Analytic Loss Distributional Approach Models for Operational Risk from the Α-Stable Doubly Stochastic Compound Processes and Implications for Capital Allocation

29 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

Pavel V. Shevchenko

Macquarie University; Macquarie University, Macquarie Business School

Mark Young

affiliation not provided to SSRN

Wendy Yip

affiliation not provided to SSRN

Date Written: 2011

Abstract

Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach is not prescriptive regarding the class of statistical model utilised to undertake capital estimation. It has however become well accepted to utlise a Loss Distributional Approach (LDA) paradigm to model the individual OpRisk loss process corresponding to the Basel II Business line/event type. In this paper we derive a novel class of doubly stochastic α-stable family LDA models. These models provide the ability to capture the heavy tailed loss process typical of OpRisk whilst also providing analytic expressions for the compound process annual loss density and distributions as well as the aggregated compound process annual loss models. In particular we develop models of the annual loss process in two scenarios. The first scenario considers the loss process with a stochastic intensity parameter, resulting in an inhomogeneous compound Poisson processes annually. The resulting arrival process of losses under such a model will have independent counts over increments within the year. The second scenario considers discretization of the annual loss process into monthly increments with dependent time increments as captured by a Binomial process with a stochastic probability of success changing annually. Each of these models will be coupled under an LDA framework with heavy-tailed severity models comprised of α-stable severities for the loss amounts per loss event. In this paper we will derive analytic results for the annual loss distribution density and distribution under each of these models and study their properties.

Keywords: Operational Risk, Loss Distributional Approach, Doubly stochastic Poisson Process, α-Stable, Basel II, Solvency II

Suggested Citation

Peters, Gareth and Shevchenko, Pavel V. and Young, Mark and Yip, Wendy, Analytic Loss Distributional Approach Models for Operational Risk from the Α-Stable Doubly Stochastic Compound Processes and Implications for Capital Allocation (2011). Available at SSRN: https://ssrn.com/abstract=2980460 or http://dx.doi.org/10.2139/ssrn.2980460

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

Pavel V. Shevchenko

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

HOME PAGE: http://www.businessandeconomics.mq.edu.au/contact_the_faculty/all_fbe_staff/pavel_shevchenko

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

Mark Young

affiliation not provided to SSRN

Wendy Yip

affiliation not provided to SSRN

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