Chapter 11. Trading Strategies with Options
© Paul Koch 1-1
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.
+c
_______│_______S
-c
_______│________S
__________K
b. Puts.
K
+p
_______│_______S
-p
_______│________S
K___________
K
3. Consider payoffs for long & short positions on:
a. Stocks.
+S
_______│_______S
K
_______│_______S
K
_______│________S
K
+B
b. Bonds.
-S
-B
_______│________
S
_ _ _ _ _ _K _ _ _ _ _ _ _
I.B. Protective Put (S+P)
© Paul Koch 1-2
B. Buy Stock (+S) and Buy Put (+P)
Value
+S
+P
S+P
S
I.C. Principal - Protected Note* (B+C)
© Paul Koch 1-3
C. Buy Bond (+B) and Buy Call (+C)
Value
+B
+C
B+C
S
* 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).
I.D. Put-Call Parity (S+P = B+C)
© Paul Koch 1-4
D. B & C give same payoff pattern (S+P = B+C)
Value
+S
+P
S+P
+B
+C
B+C
S
I.E. Writing a Covered Call (+S - C)
© Paul Koch 1-5
E. Buy Stock (+S) and Sell Call (-C)
Value
+S
-C
S-C
S+P = B+C
↓
+S-C -B = -P
S
I.F. Buying a Straddle (+C+P)
© Paul Koch 1-6
F. Buy Call (+C) and Buy Put (+P), with same K
Value
+C
+P
C+P
S
I.G. Selling a Straddle (-C-P)
© Paul Koch 1-7
G. Sell a Call (-C) and Sell a Put (-P), with same K
Value
-C
-P
-C - P
S
I.H. Buying a Strangle (+C+P) – with Different K’s
© Paul Koch 1-8
H. Buy Call with K2; Buy Put with K1, with different K (K1 < K2)
Value
+C2
+P1
C2+P1
S
K1
K2
II. How to Plot Payoff Pattern for Any Combination
© Paul Koch 1-9
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.
II. How to Plot Payoff Pattern for Any Combination
© Paul Koch 1-10
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 = -$17 + 1(S - K).
(coeff. of S = +1)
3. If S < $50, Puts ITM,
Combination Value = -$17 + 2(K - S).
(coeff. of S = -2)
K = $50
____________________________________________________________
$41.50
│
$67
│
│
│
slope = -2
│
slope = +1
│
│
│
│
-17 │
│
S
II. How to Plot Payoff Pattern for Any Combination
© Paul Koch 1-11
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 = +$2.
(coeff of S = 0)
2. If 40 < S < $45, C1 is ITM,
Value = +$2 + 1(S - K1).
(coeff = +1)
3. If S > $45, C1 & C2 are ITM,
Value = +$2 + 1(S - K1) - 2(S - K2).
(coeff = -1)
K = $40
K = $45
│
7│
│
│ slope = +1
│
│
slope = -1
2│
slope = 0
│
_____________________________________________________ S
│
$45
$52
│
II.A. Bull Spread with Calls (C1 - C2)
© Paul Koch 1-12
A. Buy Call with K1 (pay C1); Sell Call with K2 (receive C2)
Value
(K1 < K2); Thus (C1 > C2); So (-C1 +C2) < 0; initial outflow (left)
+C2
K1
(-C1 +C2)
-C1
K2
S
II.B. Bull Spread with Puts (P1 - P2)
© Paul Koch 1-13
B. Buy Put with K1 (pay P1);
Value
Sell Put with K2 (receive P2)
(K1 < K2); Thus (P1 < P2); So (-P1 +P2) > 0; initial inflow (right)
+P2
(-P1 +P2 )
K1
-P1
K2
S
II.C. Bear Spread with Calls (C2 - C1)
© Paul Koch 1-14
C. Sell Call with K1 (receive C1); Buy Call with K2 (pay C2)
Value
(+C1 -C2)
(K1 < K2); Thus (C1 > C2); So (+C1 -C2) > 0; initial inflow (left)
C1
K1
C2
S
K2
II.D. Bear Spread with Puts (P2 - P1)
© Paul Koch 1-15
D. Sell Put with K1 (receive P1); Buy Put with K2 (pay P2)
Value
(K1 < K2); Thus (P1 < P2); So (+P1 -P2) < 0; initial outflow (right)
P1
K1
S
K2
P2
(+P1 -P2)
II.E. Butterfly Spread with Calls (C1 - 2C2 + C3)
© Paul Koch 1-16
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).
