6.2期权交易策略.ppt

1、期权交易策略,南开大学数学科学学院 白晓棠,Nankai University,Contents,期权组合,上节课我们谈到，有四种类型的期权头寸： 看涨期权的多头头寸； 看跌期权的多头头寸； 看涨期权的空头头寸； 看跌期权的空头头寸。 如果将这些期权头寸与标的股票的头寸进行组合，或将这些期权头寸进行组合，我们将有什么样的损益状态？,Nankai University,期权组合,股票多头头寸和看涨期权空头头寸的组合(covered call),Nankai University,期权组合,At expiration, the following relationships hold for th

2、e investor that both buys the stock and sells the call Profit = -max(0,ST-K)+(ST-S0)+C0 Maximum profit = K+C0-S0 Maximum loss = S0-C0 Breakeven price = S0-C0,Nankai University,期权组合,Example: covered call An investor purchases a stock for S0=$43 and sells a call for C0=$2.10 with a strike price, K=$45

3、. (1) Show the expression for profit and compute the maximum profit and loss and the breakeven price. (2) Compute the profits when the stock price is $0,$35,$40,$45,$50, and $55,Nankai University,期权组合,Answer(1) Profit = -max(0,ST-$45)+(ST-$43)+$2.1 Maximum profit = $45 +$2.1-$43=$4.1 Maximum loss =

4、$43-$2.1=$40.9 Breakeven price = $43-$2.1=$40.9 (2) ST=$35: $2.1+$35-$43=-$5.9 ST=$45: $2.1+0+$45-$43=$4.1 ST=$55: $2.1+($45-$55)+($55-$43) =$4.1,Nankai University,期权组合,The characteristics of a covered call are that the sale of the call adds income to the position at a cost of limiting the upside ga

5、in. It is an ideal strategy for an investor who thinks the stock will neither go up nor down in the near future. As long as the STS0-C0, the investor benefits from the position.,Nankai University,期权组合,股票空头头寸和看涨期权多头头寸的组合,Nankai University,期权组合,Nankai University,股票多头头寸和看跌期权多头头寸的组合(protective put),期权组合

6、,At expiration, the following relationships hold Profit = max(0,K-ST)+(ST-S0)-P0 Maximum profit = ST-S0-P0 Maximum loss = S0-K+P0 Breakeven price = S0+P0,Nankai University,期权组合,Example: protective put An investor purchases a stock for S0=$37.5 and buys a put for P0=$1.40 with a strike price, K=$35.

7、(1) Show the expression for profit and compute the maximum profit and loss and the breakeven price. (2) Compute the profits when the stock price is $0,$30,$35,$40,$45, and $50.,Nankai University,期权组合,Answer(1) Profit = max(0,$35-ST)+(ST-$37.5)-$1.4 Maximum profit = ST-S0-P0=ST-$38.9 Maximum loss = S

8、0-K+P0=$3.9 Breakeven price = S0+P0=$38.9 (2)ST=$30: ($35-$30)-$1.4+$30-$37.5=-$3.9 ST=$35: -$1.4+0+$35-$37.5=-$3.9 ST=$40: -$1.4+0+($40-$37.5)=$1.1,Nankai University,期权组合,The characteristics of a protective put are that the purchase of the put provides a lower limit to the position at a cost of low

9、ering the possible profit. It is an ideal strategy for an investor who thinks the stock may go down in the near future, yet the investor wants to preserve upside protential. As long as the STS0+P0, the investor benefits from the position.,Nankai University,期权组合,Nankai University,股票空头头寸和看跌期权空头头寸的组合,价

10、差策略,价差交易策略涉及持有相同类型的两个或多个期权头寸（即两个或多个看涨期权，或是两个或多个看跌期权。 牛市差价（bull spread） 购买较低执行价格（ K1）的股票看涨期权并售出同一股票的较高执行价格（ K2）的看涨期权而构造牛市价差。 购买较低执行价格（ K1）的股票看跌期权并售出同一股票的较高执行价格（ K2）的看跌期权也可以构造牛市价差。,Nankai University,牛市差价,Nankai University,Bull Call Spread,At expiration, the following relationships hold Profit = max(0,

