174mt1 - year What is the the correct price of a one year...

Math 174
Midterm 1
February 2, 2011
Do the following problems. Show all your work. Partial credit will be given
only for exhibited work. Good Luck!
1. ( 20 points)
(a) (6 points) Graph a bull spread with a stock S as underlying made
with calls and strike prices K
1
and K
2
, with K
1
< K
2
, and
expiration date T .
(b) (6 points)Give explicit formulas, as a function of S
T
and the
other data, for the profit of the spread (assume the spread costs
nothing).
(c) (4 points)How should the graph be shifted if we include the cost
of creating the spread?
(d) (4 points) What is the profit from the spread when K
1
= 20 and
K
2
= 30 when the S
T
= 19, S
T
= 25 and S
T
= 40.
1

2. ( 20 points)
(a) (8 points) Explain what an arbitrage is.
(b) (12 points) The spot price on an asset is $ 50 per unit. The risk-
free interest rate is 10%. Suppose the six month forward price
is $51.50. Is there an arbitrage? If so, explain how you would
exploit it to make money.
2

3. (25 points)
(a) (6 points) The price of a European call option with strike price
$50 on a non-dividend-paying stock is $6. The stock price today
is $51 and the risk-free rate is 6%.