Efficient Numerical Inversion of Characteristic Functions for Computing Tails of Compound Distributions
نویسندگان
چکیده
An adaptive direct numerical integration (DNI) algorithm is developed for inverting characteristic functions of compound distributions, enabling efficient computations of high quantiles and conditional Value at Risk (CVaR). A key innovation of the numerical scheme is an effective tail integration approximation that reduces the truncation errors significantly. High precision results of the 0.999 quantile and CVaR, particularly relevant to operational risk modelling, were obtained for compound losses with heavy tails and a very wide range of loss frequencies. The performance of this new algorithm is compared with those of Fast Fourier Transform (FFT) and Monte Carlo (MC) methods. For moderate to high frequencies and heavy tails, the adaptive DNI is much faster than MC and remains competitive with FFT in computing high quantiles. For CVaR above a given threshold, the advantage of the DNI algorithm over MC and FFT is more significant.
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