This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 52 + (0.1 + 0.5 · 0.32 ) 365
50
q
= 0.5184
60
0.3 365
r
60
d2 = 0.5184 0.3
= 0.3968
365
N (d1 ) = N (0.52) = 0.6985, N (d2 ) = N (0.40) = 0.6554 d1 = e rt =e 60
0.1· 365 C = 52 · 0.6985 = 0.9837
50 · 0.9837 · 0.6554 = 4.086 13 / 25 Example 11.2. Solution (cont.)
The value of the 60day 55strike European call:
60
ln 52 + (0.1 + 0.5 · 0.32 ) 365
55
q
= 0.2652
60
0.3 365
r
60
d2 = 0.2652 0.3
= 0.3868
365
N (d1 ) = N ( 0.27) = 0.3936, N (d2 ) = N ( 0.39) = 0.3483 d1 = e rt =e 60
0.1· 365 C = 52 · 0.3936 = 0.9837
55 · 0.9837 · 0.3483 = 1.623 The portfolio is worth: 4.086
The proﬁt is: 2.463 1.994e 1.623 = 2.463
30
0.1· 365 = 0.453 14 / 25 Calendar spreads buy A calendar spread consists of selling a call and being another call
with the same strike price on the same stock but a later expiry
date.
This is a bet on volatility. 15 / 25 Example 11.3
For a calendar spread consisting of selling a 30day European call
on a stock and buying a 90day European call on the same stock,
both with strike price 45, we are given:
(i) The initial price of the stock is 50
(ii) = 0.3 (iii) r = 0.05
(iv) =0 the 1. Calculate the proﬁt on a 30th day if the stock price goes up to
50. the 2. Calculate the proﬁt on a 30th day if the stock price stays the
same at 45. 16 / 25 Example 11.3. Solution.
The investment in the spread is the di↵erence in the premiums of
the options.
The premium of the 30day call is:
30
ln 50 + (0.05 + 0.5 · 0.32 ) 365
45
q
= 1.3158
30
0.3 365
r
30
d2 = 1.3158 0.3
= 1.2298
365
N (d1 ) = N (1.32) = 0.9066, N (d2 ) = N (1.23) = 0.8907 d1 = C = 50 · 0.9066 45 · e 30
0.1· 365 · 0.8907 = 5.413 17 / 25 Example 11.3. Solution (cont.)
The premium of the 90day call is:
90
ln 50 + (0.05 + 0.5 · 0.32 ) 365
45
q
= 0.8645
90
0.3 365
r
90
d2 = 0.8645 0.3
= 0.7155
365
N (d1 ) = N (0.86) = 0.8051, N (d2 ) = N (0.72) = 0.7642 d1 = C = 50 · 0.8051 45 · e 90
0.05· 365 · 0.7642 = 6.287 The initial investment is: 6.287 5.413 = 0.874 18 / 25 Example 11.3. Solution (cont.)
After 30 days, if the stock price is 50, the value of the 90day call,
which is now a 60day call,...
View
Full
Document
This document was uploaded on 02/26/2014.
 Fall '14

Click to edit the document details