1 Trading Strategies Involving Options ── 選擇權交易策略

2 Hypothesis The underlying asset is a stock Other underlying assets can apply to similar results The options used in the strategies are European American option may probably be exercised early that leading to different profit outcome Ignore the time value of money To Simplify the exposition

3 Hypothesis Initial cost premium (權利金)-long side margin (保證金)-short side

4 Types of Strategies Hedge holding single option on a stock and the stock itself Spread taking a position in two (or more) options of the same type. Combination Taking a position in both calls and puts on the same stock

5 Hedge strategy Covered call (備兌買權) Protective call (保護性買權) Protective put (保護性賣權) Covered put (備兌賣權) holding single option on a stock and the stock itself

6 Put – Call Parity S + P = C + Ke -r*T + D S : stock price ; P : the price of put ; C : the price of call ; K : strike price / exercise price ; r : risk-free interest rate ; T : the time to maturity ; D : the present value of the dividends

7 Covered call long a stock & short a call S-C=Ke -rf*T +D – P K Profit STST +S -C C+C -(K-C) K-C

8 Protective call short a stock & long a call -S+C=-Ke -rf*T -D+P K Profit STST -S +C C K-C -C K-C

9 Protective pu t long a stock & long a put S+P=Ke -rf*T +D+C K Profit STST +S +P-P

10 Covered put short a stock & short a put -S-P=-Ke -rf*T -D-C K Profit STST -S -P+P

11 Spread trading strategy Bull Spreads (多頭價差 ) Bear Spreads (空頭價差) Box Spreads (箱形價差) Butterfly Spreads (蝶形價差) Calendar Spreads (時間價差/行事曆價差/…) Diagonal Spreads (對角價差) taking a position in two (or more) options of the same type (i.e., two calls or two puts)

12 Definition Type: two types — call & put Option series: 1.options of the same type 2.different expiration dates, the same strike price; different strike prices, the same expiration date.

13 Bull spread Both options have the same expiration date Hoping that the stock price will be up↑ Limit both the upside profit potential and the downside risk i.e. limiting both sides Three types of bull spreads can be distinguished 1. both calls are initially out of the money 2. one call is initially in the money ; the other call is initially out of the money 3. both calls are initially in the money

14 Bull Spread Using Calls Buy a call with a lower strike price and sell a call with a higher strike price Profit STST K1K1 +C K2K2 -C

15 Payoff from a bull spread created using calls Stock price range Payoff from long call option Payoff from short call option Total payoff S T ≧ K 2 S T - K 1 -(S T – K 2 )K 2 - K 1 K 1 < S T < K 2 S T - K 1 0 S T ≦ K 1 000

16 Example 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 profit is therefore as follows: Stock price rangeProfit S T ≦ < S T < 35S T – 32 S T ≧ 35 3

17 Bull Spread Using Puts Buy a put with a lower strike price and sell a put with a higher strike price Profit STST K1K1 +P K2K2 -P

18 Bear Spreads Both options have the same expiration date Hoping that the stock price will decline Limit both the upside profit potential and the downside risk

19 Bear Spread Using Puts Sell a put with a lower strike price and buy a put with a higher strike price Profit STST K1K1 -P K2K2 +P

20 Payoff from a bear spread created using puts Stock price range Payoff from long put option Payoff from short put option Total payoff S T ≧ K K 1 < S T < K 2 K 2 - S T 0 S T ≦ K 1 K 2 - S T -(K 1 – S T )K 2 - K 1

21 Example An investor buys for $3 a put with a strike price of $35 and sells for $1 a put with a strike price of $30 The profit is therefore as follows: Stock price rangeProfit S T ≦ < S T < S T S T ≧ 35 -2

22 Bear Spread Using Calls Sell a call with a lower strike price and buy a call with a higher strike price Profit STST K2K2 +c K1K1 -c

23 Box Spread A combination of a bull call spread with strike prices k 1 and k 2 and a bear put spread with the same two strike prices If all options are European a box spread is worth the present value of the difference between the strike prices( (K 2 - K 1 )e -rT ) ; If they are American this is not necessarily so.

