# Quantitative Enterprise Risk Management

**Quantitative Enterprise Risk Management specialization of the ISMA Master’s CS program****.**

**Duration of studies:***15 months***Awarded degree:***Professional Master in CS***Qualification:**Q*uant Developer***Language of studies:***English***Form of studies:***100% online*(on the basis of the Moodle platform)

**Master in Quantitative Enterprise Risk Management** is the world class professional qualification in the field of financial engineering. It satisfies quickly growing demand to be effectively delivering risk management solutions within financial organizations in the constantly evolving international regulatory environment and continually improving patented risk mitigation strategies.

Today’s sources of talent, both professional and academic, are unable to supply the sufficient number of resources with the necessary skills to deliver the above solutions.

#### I. Specialization Structure

- The course of study is divided into 4 modules consisting of 14 classes during 5 academic semesters:
- Foundation Math
- Scientific calculations, fundamentals of statistical training and data analysis
- Fundamentals of financial engineering, financial markets and products
- Enterprise risk management: market, credit and model risks

Each course includes numerous practical assignments, quizzes, verbal defences/presentations, and examinations. The curriculum is constantly updated to reflect the latest developments in the global regulatory space and risk management methodology.

#### II. Lecturers

The Program is implemented by a group of Adjunct Professors, who are at the same time top level practitioners leading teams of quantitative developers within such global financial institutions as Citigroup, Chase, Bank of America, KPMG, Bloomberg, State Street, Cantor-Fitzgerald, and others. The really elite faculty will provide very up-to-date practical content. All the instructors are personally interested in providing the highest quality training, since they are actually the potential employers for successful students and graduates.

#### III. Admissions

Each applicant shall undergo rigorous selection process, which shall include academic and professional testing, interviews, recommendations, etc.**IV. Target Candidate Group**Young specialists with academic background in mathematics, physics, or computer science with 1 or more years of professional experience utilizing quantitative and programming skills

#### V. Employment

The focus of the Curriculum and close bond between the Program and the industry, practically ensures students and graduates the employment with the world leading financial institutions. During the course of study, each student’s mastery level shall be continuously assessed with the aim of most expedited participation in the real projects, ultimately even before the Program completion. To facilitate placement with international financial companies, multi-year working visas outside of CIS and Baltic countries shall be made available to best students and graduates. Work visas shall make it possible for potential employers to effectively eliminate the lengthy engagement process for international candidates and to complete the onboarding quickly, usually within one month.**VI. To Enrol:**

1. Please submit 2 letters of recommendation from your latest school's Program Director and Dean to the Program's Admissions' Committee (PAC) with their contact information

2. Please submit a letter of recommendation to PAC from your latest place of employment (if available) from your immediate manager with his/her contact information

3. Please submit your latest academic transcript to PAC

4. Please write a 2-page autobiographical essay in English and send it to PAC - 1 hour timed and proctored exercise

5. Hold a 1-hour-long discussion about your essay with PAC (all in English)**VII. Admission Test**Three-hour timed and proctored written exercise in English:

1. Math requirements (1.5 hours)

1. Integral and differential calculus (univariate is acceptable) – 2 questions

2. Linear algebra – 2 questions

3. Theory of complex variables (don’t have to know complex analysis) – 2 questions

4. Basic Probability Theory – 2 questions

5. Fundamentals of Numerical Methods (for instance, basic numerical differentiation and integration, root - finding, etc.) – 2 questions

2. Programming skills (1.5 hours)

1. Excel (VBA is a plus) – 2 questions

2. High level programming language (C++/python preferred)

3. Algorithms and data structures – 2 questions

4. Performance optimization – 2 questions

5. Parallel computing – 2 questions

6. Basics of numerical computations (with finite precision floats) – 2 questions

**VIII. Specialization testing verbal defence – going over the written test results and discussion (2 hours)**

**More information about enrolment:**risk.management@isma.lv.

### Study plan – 5 academic semesters

- Upon completing this course, students will be capable of:
- Applying of derivatives and integrals, transcendental functions, methods of integration, integration applications, sequences, infinite series, Taylor's theorem
- Solving systems of linear equations, matrix operations including inverses, linear dependence, vector spaces, least square problems, determinants and their properties, eigenvalues and eigenvectors, linear transformations, matrix decompositions
- Using functions of several variables, limits and continuity, partial derivatives, linearization, Jacobians, higher derivatives, Taylor theorem in many dimensions
- Using discrete and continuous random variables, expectations, probability distributions, laws of large numbers, elements of Bayesian inference, random processes
- Working with complex numbers – representation and algebraic operations, analytical functions, Cauchy-Riemann equations, integration in the complex plane, series representation

- Theory of boundary value and initial value problems with emphasis on linear equations, heat equation, wave equation, Laplace equation, Sturm-Liouville theory, Greens functions, Laplace transform
- Basics of Fourier series, Fourier integrals, and orthogonal sets of functions, applications of Fourier analysis to fields such as approximation theory, signal analysis, probability, statistics, and differential equations
- Standard algorithms for numerical computations including root finding, interpolation and approximation of functions, numerical differentiation and integration, numerical solutions of ordinary differential equations and boundary value problems
- Algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control including the simplex method, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method

