423 Mathematics of Finance, Fall 2016.
Homework 2 Solution
1. In anticipation of the new iPhone and Galaxy Note, you decide to invest some of your $100,000 savings in
the Apple and Samsung stocks. The current stock prices are $112.71 for Apple and $1550.0
423 Mathematics of Finance, Fall 2016.
Homework 5 Solution
1. Consider a binomial model with the effective interest rate of 1% per period, the initial stock price
S0 = $120, and parameters u = 1.2 and d = 0.9.
(a) Find the initial price of a European put
423 Mathematics of Finance, Fall 2016.
Homework 2
Due: Thursday 6 October 2016, NO LATER than 1pm.
You may hand in your work during the class or put your solution in the dropbox on my office door. Please
include the SECTION NUMBER in your work.
The maximu
Math 423 Mathematics of Finance, Homework 4
Due Tuesday, Nov/20/12
Problem 1. (8 pts )
Consider a two step binomial tree with the following parameters: S (0) = 100, U = 10%,
D = 10% and R = 3%. Find the prices of
(1) (3 pts ) A European knock-out call opt
Math 423.120 Spring 2012: Midterm Solution
UMID:
Name:
This is a closed book exam. You are allowed one 3 5 note card and a calculator if you
wish. No others materials or devices (including cell phones) are permitted.
Please write all your solutions in thi
COMPUTER ASSIGNMENT I
Due Date: Thursday March 11, 2010 (by 5pm)
Math 423, Mathematics of Finance
Dr. Ahmet Duran, University of Michigan, Department of Mathematics
1. How many dierent values does the random variable S (30) take according to the binomial
Math 423 Mathematics of Finance, Homework 3
Due Thursday, Nov/08/12
Problem 1. (4 pts )
A gap call option is a European call option which at maturity T pays o S (T ) K1 when
S (T ) > K2 , or nothing when S (T ) K2 . Here K1 is known as the strike price an
423 Mathematics of Finance, Winter 2017.
Homework 2
Due: Thursday 9 February 2017, NO LATER than 10am.
You may hand in your work during the class or put your solution in the dropbox on my office door (please
use the folder for your section, and include yo
423 Mathematics of Finance, Winter 2017
Homework 5
Due: Thursday April 13th 2017, NO LATER than 1:00pm.
You may hand in your work during the class or put your solution in the dropbox on my office door (please
use the folder for your section, and include y
423 Mathematics of Finance, Winter 2017.
Homework 1
Due: Thursday 19 January 2017, NO LATER than 10:00am
You may hand in your work during the class or put your solution in the dropbox on my office door (please
use the folder for your section, and include
423 Mathematics of Finance, Winter 2017.
Homework 3
Due: Thursday 16 February 2017, NO LATER than 10am
You may hand in your work during the class or put your solution in the dropbox on my office door (please
use the folder for your section, and include yo
423 Mathematics of Finance, Fall 2016.
Homework 2 Solution
1. In anticipation of the new iPhone and Galaxy Note, you decide to invest some of your $100,000 savings in
the Apple and Samsung stocks. The current stock prices are $112.71 for Apple and $1550.0
423 Mathematics of Finance, Fall 2016.
Homework 4 Solution
1. (10 points) A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for
$150 per ounce and sell gold for $148 per ounce. The trader can borrow funds at 7% per ye
423 Mathematics of Finance, Fall 2016.
Homework 3 Solution
1. Consider a market with only two risky stocks, A and B, and one risk-free asset. We have the following
information about the stocks.
Stock A
Stock B
Total number of shares in the market
100
150
Formulas
1. The present value factor of an annuity is
1(1+r)n
.
r
2. Geometric series (1 + a + a2 + . . . + an ) =
1an+1
1a .
3. Probability formulas. Let a = (a1 , . . . , an ), b = (b1 , . . . , bn ), and is the covariance matrix of
(X1 , . . . , Xn ).
Practice Midterm
423-F16
1. a) What is the accumulated value of $1 after 2 years assuming a semi-annual compounding at 10%?
b) What is the continuous compounding rate in case that an investment of $1 yields $2 after 3 years?
c) Gilad deposits $50 at the e
423 Mathematics of Finance, Winter 2017.
Solution to Homework 1
1.
