Probability theory provides the formal mathematical language to describe and analyze processes with an uncertain outcome. The number of claims (and the amount of damage) an insurance company has to handle, the gain of an asset within a quarter, the spread of a virus or the concentration of a pollutant are just a few real life examples of processes which – due to their complexity – cannot be described by some deterministic physical model. This is why we then use a “stochastic” approach: we a assign a probability, i.e. a measures of uncertainty, to the event of interest.

The objective of this course is to review some main concepts of modern probability theory. The student will be familiarized with probabilistic language and concepts. At the end of the course the students will have acquainted a solid knowledge which allows them to follow other courses in the master program which are founded on probabilistic formalism.

This course will provide students with a transversal view of the financial markets and their key regulatory pillars and will therefore help students grasp the details of the other specialised courses of the programme more effectively.
The course will review the evolution of the banking business model and articulate the seeds of the financial crisis. It will outline the role of the main actors in the financial industry, including banks and investment banks, assets managers, investment funds and fund managers, global and local custodians, as well as infrastructure companies.
It will describe key financial products, such as securities and derivatives, as well as specific products such as money market funds, repurchase agreements, credit default swaps, and covered bonds.
It will also cover the basics of the securitisation process.
It will provide a high level picture of the regulatory and supervisory evolution, which will be examined in greater details in other courses. It will furthermore detail some of the important governance regulation following the financial crisis and its relevance to risk management in the financial industry.

Financial Engineering and Data Science (FEDS) is a case-oriented class where we tackle a number of problems in Quantitative Risk Management such as Value-at-Risk and Expected Shortfall computations. We teach and utilize the Python programming language to allow students to effectively perform the Quantitative Risk Management challenges. We utilize the theoretical concepts from Estimation Theory and Numerical methods and Stochastic Calculus to solve practical problems.

Stochastic calculus is a subfield of mathematics at the interplay of probability theory, stochastic processes and real analysis. The core theme is to define and analyze the properties of a “stochastic integral”, that means an integral in which the integrand and the integrator are allowed to be random processes. Applications of such a notion can e.g. be found in mathematical finance, where stochastic calculus plays a fundamental role for pricing and hedging of financial derivatives.
We will explain in detail the mathematical background necessary to give a basic understanding of this complex field. Though this will be a rigorous (mathematical precise) introduction to the topic, I will still lay emphasis on some good intuition. At the end of the course the fundamentals should be laid for using this theory in other courses (e.g. in financial mathematics) and be capable of acquiring deeper knowledge of the subject via further reading in self-study.

The main objective of this course is to describe the methods that allow to estimate the unknown parameters of statistical models. The various estimation techniques will be applied on some examples and will be compared in terms of efficiency, robustness, ease of application, etc. These theoretical notions will be complemented by numerical methods such as random number generation, numerical equation solving and optimization. In addition to the understanding of the theoretical and numerical techniques, the students will be expected to be able to select the appropriate technique to be used when facing a new problem, and to solve concrete problems on the computer.

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This course offers an up-to-date survey of theoretical and empirical asset pricing. The first part discusses classical asset pricing (CAPM, APT, C-CAPM) within the stochastic discount factor framework. The second part introduces the generalized method of moments as a basic econometric tool to test those models. The goal of the course is to give the students a strong foundation in theoretical finance, and to train them in the use of state-of-the-art empirical techniques relevant to the field.

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Students will be able to master financial concepts related to modern asset pricing theory by arbitrage. This will allow them to get the knowledge necessary to evaluate most prices of financial derivatives on stock and interest rates. We will present the main theoretical concepts and apply them in exercises to help for a better understanding.

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The use of quantitative methods in financial markets has experienced an extraordinary growth over the past three decades. Nowadays finance professionals routinely use sophisticated statistical techniques, many of which are at the frontier of academic research. The purpose of this course is to present some of the most important econometric methods usually employed in financial markets. In particular, it contains a thorough analysis of some of the statistical techniques applied to portfolio management, financial consulting, and risk control.

