Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.1
Trading Strategies
Involving Options
Chapter 8
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.2
Three Alternative Strategies
Take a position in:
–the option and the underlying
–2 or more options of the same type
This is known as a spread
–a mixture of calls and puts
This is known as a combination
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.3
Payoffs from Options
Figure 8.1 (p,186) (Remember c – p = S0 – Xe-rT)
Profit
X ST
Short Call Long Stock
X
ST
Long Call Short Stock
Profit
X
ST
Long Put Long Stock
Profit Profit
X ST
Short Put Short Stock
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.4
Bull Spread Using Calls
(Figure 8.2,page 187)
X1 X2
Profit
ST
-- requires an initial investment
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.5
Bull Spread Using Puts
Figure 8.3,page 189
X1 X2
Profit
ST
-- involves a positive cash flow
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.6
Bear Spread Using Calls
Figure 8.4,page 189
X1 X2
Profi
t
ST
-- involves a positive cash flow
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.7
Bear Spread Using Puts
Figure 8.5,page 190
X1 X2
Profit
ST
-- requires an initial investment
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.8
Butterfly Spread Using Calls
Figure 8.6,page 191
X1 X3
Profit
STX2
-- requires a small investment initially
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.9
Butterfly Spread Using Puts
Figure 8.7,page 192
X1 X3
Profit
STX2
-- requires a small investment initially
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.10
Calendar Spread Using Calls
Figure 8.8,page 193
X
Profit
ST
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.11
Calendar Spread Using Puts
Figure 8.9,page 193
X ST
Profit
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.12
A Straddle Combination
Figure 8.10,page 194
Profit
STX
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.13
Strip & Strap
Figure 8.11,page 196
Profit
X ST
Profit
X ST
Strip Strap
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.14
A Strangle Combination
Figure 8.12,page 196
X1 X2
Profit
ST
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.15
The Example
You have both puts and calls at the strikes indicated below
X1 X2 X3 S0= 100
r = 8%
95 100 105 T = 0.25
From the given call prices of
c1 = 9.00
c2 = 5.00
c3 = 2.00
What are the corresponding put prices?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.16
The Example
(continued)
We can derive the put prices as follows:
The boundary conditions are (note all prices are > 0)
Note that if the calls meet the boundary so will the puts
92.2)9 8 02.0*105(10000.2:
98.1)9 8 02.0*100(10000.5:
88.6)9 8 02.0*95(10000.9:
3
2
1



c
c
c
92.492.292.102100e105100e
02.398.102.98100e100100e
12.288.612.93100e95100e
3
25.0*08.0
3033
2
25.0*08.0
2022
1
25.0*08.0
1011






pKSpc
pKSpc
pKSpc
rT
rT
rT
)e,0m a x (
)e,0m a x (
0
0
SKp
KSc
rT
rT


Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.17
The Example
(continued)
Bull Spread with calls
t = 0 ST<95 95< ST<100 ST >100
Buy c1 -9.00 0 ST -95 ST -95
Sell c2 5.00 0 0 -(ST -100)
Net Flows -4.00 0 ST-95 100-95
Bull Spread with puts
t = 0 ST<95 95< ST<100 ST >100
Buy p1 -2.12 95-ST 0 0
Sell p2 3.02 -(100-ST) -(100-ST) 0
Net Flows 0.90 95-100 ST -100 0
Note,Graphs to different scales
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.18
The Example
(continued)
Bear Spread with calls
t = 0 ST<95 95< ST<100 ST >100
Sell c1 9.00 0 -(ST -95) -(ST -95)
Buy c2 -5.00 0 0 ST -100
Net Flows 4.00 0 95-ST 95-100
Bear Spread with puts
t = 0 ST<95 95< ST<100 ST >100
Sell p1 2.12 -(95-ST) 0 0
Buy p2 -3.02 100-ST 100-ST 0
Net Flows -0.90 100-95 100-ST 0
Note,Graphs to different scales
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.19
The Example
(continued)
Butterfly Spread with calls (note 2K2=K1+K3)
t = 0 ST<95 95< ST<100 100< ST<105 ST >105
Buy c1 -9.00 0 ST -95 ST -95 ST -95
Sell 2c2 2*5.00 0 0 -2(ST -100) -2(ST -100)
Buy c3 -2.00 0 0 0 ST -105
Net Flows -1.00 0 ST-95 105- ST 0
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.20
The Example
(continued)
Butterfly Spread with puts (note 2K2=K1+K3)
t = 0 ST<95 95< ST<100 100< ST<105 ST >105
Buy p1 -2.12 95- ST 0 0 0
Sell 2p2 2*3.02 -2(100- ST) -2(100- ST) 0 0
Buy p3 -4.92 105- ST 105- ST 105- ST 0
Net Flows -1.00 0 ST-95 105- ST 0
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.21
The Example
(continued)
Straddle at K = 100
t = 0 ST<95 95< ST<100 100< ST<105 ST >105
Buy c2 -5.00 0 0 ST -100 ST -100
Buy p2 -3.02 100- ST 100- ST 0 0
Net Flows -8.02 100- ST 100- ST ST -100 ST -100
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.22
The Example
(continued)
Strangle about K = 100
t = 0 ST<95 95< ST<100 100< ST<105 ST >105
Buy c3 -2.00 0 0 0 ST -105
Buy p1 -2.12 95- ST 0 0 0
Net Flows -4.12 95- ST 0 0 ST -105
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2003,Shanghai Normal University
8.23
Assignments
8.4,8.7,8.10,8.11,8.12,8.13,8.14,
8.16,8.17,8.18
Assignment Questions