Ateneo - UPO

The course is organized into four complementary modules covering the main quantitative methods for financial risk measurement and management, Monte Carlo simulation, algorithmic trading, and the prudential regulatory framework.

Module 1, Market and Credit Risk 6 CFU

This module introduces the main quantitative models and methods for measuring and managing market and credit risk.

Module 2, Monte Carlo Simulation and Applications to Finance 2 CFU

This module presents the main Monte Carlo simulation methods and their applications to derivative pricing and financial risk measurement.

Module 3, Algorithmic Trading 1 CFU

This module examines the structure and functioning of the central limit order book, dealer inventory management, optimal execution models, the automation of trading strategies, and the role of network latency in electronic markets.

Module 4, Counterparty Credit Risk and Capital Requirements under the Prudential Framework 1 CFU

This module examines counterparty credit risk and the related capital requirements under the prudential regulatory framework.

For international readers: CFU denotes Italian University Credits, Crediti Formativi Universitari. One CFU corresponds to approximately 25 hours of total student workload.

Teaching materials prepared by the instructors will be made available through the course online resources on the D.I.R. platform.

The following textbooks, available from the University Library, are also recommended for further study of the topics covered in the course:

1. P. Christoffersen, Elements of Financial Risk Management, Academic Press, 2nd edition.
2. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, New York, 2003.
3. J. C. Hull, Options, Futures, and Other Derivatives, Pearson, latest available edition.
4. P. Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, McGraw Hill, 3rd edition.
5. J. Hasbrouck, Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading, Oxford University Press, 2007.

Additional references and supplementary materials may be recommended by the instructors during the individual course modules.

For updated information on the course syllabus, teaching materials, and course organization, students are invited to consult the course page on the D.I.R. platform, www.dir.uniupo.it.

The course aims to provide students with the quantitative, computational, and regulatory tools required to analyse, measure, and manage major financial risks, apply simulation methods to the valuation of financial instruments, understand the foundations of algorithmic trading, and assess counterparty credit risk within the prudential regulatory framework.

Upon successful completion of the course, students will be able to:

1. Market and Credit Risk, model the Profit and Loss distribution of portfolios comprising different asset classes, including equities, bonds, and derivatives, calculate and interpret the main financial risk measures, and develop hedging strategies;
2. Monte Carlo Simulation and Applications to Finance, simulate the evolution of financial asset prices using key stochastic processes, including arithmetic Brownian motion, geometric Brownian motion, and mean reverting Gaussian processes, and apply Monte Carlo methods to derivative pricing and financial risk measurement;
3. Algorithmic Trading, understand the structure and functioning of electronic financial markets and analyse practical examples and applications of algorithmic trading strategies, with particular reference to the central limit order book, inventory management, and optimal execution problems;
4. Counterparty Credit Risk and Prudential Regulation, assess counterparty credit risk, understand the relationship between risk exposure and capital requirements, and apply the main elements of the Basel III regulatory framework relating to counterparty credit risk measurement and the determination of regulatory capital.

Taken together, the four modules will enable students to integrate quantitative models, computational methods, risk management strategies, and regulatory principles in the analysis of problems relevant to financial institutions and capital markets.

To be eligible for the coursework based assessment mode, students must have successfully completed the following courses before the beginning of the course:

1. Derivative Pricing and Portfolio Theory;
2. Statistics for Finance;
3. Business Information for Finance.

Students who have not successfully completed all the prerequisite examinations by the beginning of the course will not be eligible for the coursework based assessment mode.

For all other assessment modes, the prerequisite examinations must have been successfully completed by the date on which the examination is taken.

The course will be delivered through an integrated combination of lectures, practical classes, and computer laboratory sessions, according to the specific contents and learning objectives of the individual modules.

Lectures will introduce the main quantitative models, analytical methodologies, and theoretical and regulatory topics covered in the course, emphasizing their applications to financial risk measurement and management, derivative pricing, Monte Carlo simulation, algorithmic trading, and the determination of regulatory capital requirements.

