event description

Seminar Background

PFM01 is part I of the Essential Foundational Mathematics Program in Finance. This program does not assume that participants have prior knowledge of the topics covered, but instead takes participants through from the very basics all the way up to the requisite knowledge level, providing one with a solid foundational platform to be able to understand applications of some key concepts in financial markets. Without an understanding of the essential mathematics, one cannot be expected to understand some of the underlying concepts in financial markets, hence this foundational program is meant to provide one with the requisite platform to build upon in order to have a better understanding of the financial markets.

Seminar Content

* Preliminaries
- Sets
- Indices and Logarithms
- Group Discussion/Assignment
# Perform some basic calculations of Indices and Logarithms
# Explore the use of Indices and Logarithms in the computation of
Continuously Compounded Interest Calculations with working examples
# Series & Sequences
- Examples of Series & Sequences
- Definitions of Convergence
- Various Tests for Convergence
- Arithmetic Progressions and Series
- Geometric Progressions and Series
- Applications in Financial Markets
- Group Discussion/Assignment
# Present-values of Bond coupons can be considered as examples of Series.
Discussion to provide further examples of Series & Sequences in Finance
# Applying Progressions and Series to simplify computations in Bond Price
Analysis
# Discussion of other applications in Company Valuation
# Relations and Functions
- Definition of a Relation
- Definition of a Function
- Some Basic Algebraic Functions
- Graph of a Function
- One-to-one (Injective) Functions
- Onto (Surjective) Functions
- One-to-one and Onto (Bijective) Functions
- Inverse and Identity Functions
- Composite Functions
- Group Discussion/Assignment
# Discuss the use of Functions in Finance. Example of the Bond Price as a
function of Yield-to-maturity
# To identify other Functions commonly used in Financial markets and to
determine whether they are Injective, Surjective and Bijective

* Differentiation
- Gradient and Derivative
- The Derivative of xn
- Differentiation of Sum, Difference, Product and Quotient
- The Chain Rule
- Exponential Functions
- Logarithmic Functions
- Differentiation of Exponential and Logarithmic Functions
- Higher Derivatives
- Applications of Differentiation and Derivatives
# Rates of Change
# Maxima and Minima
# Small Increments
- Applications in Financial Markets
- Group Discussion/Assignment
# Compute Derivatives for some given known functions
# Case Study to explore the significance of Gradient, Derivative and Higher
Derivatives of Functions commonly used in financial markets
# Case Study to explore the use of Exponential Functions and Logarithmic
Functions in the financial markets
# Explore the use of Differentiation theory in Portfolio Management

* Integration
- Introduction
- The Indefinite Integral
- The Definite Integral
- Some Properties of Integrals
- Applications in Financial Markets
- Group Discussion/Assignment
# Compute Integrals for some given functions
# Interpreting results computed for Integrals in real-world sense
# Case Study to explore the use of Integration theory in Financial Markets

* Taylor Series
- Taylor’s Formula
- Maclaurin Series as a Special Case of the Taylor Series
- Applications in Financial Markets(A classic application to Bonds will be discussed in a latter module)
- Group Discussion/Assignment
# Compute Taylor’s Series for some given functions
# Case Study to explore the key fundamental use of Taylor’s Formula in Market Risk Management and other areas of Finance

* Vectors
- Introduction To Vectors
- Fundamental Results and The Ratio Theorem
- Addition of Vectors
- Multiplication of a Vector by a Scalar
- Scalar Product of Two Vectors
- Applications in Financial Markets
- Group Discussion/Assignment
# Perform some basic vector computations
# Case Study to explore the use of Vectors in Portfolio Management and
other areas in Finance

* Matrices
- Introduction To Matrices
- Square Matrices
- Transpose of a Matrix
- Addition of Matrices
- Null or Zero Matrices
- Subtraction of Matrices
- Multiplication of a Matrix by a Scalar
- Multiplication of Matrices
- Inverse of a Square Matrix and Determinants
- Applications in Financial Markets
- Group Discussion/Assignment
# Perform some basic Matrix computations
# Case Study to explore the use of Matrices in Portfolio Management and
other areas in Finance