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Links  »  Aggregation of Risks and Economic Capital

Diversification and aggregation

"Measurement and modelling of dependencies in economic capital" by R A Shaw, A D Smith and G S Spivak, May 2010 – an excellent paper on modelling dependency between variables

"Aggregation techniques for Solvency II: a practical example" (Gabriela Baumgartner & Roger Simler) - presentation to the 2010 UK Actuarial Life Insurance Conference giving a practical view of aggregation

"A Practical Concept of Tail Correlation" - 2008 paper by John Manistrea giving a practical overview of aggregation methods and tail dependency

"Modelling dependencies: an overview"  - August 2005 Staple Inn Actuarial Society paper, by Martyn Dorey, Phil Joubert and Coomaren Vencatasawmy giving an overview of copulas

"The Report of the Research Working Party on Correlations and Dependencies Among All Risk Sources - Part I, Correlation and Aggregate Loss Distributions With An Emphasis On The Iman-Conover Method" - 2005 Casualty Actuarial Society paper on the Iman-Conover approach to working with dependent random variables  

"Recipe for disaster: the formula that killed Wall Street" - 2009 article by Felix Salmon on Gaussian copulas and their (mis)use in CDO pricing.

"‘The Formula That Killed Wall Street’? The Gaussian Copula and the Material Cultures of Modelling" - follow-up paper by Donald MacKenzie and Taylor Spears, June 2012

Note the above papers criticising the Gaussian copula may overstate the weaknesses of the Gaussian copula. While it does have a zero co-efficient of tail dependency - broadly speaking, for ever more extreme occurences of risk A, the probability of an event just as extreme under a correlated risk B will tend to 0 - in my experience, this is only significant for very high percentiles (e.g. 99.9999%), beyond the confidence levels financial institutions would be interested in. To my mind, a key failing of CDO was the weakness of the correlation assumption in the face of ever increasing concentration of the underlying portfolio in sub-prime mortgages (see "The Story of the CDO Market Meltdown: An Empirical Analysis", table 2).

Allocation of aggregate capital

"Optimal Capital Allocation Principles" (Dhaene, Tsanakas et al, April 2010) - paper giving inter alia an overview of different allocation methods

"Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle" - 2008 paper by Dirk Tasche on Euler allocation

 "Variance-Covariance Based Risk Allocation in Credit Portfolios: Analytical Approximation" (Mikhail Voropaev, May 2009)


Economic Capital and Internal Models

"Range of practices and issues in economic capital frameworks - final paper" - March 2009  Bank for International Settlements (BIS) paper which provides an overview of the range of practices in economic capital at large banking organisations and discusses a range of issues and challenges surrounding economic capital (follows on from their 2008 consultation paper

"From principle-based risk management to solvency requirements" - 2008 paper by the reinsurer SCOR on their internal model, developed to meet the Swiss Solvency Test

"Specialty guide to economic capital" - Society of Actuaries, 2004

"Actuarial aspects of internal models for Solvency II" - February 2009 sessional meeting paper from the general insurance internal models working group which gives a good, if somewhat dated, overview of Solvency II internal model requirement (being somewhat optimistic in its assumption of a start date for Solvency II of 2012!!) - see also the CEIOPS response to CP56

"Economic capital: a unifying approach" - article by Vaishnavi Srinivasan and Pradip Tapadar, Risk Magazine, special report. January 2008

"Internal models benchmark study" - CRO Forum paper, January 2009.


Modelling and Model Risk 

"Difficult Risks and Capital Models" - 2013 paper by the UK Actuarial Profession's Extreme Events Working Party which gives an excellent insight into model errors and limitations

"Error of VAR by overlapping intervals" - April 2009 AsiaRisk article which suggests that using overlapping data could lead to VaR being under-estimated

"Microsoft Excel’s ‘Not The Wichmann–Hill’ random number generators" - 2008 paper by B.D. McCullough of LeBow College of Business on issues with random number generation in Excel

"The Importance of Excel" - February 2013 article by James Kwak on the role played by Excel in JP Morgan's "London Whale" trading loss

Systemic risk

"Systemic risk in financial services" (D Besar et al, November 2009) - UK Actuarial profession paper which gives some valuable insights into systemic risks

"Assessing possible sources of systemic risk from hedge funds" - a 2010 FSA report on the findings of the hedge fund as counterparty survey and hedge fund survey

"Hedge funds and systemic risk" - Banque de France, Financial Stability Review, April 2007 (Note this was produced before Lehmans and its conclusion that hedge funds are not a source of systemic risk should be treated with caution: there is evidence is that hedge fund withdrawals and resulting asset sales exacerbated the falls in market in late 2008 / early 2009 - for details of these, see the US FCIC Hedge Fund Survey)

"Hedge funds, leverage, and the lessons of Long-Term Capital Management" - report of the US President's Working Group on Financial Markets, April 1999.

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