Computing Tails of Compound Distributions Using Direct Numerical Integration
An efficient adaptive direct numerical integration (DNI) algorithm is developed for computing high quantiles and conditional Value at Risk (CVaR) of compound distributions using characteristic functions. A key innovation of the numerical scheme is an effective tail integration approximation that reduces the truncation errors significantly with little extra effort. High precision results of the 0.999 quantile and CVaR were obtained for compound losses with heavy tails and a very wide range of loss frequencies using the DNI, Fast Fourier Transform (FFT) and Monte Carlo (MC) methods. These results, particularly relevant to operational risk modelling, can serve as benchmarks for comparing different numerical methods. We found that the adaptive DNI can achieve high accuracy with relatively coarse grids. It is much faster than MC and competitive with FFT in computing high quantiles and CVaR of compound distributions in the case of moderate to high frequencies and heavy tails.
|Date of creation:||Apr 2009|
|Date of revision:||Feb 2010|
|Publication status:||Published in Journal of Computational Finance. 13(2), 73-111. (2009)|
|Contact details of provider:|| Web page: http://arxiv.org/|
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