1. Describe the profit from the following portfolio: a long forward contract on an underlying
asset, and a long European put option on the asset with the same maturity as the forward
contract.
The strike price of the option is equal to the forward price of the underlying
asset as the time the portfolio is set up.
Answer:
The terminal value of the long forward contract is:
S
T

F
0
where
S
T
is the price of the asset at maturity and
F
0
is the forward price of the asset at
the time the portfolio is set up. (The delivery price in the forward contract is
F
0
.) The
terminal value of the put option is:
max(
F
0

S
T
,
0)
The terminal value of the portfolio is therefore
S
T

F
0
+ max(
F
0

S
T
,
0) = max(0
, S
T

F
0
)
This is the same as the terminal value of a European call option with the same maturity
as the forward contract and an exercise price equal to
F
0
. The profit equals the terminal
value less the amount paid for the option.
2. A 10year 8% coupon bond currently sells for $90. A 10year 4% coupon bond currently
sells for $80. What is the 10year zero rate?
Answer:
A long position in two of the 4% coupon bonds combined with a short position
in one of the 8% coupon bonds leads to the following cash flows.
Y ear
0 : 90

2
×
80 =

70
Y ear
10 : 200

100 = 100
since the coupons cancel out. The 10year spot rate is therefore
1
10
ln
100
70
= 0
.
0357
or 3.57% per annum.
3. Suppose that you enter into a sixmonth forward contract on a nondividendpaying stock
when the stock price is $30 and the riskfree interest rate (with continuous compounding)
is 12% per annum. What is the forward price? Explain your reason clearly.
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 Winter '09
 Adam
 Derivative, Strike price

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