You will find here a description of all the classes I have taught or I am currently teaching. All of these classes have one thing in common: they provide students with the latest conceptual and mathematical tools that are used in the finance and insurance industries for risk management purposes. Moreover, several of these classes are directly useful for the preparation of professonial exams and certifications.

Financial Decision Making

Master’s Degree Class emlyon business school Lyon Currently taught in English Go to program page

The aim of this course is to present the foundations of financial decision making and some of its applications, especially in financial markets but not limited to these. The concepts of price, financial risk and asset allocation are at the heart of this course. The first part is devoted to these questions whilst the second shows how these notions are used for investment decisions. This course gives in depth analyses and contains theoretical and technical developments that ask for some prerequisites: knowledge of probability theory and stochastic processes and basic results on derivative securities and fixed income.

This course gives an overview of the methods and techniques used in financial decision-making. It begins with the foundations of finance and general principles. Then it applies these concepts to investment decisions, assets valuation and financial risk management. The emphasis of this course is more on the methods than the formulas. It outlines the validity domain of the underlying theories, pointing out their importance and drawbacks. It justifies rigorously the use of tools and results necessary in other master courses in finance and economics. The students following this course learn about arbitrage opportunities, complete markets and equilibriums, and investigate the foundations of the CAPM, of option pricing and of yield curve modeling.

Life Insurance Theory

Specialized Master’s Degree Class emlyon business school Paris Currently taught in English Go to program page

This is a first class in life insurance theory. As such, it covers only part of the syllabus of SOA exam MLC. Quoting excerpts from this syllabus, the student attending this class will be able to:  “Explain and interpret the effects of transitioning between states, the survival models and their interactions. Calculate and interpret standard probability functions including survival and mortality probabilities, force of mortality, and complete and curtate expectation of life.  For models dealing with multiple lives and/or multiple states, explain the random variables associated with the model; calculate and interpret marginal and conditional probabilities, and moments. Using the factors mentioned above, construct and interpret survival models for cohorts consisting of non-homogeneous populations, for example, smokers and non-smokers or ultimate-and-select groups. Describe the behavior of continuous-time and discrete-time Markov chain models, identify possible transitions between states, and calculate and interpret the probability of being in a particular state and transitioning between states. Apply to calculations involving these models appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler. “

Also in accordance with the syllabus of SOA exam MLC, the class enables the student to: “Calculate and interpret probabilities, means, percentiles and higher moments of present values random variables. Calculate and interpret probabilities, means, percentiles and higher moments of random variables associated with these premiums, including loss-at-issue random variables. Using any of the models mentioned above, calculate and interpret the effect of changes in policy design and underlying assumptions such as changes in mortality, benefits, expenses, interest and dividends.”

Derivatives

Master’s Degree Class emlyon business school Lyon Currently taught in English Go to program page

This class teaches how to price and hedge vanilla and exotic derivatives based on the fundamental principles of arbitrage. Some of the key concepts of the class are: pricing, hedging, replication, simulation, optimal stopping, smile, volatility surface, Greeks, Gaussian and non-Gaussian models. Here are the main topics covered: description of main derivatives products and strategies, Black Scholes formula, American options with binomial trees, path-dependent options with Monte-Carlo simulations, arbitrage-free relations, futures and forwards, options on indices, currencies and futures, limits of the Black and Scholes theory, the smile and the volatility surface, Heston’s model, applications to corporate finance. This class is technical in essence. It alternates between formal developments (mathematical proof of the Black and Scholes formula,…), exercises, and a lot of programming in VBA. Homework consists in designing a pricer similar to those found on the desks of investment banks. Students will learn useful tricks concerning derivatives for the Series 7 license. The knowledge gained in this class is also useful for SOA exam MLC and the FRM and CFA exams. Students should read the book by John Hull: Options, Futures and Other Derivatives, Pearson, at home in parallel with the class.

