曼彻斯特商学院课件——期权.ppt

1、Reading,Hull Chapter 1: Perhaps re-read the section on options which is in sections 1.5 1,10. Hull Chapter 7: This starts with the basics of options and then goes on into the specific details of trading. Read up to 7.4 for the crucial details and the rest if youre still interested. Hull Chapter 8: T

2、his is quite interesting but perhaps a little technical at this point in time. The most important part as regards the lecture is 8.4 and perhaps 8.5. 8.1 is interesting to see the crucial factors in determining the price of an option and will be useful for future reference (i.e. the last two weeks).

3、 Hull Chapter 9: Quite a nice chapter explaining options strategies, Im going to work through a sample of these in class so it may be useful to famililiarise yourselves with the principal strategies.,天马行空官方博客： ；QQ:1318241189；QQ群：175569632,Reading,HBR Article: Stock options have had a very negative p

4、ress 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 start of 2005.,Futures contracts are contracts which cost nothing to ent

5、er. 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 to a futures contract in that you have the right to buy (or sell) at

6、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 sell) at this price. Clearly you will have to pay some premium for this p

7、rivilege. How much?,Options: Introduction,Why 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 of corn, stock market value, interest rate changes) without, neces

8、sarily, 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 options as the financial instruments become more complex then t

9、here are more arbitrage opportunities to exploit.,天马行空官方博客： ；QQ:1318241189；QQ群：175569632,Options: definitions,An 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 (the expiry date), for a

10、 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 underlying asset. A Put O

11、ption gives the holder of the option the right, but not the obligation, to sell the underlying asset.,Options: Types,There 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 any time betwe

12、en 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 European.,Options:

13、Example,Consider 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 priced at $2.

14、20 and put options at $0.13. Microsoft current option prices Options Product Specifications The payoffs from these options for different values of the Microsoft shares are as follows:,天马行空官方博客： ；QQ:1318241189；QQ群：175569632,Options: example,Options: example,Clearly is the value of a Microsoft share e

15、xceeds 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 not, in this case the option expires worthless. In the case of the put option the if the Microsoft share price dr

16、ops 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 always have positive or zero value as the least they can ever be worth is zero.,天马行空官方博客： ；QQ:1318241189；QQ群：17556

17、9632,Options: leverage,Options 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 = $280 or a return of 280/220 = 127%. If instead he would have spent this money on buying the shar

18、es 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, then the investor has made returns of 100% (as the option expi

19、res worthless) compared to a loss of 7.5% from buying the shares.,Payoff from a call option,It is possible to depict the payoffs from this call option graphically:,25,Share price at expiry,Call option value at expiry (PAYOFF),Payoff from a put option,and also the put option:,25,Share price at expiry

20、,Put option value at expiry (PAYOFF),天马行空官方博客： ；QQ:1318241189；QQ群：175569632,Profit diagrams,Notice 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:,25,25,-$2.20,-$0.13,Profit from buying the Micr

21、osoft call option for $2.20,Profit from buying the Microsoft put option for $0.13,Writing (or selling) options,We 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 rece

22、ive 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 th

23、at 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 options,Returning to the Microsoft example, the payoffs are as follows:,Payoffs from writi

24、ng options,In a similar way we can graphically depict the payoffs from writing call and put options on Microsoft.,25,25,Share price at expiry,Share price at expiry,Payoff at expiry from writing a call option,Payoff at expiry from writing a put option,Profit from writing options,It is also to see the

25、 profit from writing the Microsoft call and put options:,25,25,Share price at expiry,Profit at expiry from writing a call option,Profit at expiry from writing a put option,$2.20,$0.13,Option principles,Clearly buying and writing (selling) options is a zero sum game. Everything made by the buyer is l

26、ost 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 market will go down. This option was treated as if it were a European option abut in reality this option would be American thus exercisa

27、ble 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: details,On a regulated exchange then the contract between parties is again secured by the exchange or by the Option Clearing Corporation (OCC). I

28、n 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 possible to terminate your option position before expiry simply by selling (if you had originally bought) or buying (if you had original

29、ly sold), you will make (or lose) the difference between the price you bought or sold at and the price today.,Options more terminology,Near-the-money or at-the-money are options where the exercise price is close to the current share price. Out-of-the-money options are options where immediate exercis

30、e 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 produce a positive payoff (i.e. the share price is higher than the exercise price for a call option). LEAPS are long term option

31、s 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).,Option trading strategies,There are many ways of combining different types of options contracts to suit an investors particular

32、 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: Protective positions. Spreads (vertical call, butterfly) Straddles. These will all be explained using Cisco shares as th

