Trading Strategies Involving Options

1. Trading StrategiesInvolving 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. +S C K-C -C Covered call long a stock & short a callS-C=Ke-rf*T+D–P Profit +C ST K -(K-C)

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

9. +S -P +P Protective putlong a stock & long a putS+P=Ke-rf*T+D+C Profit ST K

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

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 riski.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. +C K1 • K2 -C Bull Spread Using CallsBuy a call with a lower strike price and sell a call with a higher strike price Profit ST

15. Payoff from a bull spread created using calls

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:

17. -P K1 K2 +P Bull Spread Using PutsBuy a put with a lower strike price and sell a put with a higher strike price Profit ST

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. -P K1 K2 +P Bear Spread Using PutsSell a put with a lower strike price and buy a put with a higher strike price Profit ST

20. Payoff from a bear spread created using puts

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:

22. +c K1 K2 -c Bear Spread Using CallsSell a call with a lower strike price and buy a call with a higher strike price Profit ST

23. Box Spread • A combination of a bull call spread with strikeprices k1 and k2and 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( (K2 - K1)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 • K1 : a relatively low strike price • K3 : a relatively high strike price • K2 : halfway between K1 and K3 , close to the current stock price • Large stock price moves are unlikely

27. +C +C K1 K2 K3 -C Butterfly Spread Using CallsBuy a call option with a relatively low K1 , buy a call option with a relatively high K3 , and sell two call options with K2 Profit ST

28. Payoff from a butterfly spread

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:

30. -P K1 K2 K3 +P +P Butterfly Spread Using PutsBuy a put option with a relatively low K1 , buy a put option with a relatively high K3 , and sell two put options with K2 Profit ST

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 CallsBuy a longer-maturity call option and Sell a call option with the same strike price Profit +C ST K -C

33. Calendar Spread Using PutsBuy a longer-maturity put option and Sell a put option with the same strike price Profit -P ST K +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. Profit +C ST K +P Bottom straddle

41. Payoff from a bottom straddle

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

44. Strip & Strap Profit Profit K ST K ST Strip Strap

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 Profit +C K1 K2 ST +P

47. Profit Profit +C +C K1 K2 ST ST K +P +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

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 ST K1 K2 K3