Microsoft PowerPoint - Ch10 Trading Strategies Involving Options.ppt

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1 Notations Ch10 選擇權交易策略 Trading Strategies Involving Options S(T) : Stock price at time T C(,T) : the price of the call option with maturity T and strike price T1 < T2 < T3 < T4 1 < 2 < 3 < 4 出售備兌買權 (Writing a Covered Call) 單一選擇權加上單一股票的交易策略 Strategies involving a single option and a Stock 出售備兌買權 : -C + S 由 Put-Call Parity 可知 :-C+S = exp(-rt) P 因此, 出售備兌買權的到期損益形式與賣出賣權相同 (a) 1

2 出售備兌買權的相反部位保護賣權 (Protective Put) 出售備兌買權的相反部位 : + C - S 由 Put-Call Parity 可知 :+ C -S = P exp(-rt) 因此, 出售備兌買權的相反部位, 到期損益形式與買進賣權相同保護賣權 : + P + S 由 Put-Call Parity 可知 :+P + S = C+ exp(-rt) 因此, 保護賣權的到期損益形式與買進買權相同 (a) (b) (c) 保護賣權相反部位保護賣權相反部位 : -P -S 由 Put-Call Parity 可知 :- P -S = -C - exp(-rt) 因此, 保護賣權的相反部位, 到期損益形式與賣出買權相同價差交易 Spreads (d) 2

3 牛市價差 (Bull Spreads) 牛市價差 : + C (1, T) C(2, T) 牛市價差 (Bull Spreads) 牛市價差 : + C (1, T) C(2, T) 因為 C (1, T) > C(2, T), 所以期初需要建構成本時機 : 預期股價上漲時牛市價差的到期 : 1 2 Strike Price from from Range Long Call Option Short Call Option S(T) <S(T) 2 S(T) S(T) - 1 >0 S(T) 2 S(T) S(T) 2-1 > 0 牛市價差 (Bull Spreads) 牛市價差 (Bull Spreads) 牛市價差可以分為三種 : 兩個買權皆是 OTM ( 積極 ) 一個買權 OTM; 一個賣權 ITM ( 中等 ) 兩個買權皆是 ITM ( 保守 ) 積極成本低 1 2 中等成本中等保守成本高牛市價差也可以由賣權組成 :+ P(1,T) - P(2,T) 1 2 3

4 牛市價差 (Bull Spreads) 牛市價差也可以由賣權組成 :+ P(1,T) - P(2,T) 期初會有現金流入 : P(2,T) > P(1,T) 到期 0 Example 10.1 An investor buys for $3 a call with a strike price of $30 and sells for $1 a call with a strike price of $35. The cost of the strategy is $3-$1=$2. The profit is as follows: Strike Price from from Range Long Put Option Short Put Option S(T) S(T) < 2 0 -( 2 - S(T) ) -( 2 - S(T) ) < 0 S(T) 1 +(1- S(T)) -( 2 - S(T) ) 1 2 < 0 Strike Price from from Range Long Call Option Short Call Option S(T) <S(T) 35 S(T) S(T) - 30 > 0 S(T) 35 S(T) S(T) > 0 熊市價差 (Bear Spreads) 熊市價差 : + P (2, T) P(1, T) 熊市價差 (Bear Spreads) 熊市價差 : + P (2, T) P(1, T) 因為 P (2, T) > P(1, T), 所以期初需要建構成本時機 : 股價下跌時熊市價差到期 : 1 2 Strike Price from from Range Long Put Option Short Put Option S(T) S(T) S(T) <S(T) S(T) S(T) S(T)

5 熊市價差 (Bear Spreads) 熊市價差也可以由買權組成 : - C (1, T) + C(2, T) 熊市價差 (Bear Spreads) 熊市價差也可以由買權組成 : - C (1, T) + C(2, T) 因為 C (1, T) > C(2, T), 所以期初有現金流入到期 Strike Price from from Range Long Call Option Short Call Option S(T) <S(T) ( S(T) 1 ) - ( S(T) 1 ) 0 S(T) 2 S(T) 2 - ( S(T) 1 ) 盒型價差 (Box Spreads) A box spread is a combination of a bull spread with strike prices 1 and 2 and a bear spread with the same two strikes. Box spread Arbitrage: If the market price of the box spread is too low, it is profitable to buy the box. If the market price of the box spread is too high, it is profitable to sell the box. A box arbitrage only works with European options. 蝶式價差 (Butterfly Spreads) 蝶式價差 : + C(1) 2 C(2) + C(3) 一般來說, 2 會接近現貨價格適用時機 : 當投資人認為股價不會大幅波動時 Strike Price from from Range Long Call Option Short Call Option S(T) <S(T) 2 S(T) S(T) 2 1 S(T)