II.F. Butterfly Spread with Puts (P1 - 2P2 + P3)
© Paul Koch 1-17
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).
III.A. Graphing Total, Intrinsic, and Extrinsic Value
© Paul Koch 1-18
Total Value
S
K
Intrinsic Value
S
K
Extrinsic Value
K
S
III.B. Buy Calendar Spread using Calls (+C2 - C1)
© Paul Koch 1-19
B. Buy Call with maturity, T2 ; Sell Call with maturity, T1 ;
(T2 > T1); Thus, (C2 > C1); initial outflow (left).
III.C. Buy Calendar Spread using Puts (+P2 - P1)
© Paul Koch 1-20
C. Buy Put with maturity, T2 ; Sell Put with maturity, T1 ;
(T2 > T1); Thus, (P2 > P1); initial outflow (right).
IV. Interest Rate Option Combinations (Hull Chap 21)
© Paul Koch 1-21
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 = 100 - R = 100 - (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.)
IV.A. Using Options on ED Futures
© Paul Koch 1-22
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 invest @ 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 later @ 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. 6
May 11
June 14
|__________________________________________|_____________|
$1 MM receivable due May 11.
Cash: Plan to invest $1MM on May 11
Futures: Buy 1 ED futures.
Invest the $1 MM in ED deposits.
Sell futures contract.
IV.A. Using Options on ED Futures
© Paul Koch 1-23
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
at cash rate = S0 = 3.38%
5 / 11 bank invests $1MM in 3-mo ED
at cash rate = S1 = 3.03%
Net
Effect
opport. loss = 3.38 - 3.03 = .35%
(35) x ($25) = $875
bank buys 1 Je ED futures
at futures rate = R0 = 3.85%
.47%
bank sells 1 June ED futures
at futures rate = R1 = 3.60%
.57%
futures gain = 3.85 - 3.60 = .25%
(25) x ($25) = $625
Cumulative Investment Income:
Interest @ 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) =
3.28%
(10 bp worse than spot market = change in basis). This is basis risk.
change
.10%
.
IV.A. Using Options on ED Futures
© Paul Koch 1-24
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 (borrow @ forward ED rate).
[ Lock in R. ]
b. Call option on ED futures: Right to buy ED futures (lend @ 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.
IV.A. Using Options on ED Futures
© Paul Koch 1-25
5. Example: Building Interest Rate Collar for a bank.
Cap: Buy a Put .
Strike
Option
Price Premium
96.00
.13
96.50
.40
96.25
.23
Cap at 4%;
0.02
0.11
0.13
Floor: Sell a Call .
Strike
Option
Price Premium
96.75
.02
96.75
.02
96.50
.05
Floor at 3¼ %;
Both: Collar
.
Range of
Net
Borrowing Cost
Premium .
3¼% - 4%
.11 = $275
3¼% - 3½%
.38 = $950
3½% - 3¾%
.18 = $450 .
Collar: Net Cost = 11 basis points.
|
|
|
96.00
96.75
Sell call
|> Futures Price (Q)
|
|
Buy put
|
Loss
a. CAP borrowing rates @ 4%
Must pay 13 bp for this Put
i. If ED rates  above 4%,
ii. If ED rates  below 4%,
by buying a Put with K = 96.00 (= 100 - 4).
(13 x $25 = $325).
Q  below 96.00,
& Put is ITM – Cap at 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 = 96.75 (= 100 - 3.25). Receive 2 bp ($50).
i. If ED rates  below 3.25%, Q  above 96.75%, & Call is ITM – Floor at 3.25%.