Derivatives
Fall, 2014
Chapter 12 & 13
1. (Slide 11) S = $41, K = $40, = 0.3, r = 8%, t = 0.25, Div = $3 in one month. What
is the BS European call price?
P
F0,T
(S) = S PV (Div)
= 41 3e0.08/12
= 38. 020
P
F0,T
(K) = 40e0.08/4 = 39. 208
d1
P (S) /F P (K)

Derivatives
Fall, 2014
Chapter 9
1. Suppose that you buy a e1,000,000 call option against dollars with a strike price of
$1.2750/e. Describe this option as the right to sell a specific amount of dollars for
euros at a particular exchange rate of euros per

Derivatives
Fall, 2014
Chapter 5
1. XYZ stock costs $100 today and is expected to pay a quarterly dividend of $1.25. If
the risk-free rate is 10% compounded continuously, how much does a 1-year prepaid
forward cost?
P
F0,1
= $100
4
X
$1.25e0.025i
i=1
= $

Derivatives
Fall, 2014
Chapter 7
1. What are the implied forward rate r0 (2, 3) and forward zero-coupon bond price P0 (2, 3)
from year 2 to year 3?
The formula is
[1 + r0 (t1 , t2 )]t2 t1 =
[1 + r0 (0, t2 )]t2
P (0, t1 )
=
t
1
[1 + r0 (0, t1 )]
P (0, t2 )

Derivatives
Fall, 2014
Chapter 8
1. Suppose the forward curve for oil rises by $2 in years 1 and 2. The year 1 forward
price is $22 and year 2 is $23. The market value of the original swap is no longer
zero. With same interest, new swap price is $22.483 (

Derivatives
Fall, 2014
Chapter 3
1. Insuring a Long Position: Floors Example S&R index and a S&R put option with
a strike price of $1,000 together. Payoff is the sum of the first two columns. Cost
plus interest for the position is ($1000+74.201)1.02 = $10

Derivatives
Fall, 2014
Foreign currency forward
Consider the following set of foreign and domestic continuously compounded interest
rates and spot and forward exchange rates
Spot exchange rate ($/)
x0
360-day forward rate ($/) F0,360
U.S. interest rate
r

Derivatives
Fall, 2014
Chapter 4
A gold-mining firm Golddiggers will be selling gold in 1 year, with a production cost of
$380 per ounce. The effective interest rate is 5%.
Lets compare two hedging strategies:
1. buying a 420-strike put with premium of $8