Expert answer:Finance Assignment
Solved by verified expert:Question 1
The term structure is a basic device that provides a snapshot of the interest rate environment
in terms of lending/borrowing costs across the various terms.
(a) Describe the nature of the term structure and how it is constructed in detail. Use Excel
as an aid in your working.
(15 marks)
(b) Do the following exercises from Chapter 8 of the textbook: 81, 82. Be sure to express
your answers clearly in your own words, based on your own understanding, with
Python as an aid in your calculations and reasoning.
(5 marks)
Question 2
The principle of no-arbitrage is a fundamental notion that is applied to relate prices or rates in
the market on theoretical terms.
(a) Apply the principle of no-arbitrage to find USDSGD if it is given that a broker quotes
EURUSD as and EURSGD as .
(10 marks)
(b) Do the following exercises from Chapter 9 of the textbook: 85, 86. Be sure to express
your answers clearly in your own words, based on your understanding, with Python as
an aid in your calculations and reasoning.
(10 marks)
Question 3
The equity option market is closely linked to the stock market but at the same time it is
structurally different from the latter.
(b) Do the following exercises from Chapter 11 of the textbook: 98, 100. Be sure to
express your answers clearly in your own words, based on your own understanding,
with Python as an aid in your calculations and reasoning.
(5 marks)
Question 4
Jonathan’s portfolio of fixed income instruments comprises the following corporate bonds:
Jonathan collected the following data from government bonds:
Assume that all bonds listed pay semi-annual coupons (or none) and have $100 face
value.
(a) Compute all risk-free zero rates from the given information.
(b) Find the value of Jonathan’s portfolio.
(c) Explain what duration is and calculate the duration of bonds I, II, III and IV.
(d) Explain what convexity is and estimate, using duration and convexity, the value of
Jonathan’s portfolio if interest rate falls by 1.5%.
(5 marks)
Show your workings clearly with calculations performed with Excel.
Corporate Bond
Coupon Rate
Maturity
Convexity
Number of Bonds
I
4.5%
12 months
0.33
600
II
5.5%
18 months
0.43
1200
III
6.5%
24 months
0.53
1800
IV
7.0%
6 months
0.63
2400
Maturity
Coupon Rate
Yield
6 months
0%
1.00%
12 months
0%
1.50%
18 months
1.5%
2.00%
24 months
2.0%
2.5%
(5 marks)
(5 marks)
(5 marks)
Question 5
Answer the following questions on option pricing.
Assume that the current price of a stock is $95, the risk-free rate is 3%, the up and down
factors are 1.50 and 0.67 respectively.
(a) Compute the price of an ATM European put option that matures in 1 year by using a
3-step binomial model.
(5 marks)
(b) Compute the price of an ATM American call option that matures in 1 year by using a
3-step binomial model.
(5 marks)
(c) Compute the price of an ATM Asian put option that matures in 1 year by using a 3-
step binomial model.
(5 marks)
(d) Compare and contrast the price that is calculated in (a) with the price that is calculated
with the Black-Scholes model.
Show your workings clearly with calculations performed with Python.
fin201_assignment.pdf
fin201_study_guide.pdf
Unformatted Attachment Preview
FIN201
Financial Mathematics
Tutor-Marked Assignment/TMA02
July 2017 Presentation
FIN201
Tutor-Marked Assignment
TUTOR-MARKED ASSIGNMENT (TMA)
This assignment is worth 25% of the final mark for FIN201, Financial Mathematics.
The cut-off date for this assignment is 30 October 2017, 2355hrs.
Question 1
The term structure is a basic device that provides a snapshot of the interest rate environment
in terms of lending/borrowing costs across the various terms.
(a)
Describe the nature of the term structure and how it is constructed in detail. Use Excel
as an aid in your working.
(15 marks)
(b)
Do the following exercises from Chapter 8 of the textbook: 81, 82. Be sure to express
your answers clearly in your own words, based on your own understanding, with
Python as an aid in your calculations and reasoning.
