1. Chapter 11. Trading Strategies with Options
I. Basic Combinations.
A. Calls & Puts can be combined with other building blocks
(Stocks & Bonds) to give any payoff pattern desired.
1. Assume European options with same exp. (T), K, & underlying.
2. Already know payoff patterns for buying & selling calls & puts:
a. Calls. _______│_______S _______│________S
__________K K
b. Puts. _______│_______S _______│________S
K___________ K
3. Consider payoffs for long & short positions on:
a. Stocks. _______│_______S _______│________S
K K
b. Bonds. _______│_______S _______│________S
K _ _ _ _ _ _ K _ _ _ _ _ _ _ +c -c +p -p +S -S +B -B

2. I.B. Protective Put (S+P)
B. Buy Stock (+S) and Buy Put (+P) +S
Value
S+P +P S

3. I.C. Principal - Protected Note* (B+C)
C. Buy Bond (+B) and Buy Call (+C)
* If you buy a zero-coupon, deep discount bond, the initial outlay (B) is small (esp. if r is high);
If volatility of S is low, call (C) is cheap; Then the initial cost (B+C) may be set ≈ K (PPN).
Then your principal is protected (worst outcome; S < K, call OTM, get to keep Bond payoff (K).
B+C
Value +C +B S

4. I.D. Put-Call Parity (S+P = B+C)
D. B & C give same payoff pattern (S+P = B+C) +S +P
S+P
Value
B+C +C +B S

5. I.E. Writing a Covered Call (+S - C)
E. Buy Stock (+S) and Sell Call (-C) +S
Value -C
S - C
S+P = B+C ↓
+S-C -B = -P S

6. I.F. Buying a Straddle (+C+P)
F. Buy Call (+C) and Buy Put (+P), with same K +C
Value +P
C+P S

7. I.G. Selling a Straddle (-C-P)
G. Sell a Call (-C) and Sell a Put (-P), with same K
Value -C -P
-C - P S

8. I.H. Buying a Strangle (+C+P) – with Different K’s
H. Buy Call with K2; Buy Put with K1, with different K (K1 < K2)
+C2
Value
+P1
C2+P1 S K1 K2

9. II. How to Plot Payoff Pattern for Any Combination
Problem: Given any Combination of shares, bonds, & options,
graph the Payoff Pattern for the Intrinsic Value;
show slopes of line segments; & show break-even points.
Three Steps:
1. Compute the initial cost / revenue of the Combination,
and get values of S where all options are worth zero (ATM or OTM).
For these values of S, Combination is worth the initial cost / revenue.
2. Get values of S where one option is ITM. For these values of S,
Combination Value = initial cost / revenue + intrinsic value of this option.
3. Get values of S where next option is ITM. For these values of S,
Combination Value = old value + intrinsic value of this option.
Continue until you examine all values of S, for all options in combination.

10. II. How to Plot Payoff Pattern for Any Combination
Example 1: Strip; Buy 1 Call & 2 Puts with same K = $50; C = $5; P = $6.
1. Initial Cost = (-1) x ($5) + (-2) x ($6) = -$17.
At S = K = $50, both options ATM, Combination Value = -$17.
2. If S > $50, Call ITM, Combination Value = -$ (S - K). (coeff. of S = +1)
3. If S < $50, Puts ITM, Combination Value = -$ (K - S). (coeff. of S = -2)
K = $50
____________________________________________________________ S
$ │ $67 │
slope = -2 │ slope = +1
-17 │

11. II. How to Plot Payoff Pattern for Any Combination
Example 2: Buy 1 Call with K1 = $40 (C1 = $8); Sell 2 Calls with K2 = $45 (C2 = $5).
1. Initial Cost = (-1) x ($8) + (+2) x ($5) = +$2.
If S < K1 = $40, both options OTM, Combination Value = +$ (coeff of S = 0)
2. If 40 < S < $45, C1 is ITM, Value = +$ (S - K1) (coeff = +1)
3. If S > $45, C1 & C2 are ITM, Value = +$ (S - K1) - 2(S - K2). (coeff = -1)
K = $ K = $45 │ 7│
│ slope = +1
│ slope = -1 2│
slope = 0 │
_____________________________________________________ S
│ $ $52