The aim of the first part of this course is to make students familiar with state-of-the-art models of (strategic) asset allocation. We will investigate the properties of alternative asset classes, such as commodities, private equity, hedge funds, or inflation-link bonds, and discuss their value for different types of investors. We will learn how quantitative techniques, such as (extensions of) mean-variance optimization, can help in taking optimal asset allocation decisions. The second part of the course will firstly introduce the many aspects of the discount factor from the perspective of a portfolio manager, by concentrating on the typical risk corrections when valuing an asset. What drives systematic risk in the different asset classes, how do we estimate these risks and how can we integrate risk into the construction of an optimal portfolio will be among the questions explored. Secondly, we will examine what the concept of alpha-beta separation entails for portfolio management in terms of predictability of asset returns. Building on the risk framework developed earlier in the course, we will distinguish beta allocation from pure alpha generation and relate the latter to the efficient-market hypothesis and alternatively behavioural finance.

In FEDS II  & III we focus on: 1) research automation techniques in order to generate reproducable research output utilizing Python 2) Numerical techniques for derivatives pricing. The majority of the course is devoted to creating a project of your own choice in the field of asset management or derivatives pricing. Attention is given to oral and written presentation skills.

The objective of the course is to delve in the different types of risks and the framework of risk management. The course will enable students to understand the concepts and the jargon and how risk managers must become sceptics. The course will explain the risk typology and describe in detail credit risk, market risk, liquidity risk, operational risk, and reputation risk. It will articulate the concepts and technical tools used in risk measurement and management, including credit risk algebra, the statistical properties of ratings, V@R theory and V@R computation, the use of stress tests, and key risk indicators. It will also illustrate these in respect of a range of transactions or instruments, such as counterparty situations, collateral posting, repos and securities lending, as well as securitization. It will look at both pre- and post trade risk control, as well as explain how risk can be reduced or managed through settlement and central counterparty structures. It will describe risk appetite and risk tolerance and explain the importance of risk capital, as both a common unit of measure and a basis for shadow pricing. The course will be probing and fun, using real-life case studies and trading games to illustrate the relevance of theoretical teaching.

In this course we will present an overview of some of the latest practices in the fixed income
market and its theoretical foundations. Since the financial crisis from 2008 fixed income
markets drastically deviated from the text-book settings and we will discuss new models for this new paradigm. In this course the emphasis will lie on the quantitative methods (both stochastic calculus and financial econometrics) for valuation and risk-management of fixed income markets / products. Topics include 1) bonds and swaps portfolio management, 2) fixed income option pricing and risk-management, 3) inflation bonds and swaps. The course will involve (programming) assignments to get hands-on experience with the treated models.

The ongoing digital revolution has recently led many disciplines with a strong taste for the “empirical” to train and hire experts in big data analytics. Unsurprisingly, quantitative finance has been keeping up as proved by the pressing need for big-data qualified people in the fields of high frequency trading, microstructure effects analysis, and behavioural finance.This course, first of its kind, aims at introducing in a coherent way the major pieces composing the analysis and modelling of financial big data in the modern era. From the proper manipulation of market data to the analysis of real investors’ trading behaviour, students will be introduced to a large family of techniques used to represent, describe, and model financial big data at both the market and agent levels.Prior familiarity with statistics and time series analysis is highly recommended even though brief reminders on these subjects will be provided along the course. Students will be asked to solve theoretical exercises as well as practical problems with Matlab and C++.

The aim of this course is to introduce Derivatives (especially Equity) pricing and trading, in a very practical way. Combining experience and pure theory improves the course’s understanding. Concrete examples will be used to describe theoretical concepts. At the end of this course, students are expected to master options’ basics.

The objective of this module is to provide a clear understanding of the existing credit models used to measure and manage credit risk within the financial and commodity trading industries. The single-name and multi-name credit models will be covered from an industry practitioner stand point. Strong emphasis will be given on how to implement successfully academic models into business platforms. Through exercises and working groups, models will be selected, implemented and calibrated.

In FEDS II  & III we focus on: 1) research automation techniques in order to generate reproducable research output utilizing Python 2) Numerical techniques for derivatives pricing. The majority of the course is devoted to creating a project of your own choice in the field of asset management or derivatives pricing. Attention is given to oral and written presentation skills.