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
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
Solvin
IEOR 221 Introduction to Financial Engineering
Spring 2008
Final Exam Practice Question Solutions
Question 1
Then the risk-neutral probability is
q = (R d)/(u d) = 0.69133
.
Stock Price
300
American-S
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 fixe
- Question i
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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 va
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-fa
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
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 =
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 = 7.4
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
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 ob
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 = 7.4
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 p
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
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 ,
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
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 curren
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 bet
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
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 ye
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.
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 , t
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. Sol
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, t
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
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 polic