Lebesgue Integration Theory

Specialized Master’s Degree Class emlyon business school Lyon Previously taught in English Go to program page

This is a classic class in integration theory that allows students to understand what is behind probability theory. The class starts by defining and studying measurable spaces, by concentrating on sigma algebras - including Borel sigma algebras. Then, measurable functions and Borel functions are introduced. Within the study of measures, sigma additivity and sigma subadditivity are examined together with the Lebesgue measure and the Carathéodory condition.

All these ingredients being prepared, we arrive at the construction of Lebesgue integrals – after providing reminders on the Riemann integral viewed as a limit of Darboux sums. Fundamental theorems are obtained and illustrated: the Beppo-Levi monotone convergence theorem, the Lebesgue dominated convergence theorem - Fatou’s lemma being examined in passing. Then, we derive theorems for integrals that depend on a parameter and for multiple integrals (Fubini-Tonelli’s theorem in the latter case). Convolution is also studied.

Finance for Managers

Master’s Degree Class emlyon business school Lyon Previously taught in French Go to program page

The aim of this course is to introduce the student, in its role as a future firm manager, to the basic notions of finance and to the main criteria of an investment decision. The course provides the tools any manager should use to correctly quantify the impact of a decision in order to correctly evaluate its value creation.

This course illustrates the basic concepts of corporate finance and modern finance theory. Concepts such as the valuation of risk and the weighted average cost of capital of a firm are covered. At the end of the course, students should be able to make simple capital budgeting decisions and to evaluate financial securities.

Other main takeaways are: the estimation of cash flows, understanding the difference between earnings and cash flows, the net present value of cash flows and other methods of cash flow valuation, capital markets and the price of risk, capital asset pricing model (CAPM).

To sum it up, this course allows the student to: learn the main methods of project valuation, know the principles underlying the pricing of risk in financial markets, know the determinants of the cost of capital for corporations, compute cash flows and their net present value and internal rate of return, and compute the cost of capital for a corporation.

Derivatives and Financial Modeling

Actuarial Degree Class Centre d’Etudes Actuarielles Paris Previously taught in French

This class offers a broad investigation of derivatives and quantitative methods. It starts with reminders on stochastic processes and Brownian motion. It also covers stochastic integrals, martingales, Ito’s lemma and Girsanov’s theorem. Then, it constructs the Black Scholes framework and discusses arbitrage relationships.

This class relies a lot on numerical methods and explains the mechanics of trees, PDE schemes and Monte Carlo simulations. Other advanced concepts examined are stochastic volatility (with the Heston model derived from one end to the other) and the volatility smile.

Basic interest rate models, such as the Vasicek and CIR models are studied before looking at the Heath-Jarrow-Morton and Brace-Gatarek-Musiela frameworks. Credit intensity and structural models are also studied in this class.

Management of Extreme Risks

Master’s Degree Class University of Brescia Brescia Previously taught in English

The contents of this class are based on my book “Extreme Financial Risks and Assets Allocation” published by Imperial College Press and coauthored with Christian Walter. The first part of the class offers a broad introduction to infinitely divisible distributions and to Lévy processes. The main distributions and processes are surveyed and their main properties (activity, variation, moments…) are examined. A strong focus is made on Fourier transform methods.

The second part of the class is dedicated to applications. It shows how static and dynamic portfolio choice problems can be solved in the presence of extreme risks (modeled via Lévy processes in the dynamic case). The course also examined the management of risks and the computation of risk indicators such as Value at Risk or Tail Conditional Expectation when extreme risks are considered.

Econometrics

PhD Class emlyon business school Lyon Previously taught in English Go to program page

This class is an introduction to time series and to their broad use in management science. After some reminders on random walks and white noises, the first part of the class introduces autoregressive processes and then moves on to moving averages. It also covers more complex dynamics such as ARCH and GARCH processes.

The second part of the class consists in student presentations. These presentations can be related to Vasicek processes for instance and involve a strong implementation dimension. Students are graded via these presentations.