12. II.A. Bull Spread with Calls (C1 - C2)
A. Buy Call with K1 (pay C1); Sell Call with K2 (receive C2)
(K1 < K2); Thus (C1 > C2); So (-C1 +C2) < 0; initial outflow (left)
Value
-C1
+C2 S
(-C1 +C2) K1 K2

13. II.B. Bull Spread with Puts (P1 - P2)
B. Buy Put with K1 (pay P1); Sell Put with K2 (receive P2)
(K1 < K2); Thus (P1 < P2); So (-P1 +P2) > 0; initial inflow (right)
Value
-P1
+P2
(-P1 +P2 ) S K1 K2

14. II.C. Bear Spread with Calls (C2 - C1)
C. Sell Call with K1 (receive C1); Buy Call with K2 (pay C2)
(K1 < K2); Thus (C1 > C2); So (+C1 -C2) > 0; initial inflow (left)
Value C2 C1
(+C1 -C2) S K1 K2

15. II.D. Bear Spread with Puts (P2 - P1)
D. Sell Put with K1 (receive P1); Buy Put with K2 (pay P2)
(K1 < K2); Thus (P1 < P2); So (+P1 -P2) < 0; initial outflow (right)
Value P2 P1 S K1 K2
(+P1 -P2)

16. II.E. Butterfly Spread with Calls (C1 - 2C2 + C3)
E. Buy 1 Call with K1; Sell 2 Calls with K2; Buy 1 Call with K3
(K1 < K2 < K3); Thus, (C1 > C2 > C3); initial outflow (left).

17. II.F. Butterfly Spread with Puts (P1 - 2P2 + P3)
F. Buy 1 Put with K1; Sell 2 Puts with K2; Buy 1 Put with K3
(K1 < K2 < K3); Thus, (P1 < P2 < P3); initial outflow (right).

18. III.A. Graphing Total, Intrinsic, and Extrinsic Value
Total Value S K
Intrinsic Value S K
Extrinsic Value S K

19. III.B. Buy Calendar Spread using Calls (+C2 - C1)
B. Buy Call with maturity, T2 ; Sell Call with maturity, T1 ;
(T2 > T1); Thus, (C2 > C1); initial outflow (left).

20. III.C. Buy Calendar Spread using Puts (+P2 - P1)
C. Buy Put with maturity, T2 ; Sell Put with maturity, T1 ;
(T2 > T1); Thus, (P2 > P1); initial outflow (right).

21. IV. Interest Rate Option Combinations (Hull Chap 21)
A. Using Options on Eurodollar Futures.
1. ED Futures Contract Characteristics : (Review)
a. Underlying Asset - ED deposit with 3-month maturity.
b. ED rates are quoted on an interest-bearing basis, assuming a 360-day year.
c. Each ED futures contract represents $1MM of face value
ED deposits maturing 3 months after contract expiration.
d. 40 different contracts trade at any point in time;
contracts mature in Mar, Je, Sept, and Dec, 10 years out.
e. Settlement is in cash; price is established by a survey of current ED rates.
f. ED futures trade according to an index; Q = R = (futures rate);
e.g., If futures rate = 8.50%, Q = 91.50, and interest outlay promised would be
(.0850) x ($1,000,000) x (90 / 360) = $21,250.
g. Each basis point in the futures rate means a $25 change in value of contract:
[ (.0001) x ($1,000,000) x (90 / 360) ] = $25 ]
h. The ED futures is truly a futures on an interest rate.
(The T.Bill futures is a futures on a 90-day T.Bill.)

22. IV.A. Using Options on ED Futures
2. Example: Long Hedge with ED futures for a Bank. (more Review)
Jan. 6: Bank expects $1 MM payment on May 11 (4 months).
Anticipates investing funds in 3-month ED deposits.
Cash Market risk exposure:
Bank would like to today’s ED rate, but won’t have funds for 4 mo.
If ED rate , bank will realize opportunity loss
(will have to invest the $1 MM at lower ED rates).
Long Hedge: Buy ED futures today (promise to deposit R).
Then if cash rates , futures rates (R) will  & futures prices (Q) will .
So long futures position will  to offset opportunity loss in cash mkt.
The best ED futures to buy is June contract; expires soonest after May 11.
Jan May June 14
|__________________________________________|_____________|
$1 MM receivable due May 11.
Cash: Plan to invest $1MM on May 11 Invest the $1 MM in ED deposits.
Futures: Buy 1 ED futures Sell futures contract.

