98773 - ADVANCED METHODS FOR RISK MANAGEMENT

Learning outcomes

At the end of the course the student is familiar with the main principles and tools of market risk analysis and the hedging techniques. He knows the general theory of risk measures and the principles of market risk regulation. He is able to design a process of market risk measurement and reporting, and to make market risk management decisions.

Course contents

1. General principles

   a) A brief history of regulation from Basel I to FRTB

   b) Trading book and banking book

   c) Risk factors and risk events

   d) P&L (profit and loss) definition

2. Fixed income: General Interest Rate Risk (GIRR)

   a) Cash flow analysis: fixed and floating rate notes

   b) Sensitivity analysis

   c) Cash flow mapping and bucket hedging

3. Default risk and credit spread risk (DRC and CSR)

   a) Event risk: default and severity (LGD)

   b) Spread risk: Z-spread, ASW spread, CDS spread

   c) Default intensity and credit risk term structure

4. Non linear products: analysis of the exposure
   

   a) Replicating portfolios of non linear products

   b) Sensitivities: Delta, Gamma (Convexity), Vega

   c) Examples of structured products

5. Copula functions and multivariate risk

   a) Separating single name risk and the effect of dependence

   b) Copula functions, non-parametric correlation and tail dependence

   c) Main families of copula functions: elliptical and Archimedean

   d) Estimating and simulating copula functions (ex. DRC)

6. Risk measures

   a) Margin in futures trading and the concept of Value-at-Risk (VaR)

   b) Coherent risk measures and spectral measures

   c) Estimation and simulation of VaR ad ES

   d) Elicitability and validation of risk measures.

7. Counterparty risk and XVA

   a) The replicating portfolio of OTC derivatives

   b) Computing CVA and DVA with Gumbel copula

   c) Credit Support Annex (CSA): collateral and netting (FVA)

   d) EMIR regulation and MVA

8. Multi-name derivatives and securitizations

   a) Securitization market and tranches

   b) Pricing and hedging tranches (correlation trading)

   c) Large CDO (ABS) and Vasicek distribution

9. Funding liquidity risk

   a) Maturity and duration mismatching

   b) Interest rate risk in the banking book (IRBB and CSRBB)

   c) Liquidity regulatory measures (LCR and NSFR)

10. Market liquidity risk

    a) Measures of market liquidity risk

    b) Level 2 and 3 assets and exposure to market liquidity risk

    c) Market liquidity and asset pricing models: flltration reduction and Choquet pricing

    d) Prudent valuation: principles and regulation.

Readings/Bibliography

1. C. Acerbi, Coherent Representations of Subjective Risk Aversion, ch. 10 in G. Szego (ed), Risk Measures for the 21th Century, Wiley Finance Series, 2004
2. M. Bianchetti and U. Cherubini, Prudent Valuation Guidelines and Sound Practices, https://ssrn.com/abstract=2790629 , 2016
3. U. Cherubini and G. Della Lunga, Structured Finance: The Objected Oriented Approach, Wiley Finance, Chichester, 2007
4. J. Mina and J. Y. Xiao, Return to RiskMetrics: The Evolution of the Standard,RiskMetrics, New York, 2001
5. JP Morgan, RiskMetrics™ – Technical Document, Fourth Edition, New York, 1996

Additional reading will be provided during the course

Teaching methods

Classroom lectures

Assessment methods

The exam will be based on:

1. a term paper (and a PPT or PDF presentation)
   
2. an oral examination.

The term paper will be sent 5 days before the exam, which will be individual and consist of

1. 15 minute presentation of the term paper (with PPT or PDF)
2. 10-15 minutes of questions on content of the course.
   

The term paper will account for up to 6 points in the final grade.

The term paper (about 10 pages) should consist of

1. an introduction to the problem or topic chosen
2. a review of the literature on the subject
3. a mathematical treatment of the problem
4. an illustrative example with data, either real or simulated

The maximum possible score is 30 cum laude.

The grades are described as follows

< 18 failed

18-23 sufficient

24-27 good

28-30 very good

30 cum laude Excellent

Teaching tools

Portfolio case study. Computer exercises.

Office hours

See the website of Umberto Cherubini