6 蝶式價差 (Butterfly Spreads) 蝶式價差 : + C(1) 2 C(2) + C(3), where 2 =0.5(1+3). Strike Price from from from Range first long call second long call short calls S(T) < < S(T) < 2 S(T) S(T) 1 2 < S(T) < 3 S(T) 1 0-2(S(T) - 2) 3 S(T) S(T) > 3 S(T) 1 S(T) - 3-2(S(T) - 2) 0 -$1 蝶式價差 (Butterfly Spreads) Butterfly Spread 建購成本 = C1 + C3 2 C2 = =$1 $ Call Price $55 C1=10 $60 C2= 7 $65 C3= 5 蝶式價差 (Butterfly Spreads) Butterfly spreads can be created using put options, which is the same as the spreads created using call options. Butterfly spread = P(1) + P(3) 2 P(2) 時間價差 (Calendar Spreads) Calendar spreads or time spreads are created by two options with the same strike price and different expiration dates. Calendar spread = + C(, T2) C(, T1)

7 時間價差 (Calendar Spreads) 時間價差 (Calendar Spreads) Calendar spread = + C(, T2) C(, T1) 因為 C(, T2) > C(, T1), 所以需要期初建構成本當短期的買權到期時, 長期的買權也一起結束部位, 結算損益與蝶式價差相似, 當股價在附近, 沒有大幅波動, 則時間價差到期時有收益然而當股價偏離時, 則有損失 Calendar spread = + C(, T2) C(, T1) 因為 C(, T2) > C(, T1), 所以需要期初建構成本當短期的買權到期時, 長期的買權也一起結束部位, 結算損益與蝶式價差相似, 當股價在附近, 沒有大幅波動, 則時間價差到期時有收益然而當股價偏離時, 則有損失時間價差 (Calendar Spreads) 蝶式價差亦可由賣權建構 : Calendar spread = + P(, T2) P(, T1) 時間價差 (Calendar Spreads) 三種時間價差 : Neutral Calendar Spread: S(0) = Bullish Calendar Spread: S(0) < Bearish Calendar Spread: S(0) > 7

8 Neutral Calendar Spread: S(0) = Bullish Calendar Spread: S(0) < S(0) Bearish Calendar Spread: S(0) > 時間價差 (Calendar Spreads) Option Value = Intrinsic Value + Time Value Intrinsic Value = Max ( S(T), 0 ) Calendar spread = + C(, T2) C(, T1) S(0) = TV2(0) TV1(0) ---- 所以時間價差的建構成本為時間價值的差! 8

9 時間價差 (Calendar Spreads) See Fig on P At time 0: C1(0) = I1(0) + TV1(0) C2(0) = I2(0) + TV2(0) CS = C2(0) - C1(0) = TV2(0) TV1(0) = $5 - $2 = $3 At time T1: CS = TV2(T1) TV1(T1) ATM : TV2(0) = $5 TV2(T1) = $4; TV1(0) = $2 TV1(T1) = 0 CS = $4-0 =$4 Net = 4-3 = $1 ITM and OTM : TV2(0) = $5 TV2(T1) = $2; TV1(0) = $2 TV1(T1) = 0 CS = $2 -$0 =$2 Net = 2-3 = $-1 對角價差 (Diagonal Spreads ) 所謂對角化 (Diagonalization) 是指將某一價差策略中, 長部位到的期日加以延長時間價差已是對角化價差對角化牛式價差 = + C(1, T2) C(2, T1) 對角化熊式價差 = + P (2, T2) P(1, T1) 跨式交易策略 (Straddle) 組合式交易策略 (Combinations) A combination is an option trading strategy that involves taking a position in both calls and puts on the same stock. 跨式可分為兩種 : 下跨式 (Bottom straddle or straddle purchase) Bottom Straddle = + C(,T) + P(,T) 時機 : 預期股票大漲大跌上跨式 (Top straddle or straddle write) Top Straddle = - C(,T) - P(,T) 時機 : 預期股票盤整 9

10 下跨式 (Bottom straddle) 上跨式 (Top straddle) Bottom Straddle = + C(,T) + P(,T) Top Straddle = - C(,T) - P(,T) Strip Strip = C(,T) + 2 P(, T) 時機 : 股價將大漲大跌, 但大跌機會較高 Strap Strip = 2 C(,T) + P(, T) 時機 : 股價將大漲大跌, 但大漲機會較高 10

11 勒式策略 (Strangle) 勒式策略 (Strangle) 下勒式策略 (Bottom Strangle) Bottom Strangle = + C(2, T) + P(1, T) 上勒式策略 (Top Strangle) Bottom Strangle = - C(2, T) - P(1, T) Exercises 4,7,10,12,19,20,21,22 11

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