(5 marks)
Question 2
The principle of no-arbitrage is a fundamental notion that is applied to relate prices or rates in
the market on theoretical terms.
(a)
Apply the principle of no-arbitrage to find USDSGD if it is given that a broker quotes
and EURSGD as
.
EURUSD as
(10 marks)
(b)
Do the following exercises from Chapter 9 of the textbook: 85, 86. Be sure to express
your answers clearly in your own words, based on your understanding, with Python as
an aid in your calculations and reasoning.
(10 marks)
SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS)
Page 2 of 5
FIN201
Tutor-Marked Assignment
Question 3
The equity option market is closely linked to the stock market but at the same time it is
structurally different from the latter.
(a)
Describe how option prices are distributed across the option chain. Use data from
Eikon to explain your work.
(15 marks)
(b)
Do the following exercises from Chapter 11 of the textbook: 98, 100. Be sure to
express your answers clearly in your own words, based on your own understanding,
with Python as an aid in your calculations and reasoning.
(5 marks)
SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS)
Page 3 of 5
FIN201
Tutor-Marked Assignment
Question 4
Jonathan’s portfolio of fixed income instruments comprises the following corporate bonds:
Corporate Bond
I
II
III
IV
Coupon Rate
4.5%
5.5%
6.5%
7.0%
Maturity
12 months
18 months
24 months
6 months
Convexity
0.33
0.43
0.53
0.63
Number of Bonds
600
1200
1800
2400
Jonathan collected the following data from government bonds:
Maturity
6 months
12 months
18 months
24 months
Coupon Rate
0%
0%
1.5%
2.0%
Yield
1.00%
1.50%
2.00%
2.5%
Assume that all bonds listed pay semi-annual coupons (or none) and have $100 face
value.
(a)
Compute all risk-free zero rates from the given information.
(5 marks)
(b)
Find the value of Jonathan’s portfolio.
(5 marks)
(c)
Explain what duration is and calculate the duration of bonds I, II, III and IV.
(5 marks)
(d)
Explain what convexity is and estimate, using duration and convexity, the value of
Jonathan’s portfolio if interest rate falls by 1.5%.
(5 marks)
Show your workings clearly with calculations performed with Excel.
SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS)
Page 4 of 5
FIN201
Tutor-Marked Assignment
Question 5
Answer the following questions on option pricing.
Assume that the current price of a stock is $95, the risk-free rate is 3%, the up and down
factors are 1.50 and 0.67 respectively.
(a)
Compute the price of an ATM European put option that matures in 1 year by using a
3-step binomial model.
(5 marks)
(b)
Compute the price of an ATM American call option that matures in 1 year by using a
3-step binomial model.
(5 marks)
(c)
Compute the price of an ATM Asian put option that matures in 1 year by using a 3step binomial model.
(5 marks)
(d)
Compare and contrast the price that is calculated in (a) with the price that is calculated
with the Black-Scholes model.
(5 marks)
Show your workings clearly with calculations performed with Python.
—- END OF ASSIGNMENT —-
SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS)
Page 5 of 5
FIN201
FINANCIAL MATHEMATICS
STUDY GUIDE (5CU)
Course Development Team
Head of Programme
:
Dr Ding Ding
Course Developer(s)
:
Dr Tan Chong Hui
Production
:
Educational Technology & Production Team
© 2017 Singapore University of Social Sciences. All rights reserved.
No part of this material may be reproduced in any form or by any means
without permission in writing from the Educational Technology &
Production, Singapore University of Social Sciences.
