2017/10/03 by Igor Halperin, Halperin, Igor
Economics, Econometrics and Finance · #58 #60 #62 #Complex Systems and Time Series Analysis #Computation (stat.CO) #Computational Finance (q-fin.CP) #Data Analysis #FOS: Computer and information sciences #FOS: Economics and business #FOS: Physical sciences #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.1710.01227
openalex publication_date 2017/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation of the tail probability of a compound distribution in the form of a rapidly convergent one-dimensional integral involving a discontinuity of the imaginary part of its moment generating function across a branch cut. The latter integral can be evaluated in quadratures, or alternatively represented as an asymptotic expansion. Our approach thus offers a viable (especially at high percentile levels) alternative to more standard methods such as Monte Carlo or the Fast Fourier Transform, traditionally used for such problems. As a practical application, we use our method to compute the operational Value at Risk (VAR) of a financial institution, where individual losses are modeled as spliced distributions whose large loss components are given by power-law or lognormal distributions. Finally, we briefly discuss extensions of the present formalism for calculation of tail probabilities of compound distributions made of compound distributions with heavy tails.