11、 ST-K1)-max(0, ST-K2)-C1+C2 Maximum profit = K2-K1 -C1+C2 Maximum loss = C1-C2 Breakeven price = K1+C1-C2,Nankai University,Bull Call Spread,Example: bull call spread An investor purchases a call for C1=$2.1 with a strike price of K1=$45 and sells a call for C2=$0.5 with a strike price of K2=$50. (1

12、) Show the expression for profit and compute the maximum profit and loss and the breakeven price. (2) Compute the profits when the stock price is $0,$35,$45, $50and $55.,Nankai University,Bull Call Spread,Answer(1) Profit = max(0, ST-$45)-max(0, ST-$50)-$2.1+$0.5 Maximum profit = K2-K1 -C1+C2 =$3.4

13、Maximum loss = C1-C2 =$1.6 Breakeven price = K1+C1-C2=$46.6 (2)ST=$35: $0+$0-$2.1+$0.5=-$1.6 ST=$45: $0+$0-$2.1+$0.5 =-$1.6 ST=$50: $5+0-$2.1+$0.5=$3.4,Nankai University,Bull Call Spread,The characteristics of a long bull spread are that it provides a potential gain if the stock increases in price,

14、but at a lower cost than the single lower exercise-price call alone. The upper limit is capped, however, which is the price of lowering the cost. It is obviously a strategy for an investor with an expectation of the stocks price increasing in the near term.,Nankai University,熊市差价,持有牛市价差的投资者希望股票价格会上升

15、，而持有熊市 差价（bear spread）的投资者希望股票价格下降。 购买入较高执行价格（K2 ）的股票看跌期权并售出同一 股票的较低执行价格（K1 ）的看跌期权而构造牛市价 差。 购买较高执行价格（K2 ）的股票看涨期权并售出同一股 票的较低执行价格（K1 ）的看涨期权也可以构造熊市价 差。,Nankai University,熊市差价,Nankai University,Bear Put Spread,In a bear put spread the investor buys a put with the higher exercise price and sells a put wi

16、th a lower exercise price. The important relationships are: Profit = max(0, K2-ST)-max(0, K1-ST) +P1-P2 Maximum profit = K2-K1+P1-P2 Maximum loss = P2-P1 Breakeven price = K2+P1-P2,Nankai University,Bear Put Spread,Example : bear put spread An investor purchased a put for PH0=$4 with a strike price

17、of XH=$25 and sells a put for PL0=$1.8 with a strike price of XL=$20. (1) Demonstrate the expression for the profit and compute the maximum profit and loss and the breakeven price. (2) Compute the profits for when the price is $0, $15, $20, $22, $25, and $30.,Nankai University,Bear Put Spread,Answer

18、(1) Profit = max(0, 25-ST)-max(0, 20-ST) +$1.5-$4 Maximum profit = K2-K1+P1-P2=$2.8 Maximum loss = P2-P1=$2.2 Breakeven price = K2+P1-P2=$22.8 (2)ST=$20: $0+$5-$4+$1.8=$2.8 ST=$25: $0+$0- $4+$1.8=-$2.2 ST=$30: $0+$0- $4+$1.8 =-$2.2,Nankai University,盒式差价,盒式差价（box spread）是由执行价格为K1 和K2的牛市看涨价差以及相应执行价格的

19、熊市看跌价差组合而成。 盒式差价的总收益为K2 -K1 ，其价值是这一收益的现值，即 (K2 -K1) e-rT，如果它的价格不是这个值就会存在 套利的机会。 但是，盒式差价的套利策略仅对欧式期权起作用，对美式期权是不起多大作用的。,Nankai University,Box Spread,Example : box spread An investor buys a call and sells a put with a strike price of K1=$25. The call and put premiums are C1=$1.75 and P1=$0.5. the invest

20、or then sells a call and buys a put with a strike price of K2=$30. For the second pair of options, the call and put premiums are C2=$0.2 and P2=$3.9. The options all expire in two months. Compute the profit and the annualized return on the investment and determine whether this a worthwhile investmen

