Example of an option strategy
Financial risk management
Example of an option strategy
Jukka Perttunen
University of Oulu - Department of Finance
Spring 2017
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
5
0
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
5
0
(1) We receive ST :
Jukka Perttunen
+ SN(d1 , X = 10)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
Jukka Perttunen
−rT
N(d2 , X = 10)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
If the asset price is ST > 15:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
We cancel (1):
− SN(d1 , X = 15)
Jukka Perttunen
−rT
N(d2 , X = 10)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
If the asset price is ST > 15:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
−rT
N(d2 , X = 10)
We cancel (1):
− SN(d1 , X = 15)
We cancel (2):
+ 10 e
Jukka Perttunen
−rT
N(d2 , X = 15)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
If the asset price is ST > 15:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
−rT
N(d2 , X = 10)
We cancel (1):
− SN(d1 , X = 15)
We cancel (2):
+ 10 e
(3) We receive e5:
Jukka Perttunen
+ 5e
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
If the asset price is ST > 15:
If the asset price is ST > 20:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
−rT
N(d2 , X = 10)
We cancel (1):
− SN(d1 , X = 15)
We cancel (2):
+ 10 e
(3) We receive e5:
+ 5e
We cancel (3):
− 5e
Jukka Perttunen
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
N(d2 , X = 20)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
If the asset price is ST > 15:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
N(d2 , X = 10)
We cancel (1):
− SN(d1 , X = 15)
We cancel (2):
+ 10 e
(3) We receive e5:
If the asset price is ST > 20:
−rT
+ 5e
We cancel (3):
− 5e
(4) We receive e25:
+ 25 e
Jukka Perttunen
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
N(d2 , X = 20)
N(d2 , X = 20)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
If the asset price is ST > 15:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
N(d2 , X = 10)
We cancel (1):
− SN(d1 , X = 15)
We cancel (2):
+ 10 e
(3) We receive e5:
If the asset price is ST > 20:
−rT
+ 5e
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
We cancel (3):
− 5e
(4) We receive e25:
+ 25 e
(5) We pay ST :
− SN(d1 , X = 20)
Jukka Perttunen
−rT
N(d2 , X = 20)
N(d2 , X = 20)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
If the asset price is ST > 15:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
If the asset price is ST > 25:
N(d2 , X = 10)
We cancel (1):
− SN(d1 , X = 15)
We cancel (2):
+ 10 e
(3) We receive e5:
If the asset price is ST > 20:
−rT
+ 5e
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
We cancel (3):
− 5e
(4) We receive e25:
+ 25 e
(5) We pay ST :
− SN(d1 , X = 20)
We cancel (4):
− 25 e
Jukka Perttunen
−rT
−rT
N(d2 , X = 20)
N(d2 , X = 20)
N(d2 , X = 25)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
If the asset price is ST > 10:
If the asset price is ST > 15:
5
0
(1) We receive ST :
+ SN(d1 , X = 10)
(2) We pay e10:
− 10 e
If the asset price is ST > 25:
N(d2 , X = 10)
We cancel (1):
− SN(d1 , X = 15)
We cancel (2):
+ 10 e
(3) We receive e5:
If the asset price is ST > 20:
−rT
+ 5e
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
We cancel (3):
− 5e
(4) We receive e25:
+ 25 e
(5) We pay ST :
− SN(d1 , X = 20)
We cancel (4):
− 25 e
We cancel (5):
+ SN(d1 , X = 25)
Jukka Perttunen
−rT
−rT
N(d2 , X = 20)
N(d2 , X = 20)
N(d2 , X = 25)
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
5
0
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
5
0
+ SN(d1 , X = 10)
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
5
0
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
5
0
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
N(d2 , X = 15)
N(d2 , X = 15)
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
5
0
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 15 e
−rT
N(d2 , X = 15)
6
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
5
0
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 15 e
−rT
N(d2 , X = 15)
6
N(d2 , X = 20)
N(d2 , X = 20)
?−rT
+ 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
−rT
0
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 15 e
−rT
N(d2 , X = 15)
6
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
5
?−rT
+ 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
−rT
0
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 15 e
−rT
N(d2 , X = 15)
6
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
5
N(d2 , X = 25)
?−rT
+ 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
−rT
0
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 15 e
−rT
N(d2 , X = 15)
6
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
5
N(d2 , X = 25)
+ SN(d1 , X = 25)
?−rT
+ 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
−rT
0
SN(d1 , X = 10) − 10 e
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 15 e
−rT
N(d2 , X = 15)
6
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
5
N(d2 , X = 25)
+ SN(d1 , X = 25)
?−rT
+ 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
−rT
6
N(d2 , X = 10)
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
−rT
0
SN(d1 , X = 10) − 10 e
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
+ 15 e
N(d2 , X = 20)
N(d2 , X = 15)
6
N(d2 , X = 25)
+ SN(d1 , X = 25)
?−rT
+ 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
N(d2 , X = 10)
−rT
− SN(d1 , X = 15) − 15 e
N(d2 , X = 15)
− SN(d1 , X = 15)
−rT
−rT
6
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
5
Financial risk management
6
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
−rT
0
SN(d1 , X = 10) − 10 e
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
+ 15 e
N(d2 , X = 10)
6
−rT
− SN(d1 , X = 15) − 15 e
N(d2 , X = 15)
− SN(d1 , X = 15)
−rT
−rT
N(d2 , X = 15)
6
6
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
5
N(d2 , X = 25)
+ SN(d1 , X = 25)
?−rT
+ 20 e
N(d2 , X = 20)
?
−rT
− SN(d1 , X = 20) − 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
Financial risk management
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
−rT
0
SN(d1 , X = 10) − 10 e
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
+ 15 e
N(d2 , X = 10)
6
−rT
− SN(d1 , X = 15) − 15 e
N(d2 , X = 15)
− SN(d1 , X = 15)
−rT
−rT
N(d2 , X = 15)
6
6
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
5
N(d2 , X = 25)
+ SN(d1 , X = 25)
?−rT
+ 20 e
N(d2 , X = 20)
?
−rT
− SN(d1 , X = 20) − 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
?−rT
SN(d1 , X = 25) − 25 e
Financial risk management
N(d2 , X = 25)
Example of an option strategy
Example of an option strategy
Asset price at the maturity
Option payoff
ST < 10
0
10 ≤ ST < 15
15 ≤ ST < 20
ST − 10
20 ≤ ST < 25
ST ≥ 25
25 − ST
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
− SN(d1 , X = 15)
+ 10 e
+ 5e
− 5e
+ 25 e
−rT
−rT
−rT
−rT
N(d2 , X = 15)
N(d2 , X = 15)
−rT
c10 − c15 − c20 + c25
5
0
SN(d1 , X = 10) − 10 e
+ SN(d1 , X = 10)
− 10 e
−rT
N(d2 , X = 10)
+ 15 e
N(d2 , X = 10)
6
−rT
− SN(d1 , X = 15) − 15 e
N(d2 , X = 15)
− SN(d1 , X = 15)
−rT
−rT
N(d2 , X = 15)
6
6
N(d2 , X = 20)
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
Condor:
N(d2 , X = 25)
+ SN(d1 , X = 25)
?−rT
+ 20 e
N(d2 , X = 20)
?
−rT
− SN(d1 , X = 20) − 20 e
N(d2 , X = 20)
− SN(d1 , X = 20)
− 25 e
−rT
N(d2 , X = 25)
+ SN(d1 , X = 25)
Jukka Perttunen
?−rT
SN(d1 , X = 25) − 25 e
Financial risk management
N(d2 , X = 25)