Educational Technology & Production
Singapore University of Social Sciences
461 Clementi Road
Singapore 599491
Release V2.2
CONTENTS
COURSE GUIDE
1. Welcome ……………………………………………………………………………………………….1
2. Course Description and Aims ……………………………………………………………….1
3. Learning Outcomes ……………………………………………………………………………… 3
4. Learning Material ………………………………………………………………………………… 4
5. Assessment Overview ………………………………………………………………………….. 5
6. Course Schedule …………………………………………………………………………………… 6
7. Learning Mode ……………………………………………………………………………………..7
STUDY UNIT 1
TIME VALUE OF MONEY
Learning Outcomes …………………………………………………………………………….. SU1-1
Chapter 1 Concept: Interest Rates ……………………………………………………….. SU1-2
Chapter 2 Concept: Time Value of Money …………………………………………… SU1-8
Chapter 3 Calculation ………………………………………………………………………… SU1-13
Quiz …………………………………………………………………………………………………… SU1-20
Solutions or Suggested Answers ……………………………………………………….. SU1-22
STUDY UNIT 2
STATISTICS AND NUMERICAL METHODS WITH EXCEL
AND PYTHON
Learning Outcomes …………………………………………………………………………….. SU2-1
Chapter 1 Basics of Statistics ……………………………………………………………….. SU2-2
Chapter 2 Basics of Numerical Methods ……………………………………………. SU2-20
Chapter 3 Using Excel ……………………………………………………………………….. SU2-23
Chapter 4 Using Python …………………………………………………………………….. SU2-32
Quiz …………………………………………………………………………………………………… SU2-46
Solutions or Suggested Answers ……………………………………………………….. SU2-48
STUDY UNIT 3
EQUITIES
Learning Outcomes …………………………………………………………………………….. SU3-1
Chapter 1 Market ………………………………………………………………………………… SU3-2
Chapter 2 Signals and Quotes ……………………………………………………………… SU3-4
Chapter 3 Instruments…………………………………………………………………………. SU3-9
Chapter 4 Calculations ………………………………………………………………………. SU3-12
Chapter 5 Concept: The Capital Asset Pricing Model ………………………… SU3-16
Chapter 6 Analyses and Strategies …………………………………………………….. SU3-19
Quiz …………………………………………………………………………………………………… SU3-21
Solutions or Suggested Answers ……………………………………………………….. SU3-23
STUDY UNIT 4
FIXED INCOME
Learning Outcomes …………………………………………………………………………….. SU4-1
Chapter 1 Market ………………………………………………………………………………… SU4-2
Chapter 2 Signals and Quotes ……………………………………………………………… SU4-4
Chapter 3 Instruments……………………………………………………………………….. SU4-10
Chapter 4 Calculations ………………………………………………………………………. SU4-17
Quiz …………………………………………………………………………………………………… SU4-51
Solutions or Suggested Answers ……………………………………………………….. SU4-53
STUDY UNIT 5
FOREIGN EXCHANGE
Learning Outcomes …………………………………………………………………………….. SU5-1
Chapter 1 Market ………………………………………………………………………………… SU5-2
Chapter 2 Signals and Quotes ……………………………………………………………… SU5-4
Chapter 3 Interest Rate Parity ……………………………………………………………. SU5-12
Chapter 4 Instruments……………………………………………………………………….. SU5-15
Chapter 5 Calculations ………………………………………………………………………. SU5-21
Chapter 6 Analyses and Strategies …………………………………………………….. SU5-26
Quiz …………………………………………………………………………………………………… SU5-27
Solutions or Suggested Answers ……………………………………………………….. SU5-29
STUDY UNIT 6
OPTIONS
Learning Outcomes …………………………………………………………………………….. SU6-1
Chapter 1 Market ………………………………………………………………………………… SU6-2
Chapter 2 Signals and Quotes ……………………………………………………………… SU6-5
Chapter 3 Instruments…………………………………………………………………………. SU6-7
Chapter 4 Concept: Market Price vs Theoretical Price ……………………….. SU6-10
Chapter 5 Calculations ………………………………………………………………………. SU6-14
Chapter 6 Analyses and Strategies …………………………………………………….. SU6-22
Quiz …………………………………………………………………………………………………… SU6-26
Solutions or Suggested Answers ……………………………………………………….. SU6-28
COURSE GUIDE
FIN201 COURSE GUIDE
1. Welcome
(Access video via iStudyGuide)
Welcome to the course FIN201 Financial Mathematics, a 5 credit unit (CU) course.