21、t, Rf=5%.,Nankai University,Box Spread,Answer : Profit=K2-K1+P1-P2-C1+C2 =$0.05 The initial cost=-P1+P2+C1-C2=$4.95 The holding return=0.05/4.95=0.0101 The annualized return=1.010112/2-1=0.06216 Since 5%6.2%, an arbitrage profit is possible.,Nankai University,蝶式价差,蝶式差价（butterfly spread）涉及三个不同执行价 格的期

22、权的头寸。 买入一个具有相对较低执行价格（K1）的看涨期权，买 入一个相对较高执行价格（K3）的看涨期权，同时出售 两个执行价格为K2 的看涨期权，其中K2 为K1 和K3 的中间值。 思考一下还有什么方式可以构造蝶式差价？,Nankai University,蝶式价差,由看涨期权构造的蝶式价差的利润,Nankai University,Butterfly Spread,The important relationships are: Profit = max(0, ST-K1)-2max(0, ST-K2) + max(0, ST-K3) -C1+2C2-C3 Maximum profit

23、= K2-K1-C1+2C2-C3 Maximum loss = C1-2C2+C3 Breakeven price = K1+C1-2C2+C3 and 2K2-K1-C1+2C2-C3,Nankai University,Butterfly Spread,A long butterfly spread with puts Buying one put with a low exercise price Buying a second put with a higher exercise price Selling two puts with an intermediate exercise

24、 price,Nankai University,Butterfly Spread,Example: butterfly spread with puts An investor composes a butterfly spread by buying puts with premiums of $0.80 and $5.5 and exercise prices of $40 and 50, respectively. The investor sells two puts with a premium of $3 and an exercise price of $45. calcula

25、te the profit if the value of the underlying stock at expiration is $46.3 Answer : 0+(50-46.3)+0-0.8-5.5+23=$3.4,Nankai University,组合策略,组合策略（combination）是一种期权交易策略，该策略涉及同时持有同一种股票的看涨期权和看跌期权的头寸。 我们将讨论其中的跨式组合、条式组合、带式组合和宽跨式组合。 跨式组合（straddle）涉及同时买入具有同一执行价格 和到期日的看涨和看跌期权。,Nankai University,组合策略,如果在期权到期时股票价格

26、接近于执行价格，跨式组合会带来损失；但是，如果股票价格在任何方向上有较大偏移，该期权就会产生显著的利润。,Nankai University,Straddle,For the long straddle, the important relationships are: Profit = max(0, ST-K)+ max(0, K-ST)-C-P Maximum profit = ST-K -C-P Maximum loss = C+P Breakeven price K -C-P and K +C+P,Nankai University,组合策略,上面图中的跨式组合为底部跨式组合（bott

27、om straddle）或买入跨式组合（straddle purchase）。 顶部跨式组合（top straddle）或卖出跨式组合 （straddle write）是由卖出同一执行价格和到期日的 看涨期权和看跌期权构造的。 顶部跨式组合是一个高风险的策略。只有在到期日的股票价格与执行价格相近时才会产生一定利润，其它情况下都 会有损失，而且损失是无限的。,Nankai University,Collar,A collar is the combination of a protective put (+S+P) and covered call (+S-C). Purchasing a st

28、ock and a put , selling a call at the same time. Zero-cost collar Put strike K1 call strike K2,Nankai University,Collar,Nankai University,Collar,Example : Zero-cost collar An investor purchases a stock for $29 and a put for P=$0.2 with a strike price of K1=$27.5. The investor sells a call for C=$0.2

29、 with a strike price of K2=30 Demonstrate the expression for the profit and calculate the maximum profit and loss and the breakeven price.,Nankai University,Collar,Answer : Profit=max(0, K1-ST)-max(0, ST-K2)+ST-S0 =max(0, $27.5-ST)-max(0, ST-$30)+ST-$29 Maximum profit= K2-S0=$30-$29=$1 Maximum loss= S0-K1=$29-$27.5=$1.5 Breakeven price=S0=$29,Nankai University,组合策略,条式组合（strip）是具有相同执行价格和到期日的一个 看涨期权和两个看跌期权多头构成的。 带式组合（strap）是由具有相同执行价格和