Quantitative Foundations of Finance

The details
Essex Business School
Colchester Campus
Undergraduate: Level 5
Monday 15 January 2024
Friday 22 March 2024
16 November 2023


Requisites for this module
BE300 or BE303 or EC111 or IA712



Key module for

BSC GN13 Finance and Mathematics,
BSC GN15 Finance and Mathematics (Including Placement Year),
BSC GN18 Finance and Mathematics (Including Foundation Year),
BSC GN1H Finance and Mathematics (Including Year Abroad)

Module description

This module carefully examines the building blocks of modern finance theory and focuses on the theoretical and analytical cornerstones on which the building blocks are placed. We study how these building blocks can, in certain cases, help us identify potentially optimal decisions now, even though their future consequences are still uncertain.

Module aims

The aim of this module is:

  • To familiarize you with the mathematical tools and the analytical skills necessary to understand the theory of finance.

Module learning outcomes

By the end of this module, students will be expected to be able to:

  1. Apply mathematical techniques and tools employed in finance.

  2. Describe and evaluate measures of risk aversion using expected utility theory.

  3. Understand the concept of ‘efficient frontier’ when investing in risky assets.

  4. Evaluate investment decisions employing Real Options and NPV approaches.

Skills for Your Professional Life (Transferable Skills)

This module, class activities and coursework will help you to develop the following transferable skills:

  1. To solve practical problems that need to make best use of limited resources.

  2. To choose a portfolio of assets that best suit the needs of professional investors.

  3. To employ Maple software to solve quantitative problems in finance.

  4. To support the decision making activities associated with capital budgeting decisions.

Module information

This is not an introductory module in finance. Tools and techniques that are basic for a quant career in finance, from mathematics, such as algebra and calculus will be taught on the module. Some prior computing skill in managing large amounts of data is necessary as well as a willingness to learn further computing skills in Maple, which will be demonstrated on the module.

A common feature of finance is the need to make good use of, and where possible the best use of limited resources; constrained optimization techniques, which are taught on the module, can often guide us in this need. Since concepts in probability are widely employed in finance to describe the inevitable uncertainty regarding the future, we examine its basic elements. It is a near universal truth that most of us dislike risk and prefer to avoid risk. We also find that we will avoid risks only if the price for avoiding that risk is acceptable. We study how expected utility theory helps us measure how averse we are to taking such risks.

We then proceed to apply these building blocks to examine several concepts: choice under uncertainty, maximizing returns and minimizing risk subject to constraints, mean-variance analysis and the capital asset pricing model. Finally, we show how real options can often help improve corporate investment decisions as compared to traditional approaches that employ the net present value rule.


Learning and teaching methods

This module will be delivered via:

  • One 1-hour lecture per week.
  • One 1-hour class per week.

The class will lag the corresponding lecture by one week. There are weekly class exercises, which will normally be released before the relevant class but after the associated lecture. You are advised to make an attempt at all the exercises. Class work will need to be handed in each week but are neither marked nor evaluated.

Several exercises are solved using the mathematical software called Maple, which can be accessed from the machines in the university's labs. It is good to know how to use at least one mathematical and modelling software and Maple is adequate for that.


The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Assignment  29/03/2024   
Exam  Main exam: In-Person, Open Book, 120 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book, 120 minutes during September (Reassessment Period) 

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
40% 60%


Coursework Exam
40% 60%
Module supervisor and teaching staff
Dr Liya Shen, email:
Liya Shen & Luiz Vitiello



External examiner

Dr Hf Guo
University of Durham
Assistant Professor in Finance
Available via Moodle
Of 32 hours, 32 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.


Further information
Essex Business School

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