Belgrade, Serbia

The role of risk management in financial firms has evolved far beyond the simple insurance of identified risks. Risk assessment is a common first step in a risk management process. Risk assessment is the determination of quantitative or qualitative value of risk related to a concrete situation and a recognized threat. However, for a good risk manager it is not only essential to have quantitative skills required for risk assessment, but also to have substantial knowledge of pricing and hedging financial instruments.

The course is aimed at students having no quantitative background at all. Course content is entirely based on The Professional Risk Manager’s Handbook: A Comprehensive Guide to Current Theory and Practice. Since it covers the second part of the examination, it rests on the Volume II of the Handbook titled as Mathematical Foundations of Risk Measurement. It introduces and explains all the mathematics and statistics that are essential for financial risk management and provides appropriate applications in finance.

Course begins with review of the fundamental mathematical concepts: the symbols used and the basic rules for arithmetic, equations and inequalities, functions and graphs, etc. It continues with introduction of the descriptive statistics that are commonly used to describe the historical characteristics of financial data: the sample moments of returns distributions, ‘downside’ risk statistics, and measures of covariation (e.g. correlation) between two random variables. There is topic on calculus that focuses on differentiation and integration, Taylor expansion and optimization. Financial applications include calculating the convexity of a bond portfolio and the estimation of the delta and gamma of an options portfolio. Special attention is paid to Linear Mathematics and Matrix Algebra which covers matrix operations, special types of matrices and the laws of matrix algebra, the Cholesky decomposition of a matrix, and eigenvalues and eigenvectors with examples of its applications in finance such as: manipulating covariance matrices; calculating the variance of the returns to a portfolio of assets; hedging a vanilla option position; and simulating correlated sets of returns. Course also provides introduction of the concept of probability and the rules that govern it. Then some common probability distributions for discrete and continuous random variables are described, along with their expectation and variance and various concepts relating to joint distributions, such as covariance and correlation, and the expected value and variance of a linear combination of random variables. Topic on Regression Analysis covers the simple and multiple regression models, with applications to the capital asset pricing model and arbitrage pricing theory. The statistical inference section deals with both prediction and hypothesis testing, for instance, of the efficient market hypothesis. Finally, it is necessary to introduce the Numerical Methods that look at solving implicit equations (e.g. the Black–Scholes formula for implied volatility), lattice methods, finite differences and simulation. Financial applications include option valuation and estimating the ‘Greeks’ for complex options.