Homework 8, FINA 471
Fall, 2012
The following problems assume the effective 1-year interest rate of 2% and use the
premiums in the table for the options on a stock with 1 year to expiration:
Strike
95
100
105
Call
12.04
9.38
7.18
Put
5.18
7.42
10.12
Probl
Homework 9, FINA 471 Fall, 2011
PROBLEM 1 The current exchange rate is $1.44/, the euro interest rate is 3.5%, the dollar interest rate is 2%, and the price of a 3-month $1.45-strike European
put option is $0.12. What is the price of a 3-month $1.45-strik
Homework 2, FINA 471
Fall, 2013
1. A. The initial spot price is irrelevant. The profit of the short position is 1465 1460 = 5.
2. B. 47.5 50 = -2.5
3. C. Note that the yen exchange rate is quoted in terms of yen price per dollar. The profit of short
posit
Homework 2, FINA 471
Fall, 2013
Problem 1
The spot price of gold is $1450/oz. A 3-month gold forward contract is priced at
$1465/oz. What is the profit to a trader who has a short position in the forward contract
if the spot price of gold increases to $14
Homework 1, FINA 471
Fall, 2013
1. D. 1000*(1+0.1/2)2 = 1102.50.
2. A. 1200*e-0.10*2 = 982.48.
3. D. Trader A starts with 5 long contracts and is involved in three transactions during the day. 5 +
20 10 35 = 20.
4. C. 20 + 5 + 10 + 35 = 70.
5. D. From pro
Homework 3, FINA 471
Fall, 2013
1. C. When the stock price is 110, both options are exercised. Profit = (12.04 + 7.18)*1.02 + (110
95) (110 105) = 5.04
2. C. When the stock price is 100, the 95-call is exercised but the 105-call expires. Profit = (100
9
Homework 1, FINA 471
Fall, 2013
Problem 1
An investment of $1000 today pays an annual interest rate of 10%. How much is the investment worth
after one year if the interest is compounded semi-annually?
A.
B.
C.
D.
$1050
$1050.63
$1100
$1102.50
Problem 2
Th
Homework 3, FINA 471
Fall, 2013
The following problems assume the effective 1-year interest rate of 2% and use the
premiums in the table for the options on a stock with 1 year to expiration:
Strike
95
100
105
Call
12.04
9.38
7.18
Put
5.18
7.42
10.12
Probl
Homework 8, FINA 471
Fall, 2012
1. B. When the stock price is 100, the 95-call is exercised but the 105-call expires. Profit = (12.04 +
7.18)*1.02 + (100 95) = 0.04
2. B. Both options are exercised. Profit = (110 95) + (110 105) + (12.04 7.18)*1.02 = 5.04
Homework 4, FINA 471
Fall, 2013
Problem 1
The current stock price is $65. A trader writes a covered put on the stock by short selling the
stock and selling the 6-month 60-strike put option on the stock for $2. The effective 6-month
interest rate is 1%. Wh
Homework 4, FINA 471
Fall, 2013
1. B. Profit from short stock is 65*1.01 75 = -9.35. The option is not exercised. Profit from write
option is 2*1.01 = 2.02. Total profit is -9.35 +2.02 = -7.33.
2. A. Profit from long stock is 65 - 65*1.01 = -0.65. The opt
Homework 7, FINA 471
Fall, 2013
B. Solve equation 95.5 = 100/(1+r)3 to find r = (100/95.5)1/3 -1 = 1.547%.
B. Use the pricing formula for zero-coupon bonds P = 100/(1+1.2%)2 = 97.643.
C. Use the pricing formula for coupon bonds P = 0.04*99.25 + 0.04*98.1
Homework 6, FINA 471
Fall, 2013
1. C. F = 1.3620*e(0.02-0.01)*0.5 = 1.3688.
2. D. The forward exchange rate of 1.3620 is too cheap, relative to the fair forward exchange rate
obtained in the previous problem. An arbitrager should buy the forward contract
Homework 6, FINA 471
Fall, 2013
Problem 1
The spot $/ exchange rate is $1.3620, the annual continuously compounded dollar interest rate is
2%, and the annual continuously compounded euro interest rate is 1%. The no-arbitrage 6-month
forward $/ exchange ra
Homework 5, FINA 471
Fall, 2013
1. B. F = 1680*e(0.01-0.03)*9/12 = 1654.99.
2. A. From problem 1, the no-arbitrage price is 1654.99. So the forward price of 1670 is too high,
relative to the fair value. The arbitrager should short the forward at 1670, and
Homework 5, FINA 471
Fall, 2013
Problem 1
The current S&P 500 index is 1680. The annual dividend yield on the index is 3%. The
continuously compounded annual interest rate is 1%. What should be the fair price of a
forward contract on the index that expire
Homework 8, FINA 471
Fall, 2013
1. B. The buyer receives because the spot price is higher than the swap price. Receipt = (98.5
98)*100000 = $50,000.
