INTRODUCTION TO MATHEMATICAL FINANCE I
MATH 356
Fall 2016
Homework # 1
Solve the following 5 problems:
1) Consider a simple nancial market in which the price of the bond is
given by A(0) = 50 and A(T ) = 60. The price of the stock follows a one-step
binom

Math 356: Homework no.6
Due December 4th, 2015 before 12:50.
Problem 1
Consider two stocks with price processes given by
S1 (0) = 21,
S2 (0) = 25,
S1 (1) =
S2 (1) =
31,
19,
42,
18,
for
for
for
for
scenario
scenario
scenario
scenario
1
,
2 ,
1
2 ,
1) Com

Math 356: Sample Final
Instructor: Dr. Tahir Choulli
It will be solved and discussed in detail in
class on Monday December 7, 2015,
All examples, remarks, notes, exercises
treated/given in class, the assignments, the
midterms and their samples are conside

Math 356 Fall 2015: Homework no.3
Due October 26, 2015 before 12:50:
Problem 1 Consider the model constituted by three securities. The bank account
whose price process is A(0) = A(1) = A(2) = 1, and two stocks with the price
processes defined by
S1 (0) =

Math 356 Fall2015: Sample Midterm
To be solved in class on Monday October 19, 2015.
All examples, remarks, notes, exercises treated and/or mentioned
in class, and the assignments are considered as part of the sample
midterm.
Problem
Let a, u, d and r be t

Math 356: Homework no.5
Due November 20th, 2015 before 12:50.
Problem 1: Consider two stocks with price processes given by
S1 (0) = 21,
S1 (1) =
31 for 1
, S2 (0) = 25,
19 for 2
S2 (1) =
42 for 1
.
18 for 2
The probabilities for the scenarios are given

Math 356 Fall2015: Sample Midterm 2
To be solved in class on Monday November 23, 2015.
Remark 1: All examples, remarks, notes, exercises treated and/or
mentioned in class, and the assignments are considered as part of
the sample midterm.
Remark 2: MIDTERM

Math 356: Homework no.4
Due November 6 before 12:50pm.
k Problem 0: Consider the model constituted by three securities. The bank
account whose price process is A(0) : A(1) 2 A(2) 2 1, and two stocks
with the price processes dened by
a
0.8 for n11
81(0

Math 356 Fa112015: Homework no.1
Due Friday September 25th 2015, before 12:50pm.
/ a.
if] (36;? Exercise 1
3%; Let a and s be two positive constants. Consider a. stock whose present price is
g 3(0) 2 8 dollars, and its tomorrow price have the following di

Ts: tool Mar/EL l
Math 356 Fall2015: Homework no.2
Due October 9, 2015, before 12:50.
Exercise 1 Suppose that you deposit your money in a bank that pays
interest at a rate of 18 percent per year. How long will it take for your
Emoney to triple if the inte

INTRODUCTION TO MATHEMATICAL FINANCE I
MATH 356
Fall 2016
Homework # 2
Solve the following 5 problems:
1) Suppose that you take a mortgage of 300000.00 Canadian dollars on
a condominium near Jasper Avenue to be paid in full by 15 equal annual
payments. As

INTRODUCTION TO MATHEMATICAL FINANCE I
MATH 356
Fall 2016
Solution of Homework # 2
1) Here, r = 0.04, P = 300000.00, n = 15. Then, each annual payment
amounts to
C=
P
300000
300000
=
=
= 26982.33012 26982.33.
P A(r, n)
P A(0.04, 15)
11.11838743
To calcula

INTRODUCTION TO MATHEMATICAL FINANCE I
MATH 356
Fall 2016
Solution of Homework # 3
1)[50 points] We have
u = (1, 1, 1)
and
m = (0.08, 0.10, 0.14).
From cij = ij i j , we get the covariance matrix
0.0225 0.01650 0.01170
C = 0.01650 0.0484 0.01716
0.01170

Math 356 Fall2015: Homework no.1
Due Friday September 25th 2015, before 12:50pm.
Exercise 1
Let a and s be two positive constants. Consider a stock whose present price is
S(0) = 8 dollars, and its tomorrow price have the following distribution
S(1) =
2s,

Math 356 Fall2015: Homework no.2
Due October 9, 2015, before 12:50.
Exercise 1 Suppose that you deposit your money in a bank that pays
interest at a rate of 18 percent per year. How long will it take for your
money to triple if the interest is
compounded

Math 356: Homework no.4
Due November 6 before 12:50pm.
Problem 0: Consider the model constituted by three securities. The bank
account whose price process is A(0) = A(1) = A(2) = 1, and two stocks
with the price processes defined by
0.8 for 1
S1 (0) = 1.1

INTRODUCTION TO MATHEMATICAL FINANCE I
MATH 356
Fall 2016
Solution of Homework # 1
1) Consider the portfolio (x, y) = (1, 1). Then,
V (0) = (1)(50) + (1)(50) = 0,
10 with probability p
V (T ) = (1)S(T ) + (1)(60) =
0
with probability 1 p
and
P cfw_V (T )

II. RISK-FREE ASSETS
1
1. Time Value of Money
Note 1. As examples of risk-free assets, we
will consider a bank account or a bond.
Questions 1.[Time Value of Money] Consider a risk-free asset.
1) What is the future value of an amount invested or borrowed t

III. PORTFOLIO MANAGEMENT
http:/www.nobelprize.org/nobel_prizes/
1
1. Model Specifications: Risk and Return
Consider a nancial market with
a) Two trading dates: t = 0 and t = T .
b) A nite sample space with K < elements:
= cfw_1, 2, , K .
c) A -eld of ev

I. A SIMPLE MARKET MODEL
1
1. Model Specifications
Consider a nancial market with
a) Two trading dates: t = 0 and t = T .
b) A risk-free security process (a bank account
or a bond).
If the risk-free security is a bond, then its price
is given by
A = cfw_A

University of Alberta
Department of Mathematical & Statistical Sciences
Introduction to Mathematical Finance I, A1
Fall 2016
Instructor:
Oce:
Phone:
E-mail:
Personal Web Page:
Dr. Abel Cadenillas
CAB 639
780-492-0572
[email protected]
https:/www.math.ualbe

4. Stock Market
ECON 341 - Fall 106
Yingfeng Xu
October 5, 2016
Topics
Contents
1 Valuation of stock price
1
2 Adaptive and rational expectations
4
3 Efficient market hypothesis
5
1
Valuation of stock price
Common stock
Common stock is the principal way t

Chapter 5: Portfolio Management
Risk
Two Securities
Several Securities
Capital Asset Pricing Model
1
Risk
Measure of risk in a risky investment:
K:= the retun of a risky investment.
V ar(K) is the measure of risk, and K is also a measure of risk.

Chapter 2: Risk-free Assets
PART I: Time Value of money
Simple Interest
Periodic Compounding
Streams of payments
Continuous compounding
Comparison of compounding methods
1
Simple interest rate
P := is the principal (initial wealth)
r= the interest

Chapter 2: Risk-free Assets
PART II: Money Market
Zero-coupon Bonds
Coupon Bonds
Money Market Account
1
Bond is an example of risk-free asset (or security).
It is a financial security that guarantee to its holder a sequence of
future payments.
Zero-cou