Model Implementation

Specialized Master’s Degree Class emlyon business school Lyon Previously taught in English Go to program page

All sessions start with the description of a numerical method to be implemented and are followed by an actual implementation in Matlab by the students. Among the methods that are studied, we can cite: Monte-Carlo simulations, numerical PDE solving, design of binomial trees, and the implementation of Fourier transforms.

Therefore, the students learn how to price various types of options (path-dependent and American) assuming various types of models (diffusive, with jumps, with stochastic volatility,...). When implementing Monte Carlo simulations, a special focus is made on the computation and interpretation of confidence intervals.

Probability Theory and Stochastic Processes

Master’s Degree Class emlyon business school Lyon Previously taught in English and in French Go to program page

The objectives of this class are two-fold. Half of the sessions are dedicated to classic probability (and correspond to about two thirds of the syllabus of SOA exam P) and half of the sessions provide an introduction to stochastic processes. The student who attends this class gains knowledge about all the necessary tools that are prerequisite to the study of option pricing and hedging. This class is also useful to those who contemplate furthering their studies in risk management or actuarial science. 

The contents are as follows. Quick reminders on set theory. Independent and mutually exclusive events. Bayes theorem and law of total probability. Moments, including high-order moments, of probability distributions. Main probability distributions. Brownian motion. Martingales and Markov processes. Stochastic differential equations. Ito’s lemma. Girsanov’s theorem. Change of numéraire.

Financial Mathematics

Master’s Degree Class emlyon business school Shanghai Previously taught in English Go to program page

This course presents the fundamental principles of financial mathematics, as applied in the fixed income departments of banks and in the life insurance and pensions businesses.  The syllabus exactly follows the first part of the 2015 syllabus of the financial mathematics exam of the Society of Actuaries (the second part of this latter exam is about derivatives and is not covered). See www.soa.org. This syllabus is as follows.

“Definitions of the following terms: interest rate (rate of interest), simple interest, compound interest, accumulation function, future value, current value, present value, net present value, discount factor, discount rate (rate of discount), convertible m-thly, nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value. Given any three of interest rate, period of time, present value and future value, calculate the remaining item using simple or compound interest. Solve time value of money equations involving variable force of interest. Given the effective discount rate, the nominal discount rate convertible m-thly, or the force of interest, calculate any of the other items. Write the equation of value given a set of cash flows and an interest rate.

Definitions of the following terms: annuity-immediate, annuity due, perpetuity, payable m-thly or payable continuously, level payment annuity, arithmetic increasing/decreasing annuity, geometric increasing/decreasing annuity, term of annuity. For each of the following types of annuity/cash flows, given sufficient information of immediate or due, present value, future value, current value, interest rate, payment amount, and term of annuity, the candidate will be able to calculate any remaining item. Arithmetic progression, finite term. Level annuity, finite term. Arithmetic progression, perpetuity. Level perpetuity. Geometric progression, finite term. Non-level annuities/cash flows. Geometric progression, perpetuity. Other non-level annuities/cash flows.

Definitions of the following terms: principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, sinking fund. Given any four of term of loan, interest rate, payment amount, payment period, principal, calculate the remaining item. Calculate the outstanding balance at any point in time. Calculate the amount of interest and principal repayment in a given payment. Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.”

EML SPECIALIZED MASTER CLASSES

Treasury Management

Master’s Degree Class emlyon business school Lyon Previously taught in French Go to program page

La trésorerie est aujourd'hui le cœur opérationnel de la moyenne ou grande entreprise. Pas de solvabilité et donc pas pérennité de l'entreprise sans trésorier. Au-delà du rôle fondamental de garant de la survie de l'entreprise, le trésorier assure aussi de plus en plus le rôle de stratège : par le recours à des outils financiers adaptés, il intervient dans la gestion des risques de taux et de change.

Ce cours couvre les sujets suivants : budgets de trésorerie, échelles d’intérêts et dates de valeurs, modes de financement, arbitrages de financement, cash management, gestion du risque de change (théorie), gestion du risque de change (pratique), gestion du risque de taux (théorie), gestion du risque de taux (pratique), économie financière.