This Study Guide will be your personal learning resource to take you through the
course learning journey. The guide is divided into two main sections – the Course
Guide and Study Units.
The Course Guide describes the structure for the entire course and provides you with
an overview of the Study Units. It serves as a roadmap of the different learning
components within the course. This Course Guide contains important information
regarding the course learning outcomes, learning materials and resources, assessment
breakdown and additional course information.
2. Course Description and Aims
The study of finance requires the understanding of fundamental financial concepts as
well as the proficiency in applying basic mathematics to these concepts with the aid
of robust computational tools. FIN201 Financial Mathematics is designed to equip
students with the ability to understand the real-world issues and the proficiency to
calculate with a full range of products in the world of finance. Software tools used for
the course include a computational platform for statistics (e.g. Python) and
spreadsheet software (e.g. Excel).
Course Structure
This course is a 5-credit unit course presented over 6 weeks.
There are six Study Units in this course. The following provides an overview of each
Study Unit.
1
FIN201 COURSE GUIDE
Study Unit 1 – The Time Value of Money
This unit helps you understand the concept of the time value of money.
Study Unit 2 – Statistics and Computing with Python and Excel
This unit helps you to recall some statistical concepts essential to finance and
introduces Python and Excel as computing platform for the course.
Study Unit 3 – Equities
The unit covers the basic mathematics and computations that you will encounter in
equities.
Study Unit 4 – Fixed Income
The unit covers the basic mathematics and computations that you will encounter in
fixed income.
Study Unit 5 – Foreign Exchange
The unit covers the basic mathematics and computations that you will encounter in
foreign exchange.
Study Unit 6 – Options
The unit covers the basic mathematics and computations that you will encounter in
options.
2
FIN201 COURSE GUIDE
3. Learning Outcomes
Knowledge & Understanding (Theory Component)
By the end of this course, you should be able to:
Compute present value (PV), future value (FV), compounding, discounting or
other associated notions
Apply the methods of statistical inference in reasoning about data
Compare between the various fixed income instruments and their quantitative
representations
Calculate prices or other quantitative information related to fixed income market
instruments
Calculate various types of interest rates (e.g. spot, forward) from the term
structure
Explain the various foreign exchange instruments and their quantitative
representations
Calculate prices or other quantitative information related to foreign exchange
market instruments
Discuss the various equity instruments and their quantitative representations
Calculate prices or other quantitative information related to equity market
instruments
Key Skills (Practical Component)
By the end of this course, you should be able to:
Use a computing tool (e.g. Excel/Google Spreadsheets or Python) for financial
calculations.
Use a financial information system (e.g. Reuters Eikon, or the Internet) for
obtaining market data and information as well as harnessing well-documented
API/library/models to make inferencing more expedient
3
FIN201 COURSE GUIDE
4. Learning Material
The following is a list of the required learning materials to complete this course.
Required Textbook(s)
Steiner, B. (2007). Mastering financial calculations: A step-by-step guide to the
mathematics of financial market instruments. Harlow, England: Financial Times
Prentice Hall.
Other recommended study material (Optional)
The following learning materials may be required to complete the learning activities:
Special Requirement (Optional)
Any other requirement(s) needed for the course such as the use of lab equipment.
