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
abel@ualberta.ca
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

Math 356 Fall2015: More Practical Examples for Chapter 1
Example 1
Consider a stock whose present price is S(0) = 9 dollars, and its tomorrow
price have the following distribution
S(1) =
6, with p
21, with 1 p
where 0 < p < 1. The risk-free asset has the

Chapter 4: Discrete Time Market Models
Stock and Money Market Models
The model
Investment Strategies
The principle of No Arbitrage
Application to the Binomial tree model
Fundamental Theorem of Asset Pricing
Extended Models
1
Stock and Money Market

Chapter 3: Risky Assets
Dynamics of stock prices
Binomial tree model
Other models
1
Dynamics of stock prices
S(0):= is the price of the stock at time t = 0. It is a positive
constant.
For t > 0, S(t)=price of the stock at time t. It is a non-trivial