Practical classes and computer laboratory sessions will consolidate students’ understanding of the theoretical concepts and develop the quantitative and computational skills required for their application. Through examples, practical applications, and case studies, students will gain experience in implementing the models and algorithms presented during the course, analysing financial data, and critically interpreting the results obtained.

Teaching materials, exercises, datasets, computer code, supporting resources, and supplementary content will be made available through the course Moodle platform.

Attendance is not compulsory but is strongly recommended, given the quantitative and applied nature of the course and the inclusion of practical classes, computer laboratory sessions, and module specific activities.

Basic proficiency in MATLAB is required. Students are expected to be able to use the software to implement quantitative models, perform simulations, analyse financial data, and apply the algorithms introduced during the course.

Eligibility for the coursework based assessment mode is subject to the following minimum attendance requirements:

1. at least 70% of the classes in Module 1;
2. at least 90% of the classes in each of Modules 2, 3, and 4.

Failure to meet any one of these minimum attendance requirements will result in ineligibility for the coursework based assessment mode. Students may still take the examination through the other available assessment modes, provided that all prerequisite examinations have been successfully completed.

Students with disabilities, Specific Learning Disorders, SLDs, or Special Educational Needs, SENs, may request dedicated services, support, and specific arrangements by contacting the University Staff responsible for Student Careers and Student Services and consulting the relevant University webpage:

Services for Students with Physical or Learning Disabilities

After contacting the relevant University Staff, students with disabilities, SLDs, or SENs may contact the course instructor to discuss the implementation of the approved measures and any specific arrangements relating to the examination.

The course is organised into four complementary modules devoted to quantitative models for the measurement and management of financial risks, to Monte Carlo simulation methods, to algorithmic trading and to the prudential regulation of counterparty risk.

Part 1, Quantitative models for market risk

The module introduces the main quantitative models for the measurement, modelling and management of market risk and credit risk.

Main topics:

• Measuring return and risk. Definition and measurement of financial returns. Distributions of returns and of profits and losses, Profit and Loss. Main descriptive measures of risk. Volatility, dependence and correlation between risk factors. Effects of diversification and aggregation of risks at portfolio level.


• Models for estimating Value at Risk and Expected Shortfall. Definition, interpretation and properties of Value at Risk, VaR, and Expected Shortfall, ES. Parametric methods, historical simulation and simulation-based approaches. Estimation of risk measures for individual positions and portfolios. Comparison of the different methodologies and analysis of their advantages and limitations.


• Market risk and derivative instruments. Risk measurement for portfolios containing derivative instruments. Effects of non-linearity on the Profit and Loss distribution. Use of sensitivities and local approximations for risk measurement. Hedging strategies and analysis of hedging effectiveness.

Part 2, Monte Carlo simulation and applications to finance

The module introduces the foundations of Monte Carlo simulation and its main applications to the modelling of financial markets, to the valuation of derivative instruments and to risk measurement.

Main topics:

• introduction to Monte Carlo methods and generation of pseudo random numbers;


• simulation of uniform, Gaussian and lognormal random variables;


• simulation of returns and prices of financial assets;


• simulation of stochastic processes used in financial modelling;


• simulation of multivariate Gaussian distributions and modelling of dependence between risk factors;


• application of Monte Carlo methods to the valuation of derivative instruments;


• application of simulation to portfolio risk measurement;


• analysis and measurement of simulation error;


• variance reduction techniques;


• applications and case studies on option valuation and financial risk management.

Part 3, Algorithmic trading in financial markets

The module introduces the main elements of the microstructure of electronic markets and the quantitative models underlying algorithmic trading strategies.

Main topics:

• The Central Limit Order Book. Structure and functioning of the order book. Order types, liquidity, bid ask spread and price formation.


• The Roll model of transaction prices. Effects of the bid ask spread on observed prices. Estimation of implicit transaction costs and analysis of the statistical properties of market prices.