23. IV.A. Using Options on ED Futures
3. Data for example – (more Review)
Jan. 6: Cash market ED rate (LIBOR) = RS = 3.38% (S1 = 96.62)
June ED futures rate (LIBOR) = RF = 3.85% (F1 = 96.15) ; Basis = (S1 - F1) = .47%
May 11: Cash market ED rate = 3.03% (S2 = 96.97)
June ED futures rate = 3.60% (F2 = 96.40) ; Basis = (S2 - F2) = .57% _______________________________________________________________________________
Date Cash Market Futures Market Basis
1 / 6 bank plans to invest $1MM bank buys 1 Je ED futures
at cash rate = S0 = 3.38% at futures rate = R0 = 3.85% .47%
5 / 11 bank invests $1MM in 3-mo ED bank sells 1 June ED futures
at cash rate = S1 = 3.03% at futures rate = R1 = 3.60% .57%
Net opport. loss = = .35% futures gain = = .25% change
Effect (35) x ($25) = $ (25) x ($25) = $ %
Cumulative Investment Income:
3.03% = $1,000,000 (.0303) (90/360) = $7,575
Profit from futures trades: = $625
Total: $8,200
Effective Return = [ $8,200 / $1,000,000 ] x (360 / 90) = %
(10 bp worse than spot market = change in basis). This is basis risk.

24. IV.A. Using Options on ED Futures
4. Using Options on ED futures to build Floors, Caps, & Collars.
a. ED futures contract:
Buy ; Promise to buy ED ( lend @ forward ED rate);
Sell ; Promise to sell ED forward ED rate). [ Lock in R. ]
b. Call option on ED futures: Right to buy ED futures forward ED rate).
c. Put option on ED futures: Right to sell ED futures (borrow @ fwd ED rate).
d. Lender? Want to buy ED in future. To hedge risk of loss with falling rates:
i. Buy ED futures. If rates , lock in min. lending rate (hedged)
But if rates , opportunity loss (could have loaned at higher rates).
ii. Buy Call option on ED futures. If rates , lock in min. lending rate.
NOW if rates , lend at higher rates! Call is OTM - interest rate Floor.
e. Borrower? Want to sell ED in future. To hedge risk of loss with rising rates:
i. Sell ED futures. If rates , lock in max. borrowing rate (hedged)
But if rates , opportunity loss (could have borrowed at lower rates).
ii. Buy Put option on ED futures. If rates , lock in max. borrowing rate.
NOW if rates , borrow at lower rates! Put is OTM - interest rate Cap.
f. Combining Call & Put on ED futures gives Collar.

25. IV.A. Using Options on ED Futures
5. Example: Building Interest Rate Collar for a bank.
Cap: Buy a Put Floor: Sell a Call Both: Collar
Strike Option Strike Option Range of Net
Price Premium Price Premium Borrowing Cost Premium .
¼% - 4% = $275
¼% - 3½% = $950
½% - 3¾% = $450 .
Cap at 4%; Floor at 3¼ %; Collar: Net Cost = 11 basis points. | |
|> Futures Price (Q)
Loss a. CAP borrowing rates @ 4% by buying a Put with K = (= ).
Must pay 13 bp for this Put (13 x $25 = $325).
i. If ED rates  above 4%, Q  below 96.00, & Put is ITM – Cap at 4%.
ii. If ED rates  below 4%, Q  above 96.00, & Put is OTM – Borrow at < 4%.
b. If you don’t think ED rates will  below, say, 3.25%, can recover some of cost
by selling a Call with K = (= ). Receive 2 bp ($50).
i. If ED rates  below 3.25%, Q  above 96.75%, & Call is ITM – Floor at 3.25%.
Buy put
Sell call
0.02
0.11
0.13