Measurement of Market Risk

Introduction of the risk factors (interest-rate-discount-factors for different maturities and currencies, spreads for different maturities, currencies, ratings, industries, stock prices or indices, foreign exchange, commodity prices, etc.); Modelling and estimation of the distribution of risk factor changes: Simple approaches such as a joint normal distribution with historical estimators (moving-average estimators); Refinement of the parameter estimation for a joint normal distribution (exponentially weighted moving average EWMA, ARCH & GARCH); Short presentation of more advanced, alternative models: e.g. modelling of stochastic differential equations (SDEs) for interest rate models, including the parameter estimation for such models, and conducting a Monte Carlo simulation; Product mapping: delta approach and delta-gamma-approach; VaR-estimation: variance-covariance approach, historical simulation, Monte Carlo simulation; Back-testing of VaR-models; Stress Testing

Mode of delivery

face to face



Recommended or required reading and other learning resources/tools

Jorion, P., 2006, Value at Risk, 3rd ed., McGraw-Hill; Alexander, C., 2008, Value-at-Risk Models, John Wiley & Sons

Planned learning activities and teaching methods

integrated class

Assessment methods and criteria

Students are assessed on the quality of their assignments, their presentations, their participation and the results of the written quizzes.

Prerequisites and co-requisites

Courses 1 - 6


Degree programme

Quantitative Asset and Risk Management (Master)



ECTS Credits


Language of instruction




Academic year



2 SS



Learning outcome

After the successful completion of the course students are able to master the various different computational approaches to estimate market risk measures (historical simulation, variance-covariance approach, advanced alternative simulation approaches). Also, they are able to test the quality of already implemented risk measurement models (back-testing) and they can conduct stress tests that analyse the impact of scarce extreme events. This detailed knowledge about market risk measurement is essential for managing market risk.

Course code