• Inventory control and the dealer problem. Management of inventory risk. Setting of quotes and trade-off between profitability and risk.


• Statistical arbitrage. Principles and applications of quantitative strategies based on identifying and exploiting statistical relationships between financial assets.


• Optimal execution. Models for the execution of large orders. Transaction costs, market impact and execution risk. Strategies for balancing speed of execution and cost containment.


• Automation and network latency. Automation of trading strategies. Architecture of electronic systems and the role of latency in the transmission and execution of orders.

Part 4, Counterparty risk and the prudential regulatory framework

The module introduces counterparty credit risk and the main methodologies laid down by the prudential framework for measuring exposures and determining capital requirements.

Main topics:

• definition, features and scope of counterparty credit risk;


• measurement of counterparty risk exposure;


• determination of capital requirements for counterparty risk;


• the Basel III regulatory framework and the main developments in prudential regulation;


• comparison between standardised approaches and internal models;


• Standardised Approach for Counterparty Credit Risk, SA CCR;


• Credit Valuation Adjustment, CVA, and the associated capital requirements;


• collateralisation and Initial Margin;


• use, validation and supervision of internal models;


• model risk and its main implications for risk measurement and for the determination of regulatory capital.

Intended Learning Outcomes

Upon successful completion of the course, students will have acquired the quantitative, computational, and regulatory skills required to analyse financial risks, apply simulation methods, understand algorithmic trading, and assess counterparty credit risk.

KNOWLEDGE AND UNDERSTANDING

Students will be able to:

1. understand the relationship between risk and return and its implications for financial positions and portfolios;
2. identify the main risk factors associated with equities, bonds, derivatives, and diversified portfolios;
3. understand quantitative models for Profit and Loss distributions and market and credit risk measurement;
4. interpret and compare the main risk measures, particularly Value at Risk and Expected Shortfall;
5. understand Monte Carlo simulation and its applications to asset price modelling, derivative pricing, and risk measurement;
6. understand the main features of electronic market microstructure and the principles of algorithmic trading, inventory management, statistical arbitrage, and optimal execution;
7. understand counterparty credit risk and its relationship with regulatory capital requirements;
8. understand the main elements of the prudential framework, including Basel III, standardized approaches, internal models, and model risk;
9. assess the assumptions, strengths, limitations, and implementation challenges of the methodologies covered.

APPLYING KNOWLEDGE AND UNDERSTANDING

Students will be able to:

1. analyse financial exposures, identify relevant risk factors, and select appropriate quantitative methodologies;
2. construct and analyse Profit and Loss distributions for financial positions and portfolios;
3. calculate and compare risk measures using parametric methods, historical simulation, and simulation methods;
4. apply Monte Carlo methods to asset price simulation, derivative pricing, and portfolio risk measurement;
5. analyse problems related to market microstructure, algorithmic trading, inventory management, and optimal execution;
6. apply the main methods for assessing counterparty credit risk and determining capital requirements;
7. use MATLAB and other computational tools to implement quantitative models, numerical methods, and financial algorithms;
8. develop MATLAB programs using scripts and functions, verify their correctness, and interpret their results;
9. apply quantitative methods to financial data and practical problems.

JUDGEMENT AND COMMUNICATION SKILLS

Students will be able to:

1. synthesize complex information to produce coherent risk assessments;
2. select appropriate models according to the problem, available data, and objectives;
3. interpret quantitative results and assess their assumptions, reliability, limitations, and model risk;
4. evaluate financial decisions by considering the relationship between risk and return;
5. prepare clear technical reports and communicate quantitative findings to technical and nontechnical audiences.

TRANSFERABLE SKILLS, VALUES, AND ATTITUDES

Students will be able to:

1. adopt a structured, rigorous, and quantitative approach to financial problem solving;
2. recognize the relevance of risk management at the trade, portfolio, institutional, and financial system levels;
3. understand the importance of model validation, model risk management, and the critical interpretation of quantitative results;
4. recognize the role of financial regulation in promoting sound risk management and financial stability.