Approximating Value at Risk in Conditional Gaussian Models
Financial institutions are facing the important task of estimating and controlling their exposure to market risk, which is caused by changes in prices of equities, commodities, exchange rates and interest rates. A new chapter of risk management was opened when the Basel Committee on Banking Supervision proposed that banks may use internal models for estimating their market risk (Basel Committee on Banking Supervision, 1995). Its implementation into national laws around 1998 allowed banks to not only compete in the innovation of financial products but also in the innovation of risk management methodology. Measurement of market risk has focused on a metric called Value at Risk (VaR). VaR quantifies the maximal amount that may be lost in a portfolio over a given period of time, at a certain confidence level. Statistically speaking, the VaR of a portfolio is the quantile of the distribution of that portfolio’s loss over a specified time interval, at a given probability level.
KeywordsTruncation Error Importance Sampling Implied Volatility Market Risk Latin Hypercube Sampling
Unable to display preview. Download preview PDF.
- Albanese, C., Jackson, K. and Wiberg, P. (2000). Fast convolution method for VaR and VaR gradients, http://www.math-point.com/fconv.ps/fconv.ps.
- Breckling, J., Eberlein, E. and Kokic, P. (2000). A tailored suit for risk management: Hyperbolic model, in J. Franke, W. Härdie and G. Stahl (eds), Measuring Risk in Complex Stochastic Systems, Vol. 147 of Lecture Notes in Statistics, Springer, New York, chapter 12, pp. 198–202.Google Scholar
- Embrechts, P., McNeil, A. and Straumann, D. (1999). Correlation and dependence in risk management: Properties and pitfalls, http://www.math. ethz.ch/~strauman/preprinta/pitfalls.pa.Google Scholar
- Engle, R. (2000). Dynamic conditional correlation — a simple class of multivariate GARCH models, http://weber.ucsd.edu/~mbacci/engle/.Google Scholar
- Fallon, W. (1996). Calculating Value at Risk, http://wrdsenet.wharton.upenn.edu/fic/wfic/papGrs/96/9649.pdf. Wharton Financial Institutions Center Working Paper 96–49.Google Scholar
- Glasserman, P., Heidelberger, P. and Shahabuddin, P. (2000). Efficient monte carlo methods for value at risk, http://www.research.ibm.com/people/b/berger/papers/RC21723.pdf. IBM Research Paper RC21723.Google Scholar
- Jorion, P. (2000). Value at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill, New York.Google Scholar
- Li, D. (1999). Value at Risk based on the volatility, skewness and kurtosis, http://www.Risk Metrics.com/research/working/var4mm.pdf/research/working/var4mm.pdf. Risk-Metrics Group.Google Scholar
- Pichler, S. and Selitsch, K. (1999). A comparison of analytical VaR methodologies for portfolios that include options, http://www.tuwien.ac.at/E330/Research/paper-var.pdf.at/E330/Research/paper-var.pdf. Working Paper TU Wien.Google Scholar
- Pritsker, M. (1996). Evaluating Value at Risk methodologies: Accuracy versus computational time, http://wrdsenet.wharton.upenn.edu/fic/wfic/papers/96/9648.pdf. Wharton Financial Institutions Center Working Paper 96–48.Google Scholar
- Rouvinez, C. (1997). Going greek with VaR, Risk 10(2): 57–65.Google Scholar
- Zangari, P. (1996a). How accurate is the delta-gamma methodology?, Risk-Metrics Monitor 1996(third quarter): 12–29.Google Scholar
- Zangari, P. (1996b). A VaR methodology for portfolios that include options, Risk Metrics Monitor 1996(first quarter): 4–12.Google Scholar