33、e underlying asset (although the prices are not actually real prices),The protective put: definition,Assume that you own Cisco shares but you are very worried about a large loss. Its current share price is $92.875. To protect against a severe drop in the share price you buy a put option expiring in

34、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 to 7.9%, but you pay for this with decreasing returns should the price go up significantly (e.g. 26.1% rather tha

35、n 40% if the share price reaches $130).,Protective put: results,Returns based on cost of $92.875 for share plus a put costing $10.25 = $103.125.,Vertical call spread: definition,Spreads consist of positions where you own portfolios entirely in options. In the vertical call spread you buy a call (wit

36、h 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 call with exercise price 100 (recouping $9.125) which costs you $2.125. It

37、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 payoff,Return based upon costs of $11.25 - $9.125 = $2.125.,95-100 Vertical spread payoff,95,Share pr

38、ice at expiry,Spread value at expiry (PAYOFF),100,5,Butterfly spread: definition,A 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 Z). The strategy is to buy a call with exercise price X,

39、write two calls with exercise price Y, and buy a call with exercise price Z. In our example, we will construct a July 90 95 100 butterfly spread. So, we: Buy one call with exercise price $90, for $13.75. Sell two calls with exercise price $95, for -$11.25 each. Buy one call with exercise price $100,

40、 for $9.125. Total cost: $0.375.,Butterfly spreads payoffs,Returns based upon investment costs of $13.75 2*$11.50 + $9.125 = $0.375.,Butterfly spread payoff,90,Share price at expiry,Spread value at expiry (PAYOFF),100,5,95,Straddle: definition,A straddle consists of buying both a call and a put opti

41、on both at the same exercise price. In our example, we buy a call with an exercise price of $95 at a cost of $11.25 and a put option at a cost of $10.25, so a total cost of $21.50.,Straddle payoff,Straddle payoff: graph,25,Share price at expiry,Straddle payoff at expiry,25,Share price at expiry,Opti

42、on pricing,It will be very tough to obtain an exact value for the options but it will be possible to establish some important bounds and relationships. First note that both call and put options must have positive value, i.e. no-one should have to pay you to take ownership of a call or put option. Th

43、is is clearly true as the least an option is worth at expiry is 0. Call 0 Put 0 American options must be worth at least as much 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 Euro

44、pean put,Put-Call parity,The most useful simple relationship between call and put option prices is the put call parity. Consider, 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 m

45、aturity. Construct two portfolios: A: Buy one European put option and also buy the share. B: Buy one European call option and invest 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 matur

46、ity of the option.,Put-call parity: cash flows,Portfolio payoffs to show Put-call parity, exercise price is 55,Put-call parity,Notice that the first portfolio is often termed the insurance portfolio as the portfolio can never have a value less than the exercise price, $55 in this case, which means t

47、hat 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 actually is). If this is true then the present value of t

48、he two portfolios must also be the same, otherwise there will be an arbitrage opportunity.,Put call parity: arbitrage,Assume 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 current price of the put option is $7, and the cu

49、rrent 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 B is $58.46. You buy low sell high i.e. buy t

50、he 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: arbitrage,Payoff from buying portfolio A and selling portfolio B, with exercise price of $55 and maturity of 1 year.,Put-call p

51、arity: result,So you are receiving $2.54 now for no cost, hence this is an arbitrage opportunity. As such these portfolios must be equal 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 X This

52、 can be rearranged to give the arbitrage portfolio: Put + Share Call Present value of X = 0 Also it can allow you to determine the value of call and put options given the value of the other: Put = Call + Present value of X Share Call = Put + Share Present value of X,Put-call parity: example,Given ou

53、r 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 and given that the current share price is $27.03 and exercise price is $25. The current value of the put option is $0.125 giving Call = $0.125 + $27.03 $25e-0.01

54、5*30/250 Call = $2.20 Thus with these assumptions put-call parity holds. Note that there is a choice of how you calculate the present value, you can use discrete and continuous compounding but with these time scales then it is probably easier to use continuous compounding.,Put-call parity:American o

55、ptions,Note 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 zero then this gives: European Call Share Present value of X European Put Present value of X Share e.g. in the Microsoft example (assuming the same time a

56、nd risk-free rate) then Call $27.03 - $24.96 = $2.07 This provides us with a very interesting result, as the American call option is worth at least as much as the European call then American call Share Present value of X,Put-call parity: American options,However, with an American option it is always

57、 possible to exercise early and receive the difference between the current share price and the exercise price Share Price X But, we know that the American call is always worth more than Share Price Present value of X which is larger than Share price X. Thus, If the share pays no dividends then it is never optimal to exercise an American call option. As such, it has the same price as a European Call option.,Put-call parity: dividends,When we consider shares which pay out dividends then the put-call parity change