- Upon completing the course, the students will know and be comfortable of applying the following concepts:
- Brownian Motion specification and construction, correlated Brownian Motions, features of the Brownian Motion path
- Martingales and their properties, conditional expectations, elements of martingale analysis
- Ito stochastic integral, Ito calculus, Ito’s lemma
- Stochastic differential equations, arithmetic Brownian motion, geometric Brownian Motion, mean reverting and OU SDEs
- Change of probability, Girsanov transformation, change in numeraire in discrete and continuous time, application to geometric Brownian Motion

- Upon completing the course, the students will be capable of applying the following concepts in the risk space:
- Basic Python: data types, operators, variables
- Branching, conditionals, iteration
- Abstraction through functions, recursion
- Bisection methods to find root, binary search, sorting
- Lists, NumPy arrays, tuples, mutability, dictionary - introduction to efficiency
- Testing and debugging
- Complexity: log, linear, quadratic, exponential
- Dynamic programming: Fibonacci, knapsack (continuous vs integral), greedy approaches - why are they sub-optimal
- Scientific libraries: NumPy, SciPy, Matplotlib
- Object oriented programming
- Simulation: random walk

- Topics covered will include:
- Population vs sample, statistical measures, confidence interval estimation, hypothesis testing
- Simple linear regression models, evaluating regression models, multiple linear regression, outliers and influential data points and how to deal with these, estimation beyond ordinary least squares
- Linear classifiers, SVM, kernel estimation, k-nearest neighbour, neural networks
- Bootstrap resampling, cross-validation, bootstrap aggregation (bagging), accuracy and precision, reliability

- Topics covered include:
- Introduction to Data Science Tools: SciKit-Learn, TensorFlow, Teano, Keras
- Algorithms for supervised and unsupervised learning: kNN, Naïve Bayes, Logistic Regression, Decision Trees, Random Forests, etc.
- Feature selection algorithms: filter methods, wrapper methods, embedded methods
- Techniques and methodologies for evaluating and tuning the models

- Topics covered include:
- Random behaviour of assets: probabilistic model for the movement of asset returns
- Binomial Model: introduction to options pricing
- Black-Scholes Model: fundamentals of Black-Scholes-Merton framework for options pricing
- Greeks and Delta Hedging: risk sensitivities in BSM framework, calculation methods, application
- Volatility Modelling: the concept of volatility, modelling fundamentals

- Upon completing this course the students will be comfortable working with:
- Equities and Equity Derivatives
- FX and FX Derivatives
- Commodity and Commodity Derivatives
- Models and methods for Valuation of Vanilla Products
- Models and methods for Valuation of Exotic and Path-Dependent products
- Fundamentals of Equities, Commodities and FX Volatility Modelling
- Basic Principles of Risk Management for Equities, Commodities and FX

- Upon completing this course the students will possess solid knowledge of:
- Rates Markets, Swaps and Derivatives
- Yield Curve Estimation in Modern Markets
- Interest Rate Models
- Interest Rate Volatility Modelling in Modern Markets
- Valuation of Vanilla Products and Exotic Interest Rate Derivatives
- Credit Markets, Vanilla Instruments (CDS/CDX), CDX Options and Correlation Trading
- Structural and Reduced Form credit models
- Fundamentals of Risk Management for Interest Rate and Credit Products

- The course will cover:
- Model Assumptions and Post-crisis Marketplace: negative interest rates and rate basis, dangers of correlation modelling, etc.
- Quality of Approximations: impact on valuations and risk, assessment of
- Model Calibration: common pitfalls, impact on valuation and risk, assessment of quality
- Methodologies for Stress Testing and Backtesting

- Topics covered will include:
- Value at Risk and Other Risk Metrics: relative merits of different risk metrics, the concept of coherent measures of risk
- Parametric Linear VaR Models
- Historical Simulation Method
- MonteCarlo Methods
- Scenario Analysis and Stress Testing

- Topics covered within this course will include:
- The concept of CVA and Credit Limits
- Methods for Hedging Counterparty Risk
- Risk Mitigation with Netting, Close Out and Collateral
- Credit Exposure and Funding
- Introduction to the concept of Capital Requirements
- The function of Clearing and Central Counterparties
- The concept of Wrong Way Risk

- Topics covered include:
- Quantifying Credit Exposure – Introduction to xVA
- xVA Management and Optimization
- Risk Neutral Vs Real Measure Models
- Modelling in Real World Measure
- Calibration of Real World Measure Models

- Charges via the application of Internal Model Method. Topics will include:
- Introduction to Risk Capital, Overview of the Latest Regulations
- Constituents of Risk Capital
- Quantifying Risk Capital – General Methodology
- Quantifying Credit, Market and Liquidity Capital Charges – Standardized vs Advanced approach
- Optimizing Risk Capital – Internal Models Method