sum games, whatever the holder gains, the writer loses.It is similar for a put option only you have to buy at the exercise price if the holder wants to sell.Payoff when writing optionsReturning to the Microsoft example, the payoffs are as follows:Value of Microsoft S

21、hares on March 20 ($)Payoff to writer of call option ($)Payoff to writer of put option ($)100-15150-10200-5250030-5035-10040-15045-200Payoffs from writing optionsIn a similar way we can graphically depict the payoffs from writing call and put options on Microsoft.2525Share price at expiryShare price

22、 at expiryPayoff at expiry from writing a call optionPayoff at expiry from writing a put optionProfit from writing optionsIt is also to see the profit from writing the Microsoft call and put options:2525Share price at expiryProfit at expiry from writing a call optionProfit at expiry from writing a p

23、ut option$2.20$0.13Option principlesClearly buying and writing (selling) options is a zero sum game. Everything made by the buyer is lost by the writer and vice versa.Note that both buying calls and selling puts are bets that the market will go up. Buying puts and writing calls are bets that the mar

24、ket will go down.This option was treated as if it were a European option abut in reality this option would be American thus exercisable at any time. This would make the analysis slightly different as you would have to consider if there are optimal times to exercise the option.Options: detailsOn a re

25、gulated exchange then the contract between parties is again secured by the exchange or by the Option Clearing Corporation (OCC). In fact if you buy an option you dont have a counterparty, rather you actually buy it from the exchange who it turn buy options from parties who want to sell.It is possibl

26、e to terminate your option position before expiry simply by selling (if you had originally bought) or buying (if you had originally sold), you will make (or lose) the difference between the price you bought or sold at and the price today.Options more terminologyNear-the-money or at-the-money are opt

27、ions where the exercise price is close to the current share price.Out-of-the-money options are options where immediate exercise would produce a negative payoff (i.e the share price is higher than the exercise price for a put option).In-the-money options are options where immediate exercise would pro

28、duce a positive payoff (i.e. the share price is higher than the exercise price for a call option).LEAPS are long term options on individual shares or stock indices.FLEX options are options where the investors determine the exercise price and expiry dates (See press release document in lecture).Optio

29、n trading strategiesThere are many ways of combining different types of options contracts to suit an investors particular belief about the market or to hedge a particular risk.We will work through three main types (although there are many more especially when you include exotic options), these are:P

30、rotective positions.Spreads (vertical call, butterfly)Straddles.These will all be explained using Cisco shares as the underlying asset (although the prices are not actually real prices)The protective put: definitionAssume that you own Cisco shares but you are very worried about a large loss. Its cur

31、rent share price is $92.875. To protect against a severe drop in the share price you buy a put option expiring in July with an exercise price of $95.This currently costs $10.25 bringing your total investment to $103.125. The payoff is given on the next page.Notice that you limit your downside loss t

32、o 7.9%, but you pay for this with decreasing returns should the price go up significantly (e.g. 26.1% rather than 40% if the share price reaches $130). Protective put: resultsStock price at option expiry ($)Payoff to put option ($)Total portfolio value% return on portfolio% return to stock alone1300

33、13026.1%40.0%120012016.4%29.2%11001106.7%18.4%1000100-3.0%7.7%95095-7.9%2.3%90595-7.9%-3.1%801595-7.9%-13.9%702595-7.9%-24.6%603595-7.9%-35.4%Returns based on cost of $92.875 for share plus a put costing $10.25 = $103.125. Vertical call spread: definitionSpreads consist of positions where you own po

34、rtfolios entirely in options.In the vertical call spread you buy a call (with exercise price X) and write a call with a higher exercise price Y). The spread is called a XY vertical call spread.Consider the Cisco July 95-100 spread. Purchase a call with exercise price 95 (cost of $11.25) and write a

35、call with exercise price 100 (recouping $9.125) which costs you $2.125.It is actually possible to simply buy the spread rather than entering into both the positions.It is also possible to do the same with puts if you have a bearish view of the share.Vertical call spread payoffStock price at expiry (