2. C. The buyer pays because the spot price is lower than the swap price. Payment = (98
96.75)*100000 =
Homework 7, FINA 471
Fall, 2013
Problem 1
Consider a 3-year zero-coupon bond with face value $100. The bond price is quoted at
95.50. The effective annual yield of this bond is _.
A.
B.
C.
D.
1.541%
1.547%
1.724%
2.329%
Problem 2
Consider a 2-year zero-co
Syllabus
Derivative Securities
FINA 471, Fall 2013
Instructor: Shu Yan
Class Meetings: Monday and Wednesday (Section 1 2:20-3:35 and Section 2 3:55-5:10)
Office Hours: Monday and Wednesday 1:00-2:00, Tuesday 2:00-5:00, or by appointment
Office: BA 475
Tel
Homework 11, FINA 471
Fall, 2012
1. D. You can use the spreadsheet from the textbook to solve this problem. To do this on your own,
you need to build a 2-step tree first. The up- and down- multipliers are: u = e(0.02-0.03)*0.25+0.30*0.5 =
1.1589 and d = e
Homework 10, FINA 471
Fall, 2012
1. C. p* = (e(0.02-0.03)*0.5 0.95)/(1.05 0.95) = 0.4501. Probability of moving down = 1- p* = 1
0.4501 = 0.5499.
2. B. The stock price after 6 months is Su = 50*1.05 = 52.5 or Sd = 50*0.95 = 47.5. The payoff of the
option
Homework 9, FINA 471
Fall, 2012
Problem 1
The current exchange rate is $1.28/, the euro interest rate is 3.5%, the dollar interest rate
is 2%, and the price of a 3-month $1.30-strike European put option on the euro is $0.12.
What is the price of a 3-month
Homework 7, FINA 471
Fall, 2012
Problem 1
An oil buyer and a seller entered into a financially settled 5-year swap for 100,000 barrels
with annual settlement and the swap price of $98/barrel. At the first settlement, the oil
spot price is $98.5/barrel. Wh
Homework 6, FINA 471
Fall, 2012
Problem 1
Consider a 3-year zero-coupon bond with face value $100. The bond price is quoted at
95.50. The effective annual yield of this bond is _.
A.
B.
C.
D.
1.541%
1.547%
1.724%
2.329%
Problem 2
Consider a 2-year zero-co
Homework 5, FINA 471
Fall, 2012
Problem 1
The spot price of gold is $1575.00/oz. The storage costs are $1.00/oz per month paid at
the beginning of a month. The annual continuously compounded interest rate is 5%.
What is the no-arbitrary 4-month forward pr
Homework 4, FINA 471
Fall, 2012
Problem 1
The current S&P 500 Index is 1350. The annual dividend yield on the index is 3%. The
continuously compounded annual interest rate is 1%. What should be the fair price of a
forward contract on the index that expire
Homework 3, FINA 471
Fall, 2012
Problem 1
A trader writes a covered put on a stock by short the stock for $65 and selling the 6-month 60strike put option on the stock for $5. The effective 6-month interest rate is 1%. What is the
traders profit in 6 month
Homework 2, FINA 471
Fall, 2012
Problem 1
The spot price of gold is $1588/oz. A 3-month gold forward contract is priced at
$1593/oz. What is the profit to a trader who has a long position in the forward contract if
the spot price of gold decreases to $158
Homework 1, FINA 471
Fall, 2012
Problem 1
An investment of $1000 today pays an annual interest rate of 5% compounded semi-annually.
How much money will you have after 3 years?
A.
B.
C.
D.
$1157.63
$1159.69
$1331.00
$1340.10
Problem 2
The continuously comp
Homework 10, FINA 471
Fall, 2012
Problem 1
The price of a dividend-paying stock in six months follows a binomial tree. Let S0 = $50,
r = 2%, = 3%, u = 1.05, d = 0.95, and h = 0.5. The risk-neutral probability that the
stock price moves down is _.
A.
B.
C.