Simulation of the Annual Loss Distribution in Operational Risk Via Panjer Recursions and Volterra Integral Equations for Value at Risk and Expected Shortfall Estimation.

27 Pages Posted: 5 Jun 2017

See all articles by Gareth Peters

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Adam M. Johansen

University of Bristol - Department of Mathematics

Arnaud Doucet

University of Cambridge - Department of Engineering

Date Written: June 4, 2017

Abstract

Following the Loss Distributional Approach (LDA), this article develops two procedures for simulation of an annual loss distribution for modeling of Operational Risk. First, we provide an overview of the typical compound-process LDA used widely in Operational Risk modeling, before expanding upon the current literature on evaluation and simulation of annual loss distributions. We present two novel Monte Carlo simulation procedures. In doing so, we make use of Panjer recursions and the Volterra integral equation of the second kind to reformulate the problem of evaluation of the density of a random sum as the calculation of an expectation. We demonstrate the use of importance sampling and trans-dimensional Markov Chain Monte Carlo algorithms to efficiently evaluate this expectation. We further demonstrate their use in the calculation of Value at Risk and Expected Shortfall.

Keywords: Importance Sampling; Trans-dimensional Markov Chain Monte Carlo; Basel II Advanced Measurement Approach; Panjer Recursions; Volterra Integral Equations; Compound Processes; Loss Distributional Approach; Operational Risk; Value at Risk; Expected Shortfall

Suggested Citation

Peters, Gareth and Johansen, Adam M. and Doucet, Arnaud, Simulation of the Annual Loss Distribution in Operational Risk Via Panjer Recursions and Volterra Integral Equations for Value at Risk and Expected Shortfall Estimation. (June 4, 2017). Available at SSRN: https://ssrn.com/abstract=2980408 or http://dx.doi.org/10.2139/ssrn.2980408

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Adam M. Johansen

University of Bristol - Department of Mathematics ( email )

Bristol, BS8 1TW
United Kingdom

Arnaud Doucet

University of Cambridge - Department of Engineering ( email )

Cambridge
United Kingdom

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