Financial modelling skills assessment
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# Financial mathematics workshop

### Overview

Value, risk and return - three of the central concerns of finance - all derive from mathematical foundations. Mathematics describes the dynamics of financial markets, it determines the values and risk exposures of financial positions and it connects the performance of financial structures to those structures' constituents. In short, mathematics pervades finance.

Mathematics allows us to describe, understand, measure, manage and engineer financial products and positions for our benefit.

This workshop seeks to make the mathematics of finance accessible by presenting it in a framework now familiar to finance practitioners - that of spreadsheets.

Framing this workshop in a spreadsheet format gives the following benefits.

• Many finance practitioners use spreadsheets day-to-day in their roles.
• Spreadsheets contain many useful and powerful mathematical and financial functions.
• Spreadsheets provide the computing power to use techniques - like iteration and simulation - that are unfeasible or too tedious to be performed by hand or on calculators.
• Spreadsheets provide extensive charting tools. Charts are useful in visualising and interpreting patterns, trends, features and anomalies in mathematical functions.
• Spreadsheets make it easy to perform sensitivity analyses, to “stress-test” mathematical formulae and to determine their behaviours in extreme conditions.
• Spreadsheets can act as an independent “reality check” on numbers generated by theory or by other methods.

## Outline

### Audience

This course is aimed at those who wish to apply key mathematical concepts and principles to understanding and analysing financial products and positions.

### Level

This is an intermediate level course.

### Duration

This is a two day course.

### Prerequisites

Participants should be able to use spreadsheet absolute and relative addressing (e.g. \$B\$5 / B5) and be able to enter mathematical formulae into cells [e.g. =1/(1+.04)^4]. Participants should understand and be able to apply the concepts of discounting, present and future value and simple and compound interest.

### Format

The course has a “hands-on” format. Each participant works with a laptop for the major part of the course on practical financial mathematics topics.

## Content

Following is an overview of this course's content.

### Mathematics concepts

The workshop begins by examining the following core mathematical functions and concepts often used in finance.

• The power function
• Sensitivity, gradient, rate of change and curvature
• Interpolating and extrapolating
• Growth and measures of growth
• Randomness and measures of randomness
• Frequency distributions
• Mean, standard deviation, variance and correlation
• Confidence intervals.
• The exponential and logarithmic functions
• Iteration

### Finance concepts

The mathematics of the preceding section is applied in order to model and work with the following finance concepts.

• Yield curves and curve construction
• Present value, future value and discounting
• Asset price evolution
• Forward pricing
• Hedging
• Arbitrage
• Internal rate of return

### Financial mathematics - useful spreadsheet features

This section reviews spreadsheet tools and functions that are often applied in financial mathematics.

• Statistical and analytic functions
• Charting tools
• Sensitivity and scenario tools

### The mathematics of financial products

In this section the following classes of financial products are examined.

• Bonds (fixed and floating)
• Swaps
• Forward and futures contracts
• Vanilla and exotic options

For these classes of products we show how mathematics can be used in

• Pricing
• Determining risk exposures and duration
• Hedging
• Defining relationships between products
• Engineering new products from existing ones