This is an introductory course to the main ideas and tools for the quantification of market risk. In the first part, the necessary concepts from Probability and Statistics will be provided. In the second part, after defining Value-at-Risk and Expected Shortfall, the main computation/estimation techniques will be presented and implemented through the software MatLab. A brief description of the Basel III regulatory framework for market risk will also be given.
Part II:
- Christoffersen P., "Elements of Financial Risk Management". (2nd Ed.), Academic Press, 2012. Available as Ebook at the library website (www.sba.unifi.it)
- slides, esercises and further material provided by the teacher (via Moodle)
Learning Objectives
To have a working knowledge of basic Probability and Statistics.
To be able to use Matlab for numerical analysis and programming.
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, recognizing the pros and cons of each approach.
To understand the basic aspects of the Basel III regulatory framework.
Prerequisites
Students should master the basic concepts of Calculus (limits, derivatives, integrals). Some prior exposure to basic financial concepts (bonds, stocks, options, CAPM) will help.
Teaching Methods
Class lectures
Further information
1. There is a Moodle page for this course. For getting the password, please write to the teacher before the beginning of the course.
2. Matlab will be used throughout. Instructions on how to get a free copy of it under the Unifi Campus License will be posted on Moodle.
Type of Assessment
Written and oral exam
Course program
Part 0: Short introduction to Matlab
Part I: Probability
- Sample spaces, probability, conditional probabilities, independence
- Random variables, discrete and continuous distributions, Expectation, variance, higher moments
- Joint distributions, covariance, correlation, multivariate normal distribution
- Law of Large Numbers and Central Limit Theorem, consistent and asymptotically normal estimators
- Conditional distributions, Markov chains
Part II: Market Risk
- Introduction to 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. Bootstrap techniques.
- Analytical approach, 1 factor. 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.
- Analytical approach, more factors. Empirical cross-section features of market returns. Multivariate EWMA and GARCH(1,1)
normal models.
- Non-linear portfolios. Portfolios with options. Delta and Delta-Gamma approximation. Monte Carlo simulation method.
- Back-testing of VaR
- A short history of regulation, from Basel I to Basel IV.
- Coherent risk measures. Coherence of ES, lack of coherence of VaR: implications.