24 Box Spread

25 Box Spread If the market price of the box spread is too low(high),it is profitable to buy(sell) the box,called “long box” or “short box” Commissions are important to be considered when implementing this strategy coz the small profit may be easily offset by commissions Alligator spread

26 Butterfly Spread Involves positions in options with three different strike prices K 1 : a relatively low strike price K 3 : a relatively high strike price K 2 : halfway between K1 and K3, close to the current stock price Large stock price moves are unlikely

27 Butterfly Spread Using Calls Buy a call option with a relatively low K 1, buy a call option with a relatively high K 3, and sell two call options with K 2 Profit STST K1K1 +C K3K3 K2K2 -C

28 Payoff from a butterfly spread Stock price range Payoff from first long call Payoff from second long call Payoff from short calls Total payoff S T < K K 1 < S T < K 2 S T - K 1 00 K 2 < S T < K 3 S T - K (S T – K 2 ) K 3 - S T S T > K 3 S T - K 1 S T - K 3 -2(S T – K 2 ) 0

29 Example The stock price is $61.An investor buys for $10 a call with a strike price of $55,$5 a call with a strike price of $65 and sells for $7 two puts with a strike price of $60 The profit is therefore as follows: Stock price rangeProfit S T < < S T < 60S T - K < S T < 65K 3 - S T -1 S T > 65

30 Butterfly Spread Using Puts Buy a put option with a relatively low K 1, buy a put option with a relatively high K 3, and sell two put options with K 2 Profit STST K1K1 +P K3K3 K2K2 -P

31 Calendar Spread The options have the same strike price and different expiration dates Neutral calendar spread : A strike price close to the current stock price is chosen Bullish calendar spread : Involves a higher strike price Bearish calendar spread : Involves a lower strike price Reverse calendar spread : Buys a short-maturity option and sells a long-maturity option

32 Calendar Spread Using Calls Buy a longer-maturity call option and Sell a call option with the same strike price Profit STST K +C -C

33 Calendar Spread Using Puts Buy a longer-maturity put option and Sell a put option with the same strike price Profit STST K +P -P

34 Brief Summary Bull and Bear spreads: different strike prices and the same expiration date Calendar spreads: the same strike price and different expiration date

35 Diagonal Spread Both the expiration date and the strike price of the calls are different Increases the range of profit patterns that are possible

36 Diagonal Bull Spread

37 Diagonal Bear Spread

38 Combinations Taking a position in both calls and puts on the same stock Straddle (跨式價差) Strips (紙帶價差) Straps (皮帶價差) Strangles (勒式價差)

39 Straddle Bottom straddle (straddle purchase) : Buying a call and put with the same strike price and expiration date ; expecting a large move in a stock price but does not know in which direction the move will be Top straddle (straddle write) : Selling a call and put with the same strike price and expiration date ; large stock price moves are unlikely

40 Bottom straddle Profit STST K +C +P

41 Payoff from a bottom straddle Stock price range Payoff from long call Payoff from long put Total payoff S T ≤ K0K - S T S T > KS T - K0

42 Strip & Strap Strip : Buy one call and two puts with the same strike price and expiration date ; Considers a decrease in the stock price to be a more likely than an increase Strap : Buy two calls and one put with the same strike price and expiration date ; Considers a increase in the stock price to be a more likely than an decrease

43 Strip & Strap callput Strip12 Strap21

44 Strip & Strap Profit KSTST KSTST StripStrap

45 Strangle Bottom vertical combination : Buy a put and a call with the same expiration date and different strike prices Top vertical combination : Sell a put and a call with the same expiration date and different strike prices The stock price has to move farther in a strangle than in a straddle for the investor to make a profit ; The downside risk is less than a straddle

46 Bottom vertical combination K1K1 K2K2 Profit STST +C +P

47 K1K1 K2K2 Profit STST +C +P Profit STST K +C +P The stock price has to move farther in a strangle than in a straddle for the investor to make a profit ; The downside risk is less than a straddle Strangle Straddle

48 Payoff from a bottom vertical combination Stock price range Payoff from long call Payoff from long put Total payoff S T ≦ K 1 0K 1 - S T K 1 < S T < K S T ≧ K 2 S T - K 2 0

49 Other Payoffs All payoff functions (at time T) can be found: if Euro options can expire (at time T) with every single possible strike price Profit STST K1K1 K2K2 K3K3