This is an introductory course to the main ideas and tools for the quantification of financial market risk. Common risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES) will be discussed and related estimation techniques will be presented and implemented through the software MatLab. A brief description of the Basel III regulatory framework will be given
Christoffersen P., Elements of financial risk management. (2nd Ed.), Academic Press, 2012. Available as Ebook at the library website (www.sba.unifi.it)
Embrechts P., Frey R., McNeil A., Quantitative risk management: concepts, techniques, and tools (1st Ed.) Princeton University Press, 2005 (or 2nd Ed. 2015)
Material (slides, notes, etc) provided by the teacher
Learning Objectives
To be able to single out the main market risk factors.
To be able to measure the risk (VaR, ES) of a simple financial portfolio, using a range of techniques.
To recognize the pros and cons of each approach.
To understand the basic aspects of the Basel III regulatory framework.
Prerequisites
Students taking this course should have a working knowledge of basic Probability Theory (random variables, distributions, moments, covariance and correlation), Statistics (point estimators, hypothesis testing) and Finance (bonds, stocks and options)
Teaching Methods
Class lectures
Further information
There is a Moodle page for this course. For getting the password, please write to the teacher.
Type of Assessment
Writen exam + group project work
Course program
- Introduction to Risk Management. Risk vs. dispersion vs. uncertainty. Risk
measurement as part of risk management. Sources of risk for a bank. A short history
of risk.
- Basic concepts. Profit and Loss variable, risk factors, risk mapping. Sensitivities
approach. Log and simple returns.
- Risk measures. Standard deviation and standard semi-deviation. Quantiles and their computation. Value-at-Risk (VaR) and Expected Shortfall (ES).
- Historical approach. The historical method with 1 and more factors. Weighted historical method. Risk estimation over a non-daily horizon. Bootstrap techniques.
- Variance-covariance approach, 1 factor. Conditional and unconditional distri-
butions. Empirical features of market returns. The EWMA (RiskMetrics) and the
GARCH(1,1) normal models. Conditionally non-normal models, t-Student innova-
tions. Non-daily risk estimation.
- Variance-covariance approach, more factors. Reminder on multivariate distri-
butions, covariance and correlation matrix, multivariate normal vectors. Empirical
cross-section features of market returns. Multivariate EWMA and GARCH(1,1)
normal models. Factor models and Principal Component Analysis (PCA). Bond
portfolios and bucketing of maturities.
- Non-linear portfolios. Portfolios with options. Delta and Delta-Gamma approximation. Monte Carlo simulation method. Volatility risk.
- Back-testing and Basel rules. Kupiec and independence tests for back-testing
VaR. Back-testing ES. A short history of regulation, from Basel I to Basel IV.
- Coherence of a risk measure. Coherent risk measures. Coherence of ES, lack of
coherence of VaR: implications. Basic examples of coherent risk measures.