Impact of Insurance for Operational Risk: Is It Worthwhile to Insure or Be Insured for Severe Losses?

64 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

Aaron Byrnes

University of New South Wales (UNSW)

Pavel V. Shevchenko

Macquarie University; Macquarie University, Macquarie Business School

Date Written: 2010

Abstract

Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach allows a provision for reduction of capital as a result of insurance mitigation of up to 20%. This paper studies different insurance policies in the context of capital reduction for a range of extreme loss models and insurance policy scenarios in a multi-period, multiple risk settings. A Loss Distributional Approach (LDA) for modelling of the annual loss process, involving homogeneous compound Poisson processes for the annual losses, with heavy-tailed severity models comprised of α-stable severities is considered. There has been little analysis of such models to date and it is believed, insurance models will play more of a role in OpRisk mitigation and capital reduction in future. The first question of interest is when would it be equitable for a bank or financial institution to purchase insurance for heavy-tailed OpRisk losses under different insurance policy scenarios? The second question pertains to Solvency II and addresses quantification of insurer capital for such operational risk scenarios. Considering fundamental insurance policies available, in several two risk scenarios, we can provide both analytic results and extensive simulation studies of insurance mitigation for important basic policies. The intention being to address questions related to VaR reduction under Basel II, SCR under Solvency II and fair insurance premiums in OpRisk for different extreme loss scenarios. In the process we provide closed-form solutions for the distribution of loss process and claims process in an LDA structure as well as closed-form analytic solutions for the Expected Shortfall, SCR and MCR under Basel II and Solvency II. We also provide closed-form analytic solutions for the annual loss distribution of multiple risks including insurance mitigation.

Keywords: Operational Risk, Loss Distributional Approach, Insurance Mitigation, Capital Reduction, α-Stable, Basel II, Solvency II

Suggested Citation

Peters, Gareth and Byrnes, Aaron and Shevchenko, Pavel V., Impact of Insurance for Operational Risk: Is It Worthwhile to Insure or Be Insured for Severe Losses? (2010). Available at SSRN: https://ssrn.com/abstract=2980441 or http://dx.doi.org/10.2139/ssrn.2980441

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

Aaron Byrnes

University of New South Wales (UNSW)

Kensington
High St
Sydney, NSW 2052
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

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
59
Abstract Views
375
rank
391,340
PlumX Metrics