Ewa Kubicka
http://www.math.louisville.edu/~ewa/
Course M (MLC & MFE) seminar: http://www.math.ilstu.edu/actuary/prepcourses.html
Course MLC Manual: http://www.neas-seminars.com/registration/
Practice Problem for exam MFE for the week after 07/07/07.
Suppose that XYZ is a nondividend-paying stock. Suppose S = $100,
σ = 40%, δ = 0, and r= 0.06.
a. What is the price of a 105-strike call option with 1 year to expiration?
b. What is the 1-year forward price for the stock?
c. What is the price of a 105-strike call option, where the underlying asset is a
futures contract maturing at the same time as the option?
Solution on the next page.
Solution (02/03/07) (problem from DM)
 ln S /K + r − δ + 1 σ 2 T 
 ln S /K + r − δ − 1 σ 2 T 
( )
( )
2
2


=
−rT
Call Price= Se N
− Ke N 




σ T
σ T




 ln(100 /105) + 0.06 + 0.16 
 ln 100 /105) + 0.06 − 0.16 
2  −105e−0.06 N  (
2  = $16.33.
= 100e−0 N




0.4
0.4




€
(
−δT
(
)
)
(
(
)
)
Forward Price = F0,T = Se rT = (100)e 0.06 = $106.1837.
€
 ln( S /K ) + 1 σ 2T 
 ln( S /K ) − 1 σ 2T 
2
2
 − Ke−rT N 
=



σ T
σ
T



 ln(100 /105) + 0.16 
 ln(100 /105) − 0.16 
2  −105e−0.06 N 
2  = $16.33.
= 100e−0.06 N
 € 0.4



0.4




€
Call Price on Futures = ( δ = r) = Se−rT N 

€

€
This exercise shows the general result that a European futures option has the same value
as the European stock option provided the futures contract has the same expiration as the
stock option.
© Copyright 2007 by Ewa Kubicka. All rights reserved. Reproduction in whole or in
part without written permission from the author is strictly prohibited.