Value at risk (VaR) 1000-1M09VAR
1) Elementary properties of VaR
2) Basic properties of quantiles and their estimators (the convergence theorem and the cent- ral limit theorem for empirical quantiles ) 3) Basic methods for VaR estimation ( the methods : variance-covariance - also the case of the loss depending linearly on elliptical risk factors, delta, delta-gamma, based on the Cornish-Fisher expansion, Fourier, historical simulation and Monte Carlo simulation)
4) Backtesting
5) Alternative measures of market risk ( expected shortfall (ES), conditional value at risk (CVaR)) and the notion of coherent risk measure
Half of the exercises will take place in the computer laboratory.
Prerequisites: Introduction to mathematical modelling in finance ( equivalently, capital markets), financial engineering.
Type of course
Bibliography
1) P. Jorion, Value at Risk: the New Benchmark for Managing Financial Risk, 3rd edition, 2007, McGraw-Hill.
2) K. Dowd, Measuring Market Risk, 2nd edition, 2005, Wiley.
3) G.A. Holton, Value-at-Risk, Theory and Practice, 2003, Academic Press.
4) J. Jakubowski, Modelowanie Rynków Finansowych, 2006, Script (in Polish).
5) C. Butler, Mastering Value at Risk:A Step-by-Step Guide to Understanding and Applying VaR, 1998, Prentice Hall.
6) P. Best, Implementing Value at Risk, 1998, Wiley.