Money Spreads

1. Money spreads Different strategies to hedge your risk using put or calls

2. The basics A spread is a strategy in which you buy one option and sell another option that is identical to the first in all respects except either exercise price or time to expiration. Our focus is on money spreads, which are spreads in which the two options differ only by exercise price. The investor buys an option with a given expiration and exercise price and sells an option with the same expiration but a different exercise price.

3. Bull Spreads Long Call Short Call Lower Exercise Price Higher Exercise Price It is designed to make money when the market goes up. In this strategy we combine a long position in a call with one exercise price and a short position in a call with a higher exercise price

4. Bull Spread The profit you will make from a bull spread is calculated by finding the value of the spread at a certain strike price less the initial value of the spread. Profit = Vt – V0 Thus therefore the profit occurs on the upside Vt = Max(0, St – X1) – Max(0, St – X2) V0 = c1 – c2 Therefore П = Max(0, St – X1) – Max(0, St – X2) - c1 + c2 Maximum Gain X2 – X1 – c1 + c2 Breakeven point St* = X1 + c1 – c2

5. Bull Spread SaT SbT ScT X2 X1 <ul><li> The exercise price, X1, you have a long position in, thus you bought this option paying c1 .

6. The exercise price, X2, you have a short position in, thus you wrote this option receiving c2.

7. Important that to remember that a call option with a lower exercise price is more expensive than a call option with a higher exercise price, therefore you pay more for the long call than you receive for the short call.

8. Thus you will have a negative starting value.</li></li></ul><li>Bear Spreads Short Call Long Call Lower Exercise Price Higher Exercise Price It is designed to make money when the market goes down. In this strategy we combine a short position in a call with one exercise price and a long position in a call with a higher exercise price

9. Bear Spreads Short Put Long Put Lower Exercise Price Higher Exercise Price There is another method to a Bear Spreads. Instead of using calls you use puts instead. You buy the put with the higher exercise price and sell the put with the lower exercise price.

10. Bear Spread The profit you will make from a bear spread is calculated by finding the value of the spread at a certain strike price less the initial value of the spread. Profit = Vt – V0 Thus therefore the profit occurs on the downside Vt = Max(0,X2 – St) – Max(0, X1 – St) V0 = p2 – p1 Therefore П = Max(0,X2 – St) – Max(0, X1 – St) – p2 + p1 Maximum Gain X2 – X1 – c1 + c2 Breakeven point St* = X2 + c1 – c2

11. Bear Spread SaT SbT ScT X2 X1 <ul><li> The exercise price, X1, you have a short position in, thus you wrote this option receiving p1 .

12. The exercise price, X2, you have a long position in, thus you bought this option paying p2.

13. Important that to remember that a put option with a higher exercise price is more expensive than a put option with a lower exercise price, therefore you pay more for the short put than you receive for the long put.

14. Thus you will have a negative starting value.</li></li></ul><li>Butterfly Spreads Long bull spread Long bull spread Short bull spread Long bear spread The following strategy the investor has to believe that the market will be less volatile than the rest expects. In this strategy this means buying a bull spread and selling a bull spread (or buying a bear spread).

15. Butterfly Spread The profit you will make from a butterfly spread is calculated by finding the value of the spread at a certain strike price less the initial value of the spread. Profit = Vt – V0 Thus therefore the profit occurs on the in the middle range, and the loss is either on the downside or the upside. Vt = Max(0, St – X1) – 2Max(0, St – X2) – Max(0, St – X3) V0 = c1 – 2c2 + c3 Therefore П = Max(0, St – X1) – 2Max(0, St – X2) – Max(0, St – X3) – c1 + 2c2 – c3

16. Butterfly Spreads There are two breakeven points X1 < St < X2 St* = X1 + c1 – 2c2 +c3 X2 <= St < X3 St* = 2X2 – X1 – c1 + 2c2 – c3 Maximum profit X2 – X1 – c1 + 2c2 – c3

17. Butterfly Spread SaT SbT ScT SDT X1 X2 X3 To brake it up into simpler components <ul><li>We own two calls with exercise price

18. X1 and X2

19. We sold two calls with exercise price

20. X2

21. If St is below X1

22. Loses limited amount of money

23. If St is at least X2

24. Profit limted to a certain amount

25. If both options out-of-the-money

26. Loses net premuim</li></li></ul><li>Buttefly Spreads When using this strategy the investor expects that the volatility in the market will be lower than that the market expects, therefore the underlying will trade near the middle exercise price. There is also a flipside to the butterfly, if the investor expects the market to be more volatile than that the market expects, he can sell the butterfly spread. This will involve selling the calls with exercise prices of X1 and X3 and buying calls with exercise prices of X2.

27. Butterfly Spreads <ul><li>Another alternative using the buttefly spread, is using puts instead of using calls.

28. Recall that the intial value of the spread (V0) is and put-call parity:

29. Vo = c1 – 2c2 + c3

30. c = p + S – X/(1 + r)T

31. By using the appropriatesubscripts and subsitutes with the put-call parity, we obtain :

32. Vo = p1 – 2p2 + p3

33. The positive signs at p1 and p3 means that we should buy the puts with exercise prices of X1 and X3 and sell two puts with exercise price X2

34. In effect we will be buying a bear spread and also selling a bear spread

35. But if the options are priced correctly, it does not matter wheter we use put or calls</li>

Money Spreads

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