21-270
February 22, 2012
INTRO TO MATH FINANCE
Spring 2012
Test 1
Name:
Write your answers clearly in the spaces provided. You may use the back of a page
for additional space; please indicate clearly when you do so. Show all work. No credit
will be given
21-270
April 30, 2012
INTRO TO MATH FINANCE
Spring 2012
Test 3
Name:
Write your answers clearly in the spaces provided. You may use the back of a page
for additional space; please indicate clearly when you do so. Show all work. No credit
will be given for
21-270
Intro to Math Finance
Spring 2012
Solutions to Assignment 2
1.13 Observe rst that
V1 (1 ) = $20, V1 (2 ) = 0, V1 (3 ) = $20.
Let us try to replicate V by purchasing shares of S 1 , shares of S 2 , and
investing in the bank at t = 0. The value of ou
21-270
Intro to Math Finance
Spring 2012
Solutions to Assignment 1
1.1
1. If S1 = 53.47, then
CT = 53.47 50 = 3.47,
PT = 0.
2. If ST = 48.52, then
CT = PT = 0.
3. If ST = 42.71, then
CT = 0,
PT = 47.5 42.71 = 4.79.
1.2 The short sale of the puts generates
21-270
Introduction to Mathematical Finance
Homework #1
Spring 2009
Problem 4 is due in class on Wednesday, January 21.
1. Assume the following exchange rates are valid:
1. US Dollar = 0.68 British Pound
1 US Dollar = 1.22 Canadian Dollars
1 US Dollar = 1
21-270
Introduction to Mathematical Finance
Homework #4 Solutions [Partial]
Spring 2009
1. [Exercise 2.8]
mN
4, 000 =
AD(
i=1
mN
1, 100 =
i=1
Since
10
i=1
i
50D( 2 )
1
10
=
i
)=
m
10
i=1
q [m]
i
F
D ( ) + F D (N ) =
m
m
10
i=1
i
500D( 2 )
=
1
4000
10
i
50
21-270
Introduction to Mathematical Finance
Homework #2
Spring 2009
Due in class on Wednesday, January 28. All problems should be turned in.
1. This problem refers to Example 1.22 in the text. In class, we used a replicating portfolio
40
to compute the in
21-270
Intro to Math Finance
Spring 2017
Information for Test 1
The test will be given in lecture on Wednesday February 22. It will be closedbook and closed-notes.
The test covers Chapter 1 and Chapter 2 thru Section 2.9.4 of the lecture notes.
(All of
21-270
Intro to Math Finance
Spring 2017
Information for Test 2
The test will be given in lecture on Wednesday March 29. It will be closed-book
and closed-notes.
The test covers Sections 2.9 Internal Rates of Return (including 2.9.1, 2.9.2,
2.9.3, 2.9.4
21—270 Introduction to Mathematical Finance D. Handron
Exam #2
March 18, 2016 Name: SOLA‘OAS
#:54—
I will pick up my exam in class, accepting the possibility that others may see my score.
I will pick up my exam from the TA during ofﬁce hours.
Cl
Chapter 4
Finite Probability Spaces
In this chapter we briefly discuss some basic concepts from the theory of finite probability. The presentation is self-contained, although it is assumed that readers have
at least some basic idea of what is meant by a s
21-270
April 27, 2015
INTRO TO MATH FINANCE
Spring 2015
Solutions to Test 3
Name:
Write your answers clearly in the spaces provided. You may use the back of a page
for additional space; please indicate clearly when you do so. Show all work. No credit
will
21-270
Intro to Math Finance
Spring 2015
Review for Test 2 Selected Numerical Answers
1. (a) 5, 089.62 = 5, 00040 + 150
(1 40 ), where
1
=
1
1+
rI [2]
2
.
(b) rI [2] < .06
2. .0525
3. 3.65% with 1 point
4. F = 71, 718.87
5. F = 51.33
K
[D(N0 + .5) + D(N0
21-270
Intro to Math Finance
Spring 2015
Review Problems for Test 3 Selected Numerical Answers
4
1
1. (a) p = , q =
5
5
(b) C0 = 22.4
(c) 0 = .7
2. S0 = 10 or S0 = 23.3333
3. Alice has an advantage.
4. r = .1, u > 1.21, d =
5.
121 99u
121 100u
(i) Model a
21-270
Intro to Math Finance
Spring 2015
Information for Test 3
The test will be given in lecture on Monday, April 27. It will be closed-book
and closed-notes.
The test covers Chapter 5 of the Lecture Notes. (You are not responsible for
things that I di
21-270
Intro to Math Finance
Spring 2015
Information for Test 1
The test will be given in lecture on Wednesday February 18. It will be closedbook and closed-notes.
The test covers Chapter 1 and Chapter 2 thru Section 2.9.4 of the lecture notes.
(all of
21-270
March 27, 2015
INTRO TO MATH FINANCE
Spring 2015
Solutions to Test 2
Name:
Write your answers clearly in the spaces provided. You may use the back of a page
for additional space; please indicate clearly when you do so. Show all work. No credit
will
1. (25 points)
(a)
Consider a simple ﬁnancial model with several banks, each with interest rates at time
0 that do not depend on the length of the deposit or loan. One bank offers interest
that is compounded quarterly at the nominal rate T[4] = .05 and tr
Chapter 5
Arbitrage-Free Pricing in
One-Period Finite Models
The simplest financial models involving random evolution of prices are those in which
there are only two trading times and the prices of the basic securities are modelled
as random variables on
21-270
Intro to Math Finance
Solutions to Assignment 10
Spring 2015
1(a.) Let y denote the number of shares of stock purchased at t = 0. Then we have
X1 (H) = (100 100y)(1.06) + 130y = 106 + 24y,
X1 (T ) = (100 100y)(1.06) + 94y = 106 12y.
Let
f (y) = E(U
21-270
Intro to Math Finance
Spring 2015
Review Problems for Test 1 Selected Numerical Answers
1. (a) 50 for both
(b) 55 for both
(c) always the same
2. (a) 160
(b) X1 > 0 for S1 < 27.69 or S1 > 51.25; X1 < 0 for 27.69 < S1 < 51.25.
3. (a) 37,000.18
(b) 3
Chapter 2
Fixed-Income Securities and
Interest Rates
We now begin a systematic study of fixed-income securities and interest rates. The
literal definition of a fixed-income security is a financial instrument that promises fixed
(or definite) payments at p
Chapter 3
Forward Contracts, European and
American Put and Call Options
Recall that a forward contract is an agreement between two parties made at some time
concerning the sale of an asset at a future time T , called the delivery time, delivery
date, or
Course Notes for Introduction to Mathematical
Finance (21-270)
William J. Hrusa & Dmitry Kramkov
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
February 3, 2017
2
Part I
Introduction to Financial Markets,
Replication a