(a) (2 pts) Assume that the interest rate r is compounded semi-annually. Find r if an investment of $80 today
yields $100 after 4 years.
Solution: Find r such that 80(1 + r/2)8 = 100. Answ
Math 423,
Practice Midterm Exam,
2016
Winter
Problem 1. (10 pts)
A 10 year coupon bond with coupon C1 and face value F = $100 sells for $100. Another 10 year
coupon bond with the same face value F = $100 but with coupon C2 sells for $80. If we know
that C
423 Mathematics of Finance, Winteer 2017.
Homework 4
Due: Thursday March 23rd 2017, NO LATER than 10am.
You may hand in your work during the class or put your solution in the dropbox on my office door. Please
include the SECTION NUMBER in your work.
The m
Math 423,
Homework 4,
Winter 2016
Due Tuesday, Apr. 5
Problem 1. (10 pts)
Consider a two-steps Binomial Tree model with S(0) = $100, U = 0.1, D = 0.1 and one-step
risk-free return R = 0.05.
(1) (5 pts) What is the price of a European call option with K =
Math 423,
Homework 2,
Winter 2016
Solutions
Problem 1. (20 pts)
Assume the same hypothesis of Example 3.29 at Page 76 of the TEXTBOOK.
(1a) (10 pts) Given risk/standard deviation
= 1.5, find the corresponding expected return
on the efficient frontier.
Math 423,
Midterm Exam,
Name:
Winter 2016
UMID
Instructions: There are 5 problems in this exam, and 60 points in total. Write down all
the necessary steps in your computations and proofs. You can write on both sides of the paper.
Partial credits are given
423 Mathematics of Finance, Fall 2016.
Homework 4 Solution
1. (10 points) A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for
$150 per ounce and sell gold for $148 per ounce. The trader can borrow funds at 7% per ye
Answer Key to Quiz 2
423-F16
Name:
1. Consider a forward contract on a stock S with the following data: the annually continuously compounded interest rate is r = 0.06, the maturity date is T = 1 years, S(0) = $100,
and dividends of $5 and $3 are to be pai
423 Mathematics of Finance, Fall 2016.
Homework 3 Solution
1. Consider a market with only two risky stocks, A and B, and one risk-free asset. We have the following
information about the stocks.
Stock A
Stock B
Total number of shares in the market
100
150
University of Michigan
Literature, Science and the Arts (LSA)
Department of Math
Actuarial & Financial
Math 423
Mathematics of Finance
What you should know in this course!
B. Roger Natarajan, PhD, FSA, MAAA
General
1. In the next 8 slides, an attempt is m
University of Michigan
Literature, Science and the Arts (LSA)
Department of Math
Actuarial & Financial
Math 423
Mathematics of Finance
Capinski-Zastawniak (Second Edition)
Chapter 2
B. Roger Natarajan, PhD, FSA
Agenda Chapter 2
1.
2.
3.
4.
5.
6.
7.
8.
Tim
University of Michigan
Literature, Science and the Arts (LSA)
Department of Math
Actuarial & Financial
Math 423
Mathematics of Finance
Capinski-Zastawniak (Second Edition)
Chapter 7
B. Roger Natarajan, PhD, FSA, MAAA
Agenda Chapter 7
General Discrete Time
423 Mathematics of Finance, Winter 2017.
Homework 2 Solution
The maximum number of points you can receive for this homework is 40.
1. In anticipation of the new iPhone and Galaxy Note, you decide to invest some of your $100,000 savings in
the Apple and Sa
Solution to Practice Midterm
423-W17
1. a) What is the accumulated value of $1 after 2 years assuming a semi-annual compounding at 10%?
Solution: 1 (1 + 0.1/2)22 = 1.21.
b) What is the continuous compounding rate in case that an investment of $1 yields $2
423 Mathematics of Finance, Winter 2017.
Solution to Homework 3
The maximum number of points you can receive for this homework is 40.
1. Consider a market with only two risky stocks, A and B, and one risk-free asset. We have the following
information abou