MGT 3084 Midterm 2 Name: _
Make sure you read the questions carefully.
c + Ke -rT = p + S0
fu f d Su Sd
p e d u d
rT
= [ p u + (1 p )d ]erT
Please return the exam to me.
1. A security giving you the right to buy IBM stock in the future but not
Assume that the stock follows a binomial model as follows:
t=0
t=1
26
t=2
30
35
31
28
25
23
If you put $100 in the cash account, w
t=0
t=1
1
t=2
1.1
1.1
1.15
1.15
1.2
1.2
Find today's price of call option which pays ( S_2 - 25, 0 ) at t=2.
Assume that the
SOLUTIONS TO HOMEWORK 1
1. If F is the forward price and S is the stock price today then
F = S exp[ rT ]
where r = 0.05 and T = 0.25 years. Therefore,
F = 100 exp[0.05 * 0.25] = 100 exp[0.0125]
After one month, the investor holds a forward contract with d
SOLUTIONS TO HOMEWORK 2
1. If p is the price of the European put option, we know that
p max( X exp(r (T t ) S ,0)
Therefore,
p max(65 exp(0.1 * 2 / 12) 58,0)
= 65 exp(0.1 / 12) 58
since 65 exp(0.1 / 12) 58 0
2. By equation (7.4) on pg. 178 of Hull, we hav
SOLUTIONS TO HOMEWORK 3
1. a) Let the riskless hedge consist of 1 call option and y shares of the stock. Then,
we have
Downtick : Value = 0 + 25*y
Uptick : Value = 15 + 75*y
Since the portfolio is riskless, we must have
25*y = 15 + 75*y
Therefore
y = 15 /
SOLUTIONS TO HOMEWORK 4 (due on April 4, 2002)
1. The volatility of a stock is 40% per annum . What is the standard deviation of the
proportional price change in one trading day ?
The standard deviation of the proportional price change is 0.4 1 / 365 .
2.
SOLUTIONS TO MIDTERM 1
1.
a) If Rc is the continuously compounded interest rate , then
Rc = 4 ln(1 + Rm / 4)
= 4 ln(1 + 0.05 / 4) = 4 ln(1 + 0.0125)
b)If F is the forward price , then
F = S exp( Rc T ) =
= S exp( Rc / 4) = 100 exp( Rc / 4)
c) The payoff o
MGT 3084: MID-TERM 2 (10/23/2002)
1. You may use sheets containing any formulae you might need
2. Please show all your working. Its not enough just to write down the answers
and there will be lots of partial credit.
1. (15 points) Consider a one-period bi
MGT 3084 Midterm 2 Name: _
Make sure you read the questions carefully.
c + Ke -rT = p + S0
fu f d Su Sd
p e d u d
rT
= [ p u + (1 p )d ]erT
Please return the exam to me.
1. A security giving you the right to buy IBM stock in the future but not
Legal Forms of Business Organization -Sole Proprietorship -Partnership -Corporation -Limited Liability Company (LLC) Variation of Basic Organizational Alternatives -Sole Proprietorship -General Partnership (GP or LP) -Limited Liability Partnership (L