APM466/MAT1856 have been set up on TopHat for lectures and a textbook will be available in that platform.

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Introduction to Mathematical Finance


Since the work of Nobel Laureates Scholes, Markowitz, Sharpe, Merton and many others, quantitative methods have  been established as a fundamental necessity in many branches of the financial sector.

APM466 (for undergraduate students) or MAT1856 (for graduate students) is an introductory course to a variety of topics in Mathematical Finance; the objective of the course is to give students a broad view of the field and assumes students have a solid background in mathematical sophistication.

The financial sector is divided into five general sectors: banking, asset management,  financial services, insurance and payment systems. In the current year, this course focuses on methods for the first three.

The themes developed in the course include bond and fixed income mathematics, asset and derivative pricing, credit risk, investments and hedge funds. The course is cross-listed as an undergraduate course and a graduate course. The course has a textbook on the Tophat platform, which also contains all the presentations given in class.

Financial Products

The themes developed in the course focus on the analysis required to understand stocks, bonds and their variants. also known as derivatives. Later in the course, we will also discuss the general area of financial services focusing on the credit perspective, which has grown to be a leading area for jobs for graduates with quantitative skills.

Understanding why things are the way they are is very important to have a successful career. Because of that, and while the focus of the course is quantitative, we will pay close attention to the elements that make financial markets the way they are.

We will learn how to value cash flows and the currency value of time. We will learn about financial derivatives and how to price them, the risks they give rise to and how to mitigate (hedge) those risks.

We will also discuss applications and similarities to other financial activity that we lead our every day lives.

Asset Management

This is a general term that makes a reference to the investment sector, where one asset (cash for example) is used to replace another asset (a stock, a bond, or other); this is done to obtain certain objectives (a return or performance target, for example). Since the 50’s, much of this has been quantified, and while there are many imperfect theories to understand how to best invest, we will focus on the investment act as an instance of a risk transfer exercise. This allows us to bring a lot of powerful quantitative techniques to define objectives and optimize results.

Financial Derivatives

Options, futures, flexicaps, etc. have become part of the lexicon of everyday financial activity; we will learn what they are, why people and institutions use them, what is difficult about them, and various methods to understand their value, price, risks, etc.

This will require that we develop a certain understanding of stochastic analysis; the course will cover an ultra-simplified chapter on stochastic calculus, Ito’s Lemma, etc. but our main focus will be on the practical. dealing with the main questions arising in this area.

Risk Management

Still one of the main areas of jobs in the financial sector for graduates with quantitative skills, we will explain the status quo and also discuss some of the new emerging areas, which employ a heavy dose of data science, machine learning techniques and in general a very deep use of technology innovation.

There will be a new section devoted to climate risk, sustainability, ESG and other topics related to social responsibility which are creating new career opportunities. While many do not require a strong quantitative background, they all are based on substantial data science frameworks, and will be an important area for students in this class.



Communications and Business skills

Knowing that many students take this course to succeed in their professional career, we will cover certain topics unrelated to finance or mathematics but important when building a career in the private sector.

These topics will be inserted in the individual lectures to provide contrasting elements and hope to eliminate the zoom fatigue unavoidable in the current e-learning environment.



Access the Course Reading Room

Here you can find all lecture notes. videos. assignments, as well as other documentation which may prove useful for the course.