Windows or Mac OS with Excel installed
4
FIN201 COURSE GUIDE
5. Assessment Overview
The overall assessment weighting for this course for the Evening Cohort is as follows:
Assessment
Description
Weight
Allocation
Assignment 1
Tutor-Marked Assignment / TMA 1
25%
Assignment 2
Tutor-Marked Assignment / TMA 2
25%
Examination
Written examination
50 %
TOTAL
100%
The overall assessment weighting for this course for the Day-time Cohort is as follows:
Assessment
Description
Weight
Allocation
Pre-Course Quiz 1
1%
Pre-Course Quiz 2
1%
Pre-Course Quiz 3
1%
Pre-Course Quiz 4
1%
Pre-Course Quiz 5
1%
Pre-Course Quiz 6
1%
Assignment 2
Tutor-Marked Assignment / TMA
17%
Assignment 3
Class Test
17%
Class Participation
Class Participation
10%
Examination
Written Examination
50%
Assignment 1
TOTAL
100%
SUSS’s assessment strategy consists of two components,
Overall Continuous
Assessment (OCAS) and Overall Examinable Component (OES) that make up the
overall course assessment score.
(a) OCAS: The sub-components are reflected in the tables above and are different for
the day-time and evening cohort. The continuous assignments are compulsory and
are non-substitutable.
5
FIN201 COURSE GUIDE
(b) OES: The Examination is 100% of this component.
To be sure of a pass result you need to achieve scores of 40% in each component. Your
overall rank score is the weighted average of both components.
Non-graded Learning Activities:
Activities for the purpose of self-learning are present in each study unit. These
learning activities are meant to enable you to assess your understanding and
achievement of the learning outcomes. The type of activities can be in the form of Quiz,
Review Questions, Application-Based Questions or similar. You are expected to
complete the suggested activities either independently and/or in groups.
6. Course Schedule
To help monitor your study progress, you should pay special attention to your Course
Schedule. It contains study unit related activities including Assignments, Selfassessments, and Examinations. Please refer to the Course Timetable in the Student
Portal for the updated Course Schedule.
Note: You should always make it a point to check the Student Portal for any
announcements and latest updates.
6
FIN201 COURSE GUIDE
7. Learning Mode
The learning process for this course is structured along the following lines of learning:
(a) Self-study guided by the study guide units. Independent study will require at
least 3 hours per week.
(b) Working on assignments, either individually or in groups.
(c) Classroom Seminar sessions (3 hours each session, 6 sessions in total).
iStudyGuide
You may be viewing the iStudyGuide version, which is the mobile version of the
Study Guide. The iStudyGuide is developed to enhance your learning experience with
interactive learning activities and engaging multimedia. Depending on the reader you
are using to view the iStudyGuide, you will be able to personalise your learning with
digital bookmarks, note-taking and highlight sections of the guide.
Interaction with Instructor and Fellow Students
Although flexible learning – learning at your own pace, space and time – is a hallmark
at SUSS, you are encouraged to engage your instructor and fellow students in online
discussion forums. Sharing of ideas through meaningful debates will help broaden
your learning and crystallise your thinking.
Academic Integrity
As a student of SUSS it is expected that you adhere to the academic standards
stipulated in The Student Handbook, which contains important information
regarding academic policies, academic integrity and course administration. It is
necessary that you read and understand the information stipulated in the Student
Handbook, prior to embarking on the course.
7
STUDY UNIT 1
TIME VALUE OF MONEY
FIN201 STUDY UNIT 1
Learning Outcomes
By the end of this unit, you should be able to:
1. Describe the significance of the time value of money.
2. Express present values and future values through the use of interest rates.
3. Give the value of the NPV from the IRR or vice versa.
SU1-1
FIN201 STUDY UNIT 1
Chapter 1 Concept: Interest Rates
In this unit, we will discuss one of the most fundamental facts in finance – that an
amount of money now will be valued differently in the future. This is known as the
time value of money.
The reason for the fact can be traced to the existence of demand for idle cash in the
financial environment. This means that if you are able to lend to the demand, you will
be rewarded by means of interest when the loan is repaid.
In a nutshell, the time value of money is a relationship between the present value and
the future value of a cash flow expressed in terms of an interest rate. This and related
notions will be explored here.
1.1 Simple and Compound Interest
Our concern is with the value of a cash flow at different points in time.
Its cur …
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