Teaching

The course is a mixture of theory and graded coding projects in Python.

• Basic notions of statistical learning

• Linear regression

• (Stochastic) gradient descent

• Logistic regression

• Kernel methods

• Neural networks

• Classification and regression trees

• Bagging and random forests

• Gradient boosted trees

• Graph neural networks and tranformers

• Dimensionality reduction and autoencoders

Coding projects:

• Pricing with linear regression

• Credit analytics

• Deep hedging

• Insurance claim frequency prediction

- Basics of financial markets

- Single-period market models

- Preliminaries on risk-neutral pricing and hedging

- Review of probability theory (Probability I + martingales)

- Discrete-time market models

    - Pricing of European Contingent Claims

    - Pricing of American Contingent Claims

- Fundamental theorems of asset pricing

    - Existence and uniqueness of an Equivalent Martingale Measure

- Optional: Introduction to continuous-time finance

    - Convergence to Brownian motion

    - Black-Scholes formula

This was a student seminar organized by me.

Description: Credit risk is the risk of financial losses arising from the failure of a counterparty to satisfy a contractual obligation. Nowadays credit risk management is of fundamental importance in almost all financial institutions, not just credit institutions. In particular, thanks to the rapid growth in credit derivative instruments (such as CDOs, CDSs, and Credit Index derivatives), credit risk has become an essential tool for risk managers and for asset managers alike. From a mathematical point of view, credit risk management relies on the correct modelling of statistical dependencies and on the efficient estimation of rare events. In this seminar we will study the models most commonly used within the financial industry for credit risk management and credit derivative pricing. 

Topics:

• Mixture models: basics

• Mixture models: large portfolio asymptotics

• Mixture models: importance sampling

• Mixture models: CreditRisk+

• Copulas: Part I

• Copulas: Part II

• Threshold models: basics

• Threshold models: the KMV model and Basel II

• Credit rating migration: part I

• Credit rating migration: part II

• Structural models

• Intensity-based models: hazard rate models

• Intensity-based models: doubly stochastic random times

• Credit portfolio products: description and pricing

Lecturer:
Gaultier Lambert

Lecturer:
Ashkan Nibeghbali