Risk Management and Capital Requirements - S. Galiani

Course Syllabus

Risk Management and Capital Requirements

II semester - Spring 2024



Stefano Galiani (stefano.galiani@uniroma1.it)

Claudia Ceci (claudia.ceci@uniroma1.it)



Office  107 - 1° piano – Ala 1 (107 - 1st floor)  and 111 - 1° piano – Ala 1 (111 - 1st floor) 


Office Hours: to be coordinated by email


Class Hours (day, time, room): 

Tuesday 10am-12pm (Didalab),  Wednesday 10am-12pm (Didalab), Thursday 10am-12pm (ECODIR Lab, 6th fl)


Total Module Hours: 72hrs / 9 CFU

Exam Sessions: 5 June 2024, 5 July 2024, 18 September 2024, 24 October 2024 (to be booked on INFOSTUD platform)

Course websitehttps://web.uniroma1.it/memotef/risk-management-and-capital-requirements-s-galiani


Recommended Textbooks 


Slides prepared by the instructors, along with Python based Jupyter Notebooks, are the course main references.


Textbooks covering the topics of the course can be found in:


  • McNeil, A., Frey, R. and Embrechts, P. (2015) Quantitative Risk Management: Concepts, Techniques and Tools, Wiley
  • O’Kane, D. (2008), Modelling Single-name and Multi-name Credit Derivatives, Wiley
  • Rösch, R., Scheule, H. (2022), Deep Credit Risk Machine Learning in Python
  • Agresti, A. and Kateri, M., Foundations of Statistics for Data Scientists: With R and Python (2021), Chapman & Hall/CRC Texts in Statistical Science


Additional Materials 

  • Notes used during the classes 
  • Financial datasets provided by the instructirs
  • Papers focusing on specific topics covered during the course 
  • Python functions and software 


The additional materials will be available in a dedicated Google ClassRoom/Drive folder reserved for the students attending the course only.



Statistics course covering probability theory and statistical inference.

Financial Mathematics concepts pertinent to present value and basic understanding of contingent claims.

Basic programming in any language, although the first part of the course will provide students with a solid foundations of relevant Python concepts.


Final and grade policy

The exam consists in two parts:


- the first one consists in a series of assignments covering empirical aspects and it is aimed at testing applied skills.

- the second one includes review questions to test theoretical knowledge and critical understanding.


Course Objectives

Credit risk is a topic of fundamental importance in modern banking systems. Quantitative credit risk methodologies play a fundamental role in the risk-management units of major investment banks. The recent crisis has led to numerous regulatory reforms requiring banks to comply with capital requirements. This can only be achieved via the implementation of a sophisticated and mathematically sound credit risk framework. This course deals with quantitative modeling and measuring of credit risk. You will learn how to price financial instruments, whose payoff is contingent to the realization of a credit event. You will also learn how to measure credit losses, manage portfolios of credit sensitive securities, and calibrate financial models to using market data.


Furthermore, in the last part of the course, a complete suite of statistical techniques, including models for probabilities of default using GLM Probit and Logit models, are then applied to a real loans dataset allowing students to learn the pre-processing, analysis and critical statistical understanding of the model outputs.


Specific educational objectives include:

- Ability to interpret results and draw appropriate conclusions.

- Ability to apply theoretical and empirical models to real world problems.

- Python and data analysis.

- Enhance organizational, analytical and communication skills through participation in group project work


Preliminary Weekly Course Calendar 


Week 1-4 (Prof. Claudia Ceci):

-Introduction: OTC Markets, Credit Risk and Measuring Credit Quality;

-Structural model of default: Merton Model (Geometric Brownian motion);

-Intensity based (or hazard rate) models: Conditional expectation and conditional survival probability.

-Pricing of (defaultable) Bonds: DZCB with and without recovery, Defaultable Coupon Bonds. Credit spread.

-Credit Default Swap pricing.


Week 5-6 (Prof. Stefano Galiani):

- Hazard rate term structure bootstrapping from market prices

- Upfront vs Running  CDS no-arbitrage pricing

- Senior vs Subordinated CDS relative value pricing

- Calibration of portfolio CDS to credit default swap indices (CDX and iTraxx) market prices.

- Brief introduction to multi-name CDS portfolio risk measures (Tail dependence)


Week 7-9 (Prof. Stefano Galiani):

-  US retail loan portfolio exploration, cleaning and preparation via Pandas.

- Validation Metrics:

-  Brier's Score

- Calibration Curve (aka Reliability Diagrams)

- Binomial Test

- Jeffrey's Prior

- Generalized Linear Models applied to credit markets:

-  Theoretical Foundation

- Link Function

- GLM/Logit Model

- GLM/Probit Model

- Comparison GLM/Logit vs GLM/Probit Models

- Multivariate Interactions

- statsmodels vs scikit-learn Python implementation

-  Default Probability Forecasting: the Comprehensive Model

- TTC (thru the cycle) vs PIT (point in time) Default Probability Estimates

-  Asymptotic Single Risk Factor (Vasicek) model within the Basel Capital Charge Framework

- EBA / FRB Stress Scenario Approaches




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