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Efficient Simulations in Finance

Sak, Halis (2008) Efficient Simulations in Finance. Research Report Series / Department of Statistics and Mathematics, 71. Department of Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna.

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Abstract

Measuring the risk of a credit portfolio is a challenge for financial institutions because of the regulations brought by the Basel Committee. In recent years lots of models and state-of-the-art methods, which utilize Monte Carlo simulation, were proposed to solve this problem. In most of the models factors are used to account for the correlations between obligors. We concentrate on the the normal copula model, which assumes multivariate normality of the factors. Computation of value at risk (VaR) and expected shortfall (ES) for realistic credit portfolio models is subtle, since, (i) there is dependency throughout the portfolio; (ii) an efficient method is required to compute tail loss probabilities and conditional expectations at multiple points simultaneously. This is why Monte Carlo simulation must be improved by variance reduction techniques such as importance sampling (IS). Thus a new method is developed for simulating tail loss probabilities and conditional expectations for a standard credit risk portfolio. The new method is an integration of IS with inner replications using geometric shortcut for dependent obligors in a normal copula framework. Numerical results show that the new method is better than naive simulation for computing tail loss probabilities and conditional expectations at a single x and VaR value. Finally, it is shown that compared to the standard t statistic a skewness-correction method of Peter Hall is a simple and more accurate alternative for constructing confidence intervals. (author´s abstract)

Item Type: Paper
Additional Information: PhD Thesis
Keywords: Monte Carlo method / variance reduction technique / financial simulation / value-at-risk / expected shortfall / credit risk
Classification Codes: RVK QK 320
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 23 Sep 2008 16:17
Last Modified: 23 Aug 2015 06:13
URI: http://epub.wu.ac.at/id/eprint/1068

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