IEOR 221 - Spring 2016
Homework 11
Due 04/29/2016
1. A stock price is currently S0 = $25. It is known that at the end of two months it
will be either ST = $23 or ST = $27. The risk-free interest rate is an APR of 10%
compounded bimonthly. What is the valu
IEOR 221 - Spring 2015
Homework 6 Solutions
1. We set up the following three equations with three unknowns rX , rY , M .
(a) rX = 0.05 + 1.5(M 0.05)
(b) rY = 0.05 + 2.0(M 0.05)
(c) rY = 1.10 rX
Solving yields rX =
1
,r
14 Y
=
11
, M
140
=
9
.
140
Since rP
IEOR 221
Ilan Adler
Asset Derivatives - Forward and Futures
A forward contract is an agreement to buy (or sell) a unit of an asset (e.g. stock,
currency, commodity, etc.) for a fixed price F at a fixed time in the future T . Note that
no money or assets a
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IEOR221-Spring 2015
Practice Final Questions
1. The following bonds are available on the domestic market:
Bond A - maturity: 1 year, zero-coupon, face value: $100
Bond B - maturity: 2 years, face value: $1000, annual coupon: $50
It is known that the spo
IEOR 221 Introduction to Financial Engineering
Spring 2008
Final Exam Practice Question
Question 1
For a three period Binomial Tree Model, assume:
Current Stock Price: $300
Up-factor: u = 1.25
Down-factor: d = 0.8
Interest rate per period: 11.11% (So R =
IEOR 221 Practice Midterm
Problem 1
An investor is trying to decide whether she should invest the $30,000 she received from the sale of her
boat in a Hi-Tech venture or in a small fast-food restaurant. If she invests in the Hi-Tech venture she will
receiv
IEOR 221
Ilan Adler
Optimal Portfolio Selection
We consider a model of investment in a portfolio of shares is purchased now (time 0) and
to be sold at a given time (say time 1) in the future. Let Ri =
Qi Pi
Pi
be random variables
representing the return r
IEOR 221 - Spring 2015
Homework 9 Solutions
1. Solution: We have u = 1.03, d = 0.99 and R = 1.01. The risk-neutral probabilities
are qu = Ru dd = 0.5 and qd = 1 qu = 0.5.
(a) K = 80, we find Cu3 = 7.418, Cu2 d = 4.023, Cud2 = 0.76 and Cu3 = 0. Thus
1 3
cf
IEOR 221 - Spring 2016
Assignment 2
Due 02/05/2016
1. When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh owers on
her grave every Sunday as long as he lived. A bunch of fresh owers that the former
baseball player thought appropriate fo
IEOR 221 - Spring 2015
Homework 7 Solutions
1. (a) The investor is obligated to sell pounds for 1.4000 when they are worth 1.3900.
The gain is (1.4000 1.3900) 100, 000 = 1, 000.
(b) The investor is obligated to sell pounds for 1.4000 when they are worth 1
IEOR 221 - Spring 2015
Homework 9 Solutions
1. Solution: We have u = 1.03, d = 0.99 and R = 1.01. The risk-neutral probabilities
= 0.5 and qd = 1 qu = 0.5.
are qu = Rd
ud
(a) K = 80, we find Cu3 = 7.418, Cu2 d = 4.023, Cud2 = 0.76 and Cu3 = 0. Thus
1 3
cf
IEOR 221 - Spring 2015
Homework 8 Solutions
1. Solution: Note that it is never optimal to exercise an American call option if the
underlying asset is non-dividend-paying stock. However, for American put, early exercise may be optimal. For instance, if the
IEOR 221 - Spring 2016
Homework 9
Due 04/15/2016
1. Explain why the arguments leading to put-call-parity for European options cannot be
used to give a similar results for American options.
2. Suppose that put options on a stock with strike prices $30 and
IEOR 221 - Spring 2016
Assignment 3
Due 02/12/2016
1. Suppose two competing projects have cash flows of the form (A1 , B1 , B1 , ., B1 ) and
(A2 , B2 , B2 , ., B2 ), both with the same length and A1 , A2 , B1 , B2 all positive. Suppose B1 /A1 > B2 /A2 . S
IEOR 221 - Spring 2016
Homework 8
Due 04/08/2016
1. A trader enters into a short forward contract to sell 100, 000 British pounds for US
dollars at an exchange rate of 1.4000 US dollars per pound. How much does the
investor gain or lose if the exchange ra
IEOR 221 - Spring 2016
Homework 10
Due 04/22/2016
1. The current stock price is $80 and the stock pays no dividend. Each month, the stock
price is either going up by 3% or going down by 1%. The current interest rate is an
APR of 12% with monthly compoundi
IEOR 221 - Spring 2016
Homework 6
Due 03/08/2015
1. The expected returns and variances (of returns) for three assets are:
ASSET RETURN VARIANCE
1
0.10
0.04
2
0.15
0.09
3
0.17
0.25
The correlations between the returns are 12 = 0.20, 13 = 0.50, 23 = 0.30. N
IEOR 221 - Spring 2016
Homework 7
Due 03/29/2016
1. Assume that CAPM holds, i.e. ri = r0 + i (m r0 ), where i =
im
2 .
m
Your goal is to create a portfolio of stocks X, Y, and the risk-free asset. The beta of
the portfolio is P = 0.70. X has a beta of 1.5
IEOR 221 - Spring 2016
Homework 5
Due 02/26/2015
1. Consider a two-year spot rate of 5% and a five-year spot rate of 6%. What is the
forward rate for a loan starting in two years and maturing three years later?
2. Suppose that today a six-year spot rate i
IEOR 221 - Spring 2016
Homework 4
Due 02/19/2015
1. Find the price and duration of a 10-year, 8% bond that is trading at a yield of 10%
(APR). (This bond has semi-annual payments) Face value is $1000.
2. Consider the four bonds having annual payments as s
IEOR 221 - Spring 2015
Homework 1 Solutions
1. The effective monthly interest rate is r = 9.6%/12 = 0.8%, and the number of assumed
payments are 12 5 = 60, assume the original monthly payment is P , then
60
X
i=1
P
= 10, 000 1, 000 = 9, 000 = P = 189.47.
IEOR 221 - Spring 2014
Homework 10 Solutions
1. Solution: We have u = 1.08, d = 0.92, so
qu =
Rd
= 0.6041,
ud
qd = 1 qu .
Hence the option price is given by
C0 =
1
[qu 729 + qd 529] = 639.18.
R
2. Solution: The Binomial Lattice is as follows:
Figure 1: Th
IEOR 221 - Spring 2015
Homework 3 Solutions
1. Periods: m = 2. Coupon rate per period: c = 8%/2 = 4%. Yield per period:
y = 10%/2 = 5%, and the number of remaining periods: n = 10 2 = 20.
Therefore, the price of the bond is
P = 1000 4%
1 (1 + 5%)20
1000
+
IEOR 221 - Spring 2015
Homework 2 Solutions
1. The monthly interest rate is 12%/12 = 1%. The present value of rent for current
apartment after penalty is:
5
X
1000
= 4853.43.
(1 + 1%)i
i=1
The present value of rent for the alternative apartment is:
6
X
90
Homework 1
IEOR 221 - SPRING 2016
Due 01/29/2016
1 + EAR = (1 + r)n
if n is number of compounding periods per year and r is the interest rate per period.
1. A well-known insurance company oers a policy known as the Estate Creator Six Pay.
Typically the po