36、$)Payoff to long 95 call ($)Payoff to writing 100 call ($)Portfolio value ($)% return on investment12025-205135.3%11015-105135.3%100505135.3%9940488.2%9830341.2%97202-5.9%96101-52.9%95000-100.0%90000-100.0%80000-100.0%Return based upon costs of $11.25 - $9.125 = $2.125.95-100 Vertical spread payoff9

37、5Share price at expirySpread value at expiry (PAYOFF)1005Butterfly spread: definitionA butterfly spread consists only of options. They involve four option positions with the same maturity but three different exercises prices X, Y and Z (where X Y 0Put 0American options must be worth at least as much

38、 as European options because American options can be exercised at any time i.e. it is a European option with extra flexibility.American call European call American put European putPut-Call parityThe most useful simple relationship between call and put option prices is the put call parity. Consider,

39、for the sake of an example, European put and call options on a share with current price $50 (paying no dividends), both options have exercise prices of $55 and the same maturity.Construct two portfolios:A: Buy one European put option and also buy the share.B: Buy one European call option and invest

40、an amount of cash which, at expiry, will have value equal to the exercise price ($55).The following table demonstrates that they both have the same value at the maturity of the option.Put-call parity: cash flowsSharePrice ($)First PortfolioSecond PortfolioPut + Share = TotalCall + Safe Asset = Total

41、70070701555706506565105565600606055555550555505555505505505555451045550555540154055055553520355505555Portfolio payoffs to show Put-call parity, exercise price is 55Put-call parityNotice that the first portfolio is often termed the insurance portfolio as the portfolio can never have a value less than

42、 the exercise price, $55 in this case, which means that the holder of this portfolio can always sell the share for $55 regardless of its price.Clearly regardless of what the share price is then these two portfolios are equal in value at the maturity of the options (regardless of how long this actual

43、ly is).If this is true then the present value of the two portfolios must also be the same, otherwise there will be an arbitrage opportunity.Put call parity: arbitrageAssume that the maturity of the options is one year and that the current share price is $50 and the 1-year risk free rate is 1%. The c

44、urrent price of the put option is $7, and the current value of the risk free asset is 55/(1.01) = $54.46.In this case the call option should have value $2.54 (i.e. $7 + $50 - $54.46 = $2.54). What happens if call options are actually $4?Well the value of portfolio A is $57 and the value of portfolio

45、 B is $58.46. You buy low sell high i.e. buy the put and the share and sell the call and borrow $54.46 for 1 year. This gives you a profit today of $2.54.What is your cash flow at the end of the year?Put call parity: arbitrageBuy share + Buy put + Write call + Repay loan = Total700-15-550650-10-5506

46、00-5-5505500-5505050-55045100-55040150-55035200-550Payoff from buying portfolio A and selling portfolio B, with exercise price of $55 and maturity of 1 year. Put-call parity: resultSo you are receiving $2.54 now for no cost, hence this is an arbitrage opportunity. As such these portfolios must be eq

47、ual in value at any point prior to maturity giving the following result (where X is the exercise price).European Put + Share = European Call + Present value of XThis can be rearranged to give the arbitrage portfolio:Put + Share Call Present value of X = 0Also it can allow you to determine the value

48、of call and put options given the value of the other:Put = Call + Present value of X ShareCall = Put + Share Present value of XPut-call parity: exampleGiven our Microsoft data, does put-call parity hold? We assume that the current risk-free rate is 1.5% p.a, there are 250 trading days in the year an

49、d given that the current share price is $27.03 and exercise price is $25. The current value of the put option is $0.125 givingCall = $0.125 + $27.03 $25e-0.015*30/250Call = $2.20Thus with these assumptions put-call parity holds.Note that there is a choice of how you calculate the present value, you

50、can use discrete and continuous compounding but with these time scales then it is probably easier to use continuous compounding.Put-call parity:American optionsNote that put call parity also provides bounds for the value of European call and put options. As we know that both must be worth at least z

51、ero then this gives:European Call Share Present value of XEuropean Put Present value of X Sharee.g. in the Microsoft example (assuming the same time and risk-free rate) thenCall $27.03 - $24.96 = $2.07This provides us with a very interesting result, as the American call option is worth at least as much as the European call thenAmerican call Share Present value of XPut-call parity: American option