Fixed Income

Master’s Degree Class emlyon business school Lyon Previously taught in English and in French Go to program page

This course offers a broad viewpoint on fixed income markets and investments. It starts with a description of bond and mortgage international markets. Then, it quickly reviews fundamental elements of financial mathematics allowing evaluators to shift money forward and backward in time. Duration, convexity, effective duration, effective convexity, option adjusted spread, Z-spread, DVO1, and other similar risk management indicators are then examined.

The class also examines complex products, like exotic floating rate notes, and lets students learn by practicing, by manipulating realistic pricers with trees implemented in XL spreadsheets. The pricing, risk management, and challenges associated with mortgage backed securities are also studied. The class also discusses callable and putable bonds and structural models such as that of Merton (1974).

Probability Theory and Stochastic Processes

Specialized Master’s Degree Class emlyon business school Lyon Previously taught in English Go to program page

The objectives of this class are two-fold. Half of the sessions are dedicated to classic probability (and correspond to about two thirds of the syllabus of SOA exam P) and half of the sessions provide an introduction to stochastic processes. The student who attends this class gains knowledge about all the necessary tools that are prerequisite to the study of option pricing and hedging. This class is also useful to those who contemplate furthering their studies in risk management or actuarial science. 

The contents are as follows. Quick reminders on set theory. Independent and mutually exclusive events. Bayes theorem and law of total probability. Moments, including high-order moments, of probability distributions. Main probability distributions. Brownian motion. Martingales and Markov processes. Stochastic differential equations. Ito’s lemma. Girsanov’s theorem. Change of numéraire.

Stochastic Processes and their Applications

Master’s Degree Class University of Lyon 1 Lyon Previously taught in French

This class is a general theoretical introduction to stochastic processes and to some of their applications. The class starts with the classic elements of the general theory of semimartingales, such as stopping times and Brownian motion. It constructs the Wiener integral and then the Ito integral. Key results such as Ito’s lemma and Girsanov’s theorem are then introduced and some illustrations are provided.

This class offers an introduction to stable distributions and stable processes, and more generally to fractals and self-similarity. It also provides a description of infinitely divisible distributions and of Lévy processes – from simple Poisson processes to the more complex and contemporaneous CGMY processes. More generally, this class develops a Fourier vision of the theory of stochastic processes.

VBA for Finance

Master’s Degree Class University of Rennes 1 Rennes Previously taught in French

This class teaches Visual Basic for Applications via the construction of an option pricer. The use of the main statements (“if” condition, “for” loop …) of this programming language is mastered at the end of the class. Students also learn how to properly indent and comment their codes, and to structure them within VBA modules.

The VBA case study that is jointly built with students is an American put option pricer. Students learn how to plot trees in XL that are controlled from VBA modules. Interfaces are also implemented that allow the students to construct a realistic option pricer. The code computes option prices but also option Greeks. 

Introduction to the Risk Management of Financial Institutions

Master’s Degree Class emlyon business school Lyon Previously taught in English Go to program page

The course is devoted to the regulation and risk management of banks and insurance companies. The goal of its first part is to learn about the nature and management of the main risks that impact financial institutions. Market, credit and operational risks are its main objects. An introduction to the risks associated with derivatives is also offered. Securitization is studied in a special session. This class offers key conceptual tools to tackle the preparation of the FRM. Useful complements in terms of ERM, multivariate risks... are given in the consecutive block of classes. In the second part, the general principles of insurance are introduced and the notion of risk for insurers is developed. This part ends with the presentation of Solvency 2, which is the equivalent of the Basle agreements in the insurance sector. Part I of this class is made of: introduction to market risks, basic statistical tools, Value-at-Risk and Expected Shortfall, introduction to credit risk, rating transitions, structural models, introduction to operational risk, introduction to options, Greeks, smile, securitization. The details of part II of this class are not given here, as it was taught by a colleague.