Quantitative Risk Management, Heavy Tails, Tail Dependence and the Credit Crisis

Transcription

1 Quantitative Risk Management, Heavy Tails, Tail Dependence and the Credit Crisis Paul Embrechts Department of Mathematics and Director of RiskLab, ETH Zurich Senior SFI Chair

2 Ex.1: 31. Jan Feb. 1953* (February floading) 1836 people killed people evacuated houses and farms floaded cattle drowned 500 km coastal defenses destroyed; more than 400 breaches of dykes ha land floaded *Antwerp (Schoten): 3rd February,1953

3 The Delta Project Coastal fload-protection Requested dyke height at l: h d (l) Safety margin at l: MYSS(l) = Maximal Yearly Sea Surge at l: Probability(MYSS(l) > h d (l)) should be small, whereby small is defined as: (Risk) 1 / in the Randstad 1 / 250 in the Deltaregion in the North Similar requirements for rivers, but with 1/10 1/100 For the Randstad (Amsterdam-Roterdam): Dyke height = Normal-level (= NAP) m

4 PE Laurens de Haan NAP Guus Balkema Wim Vervaat

5 This talk is very much based on the following 2009 RiskLab publication (*): Catherine Donnelly and Paul Embrechts, The devil is in the tails: actuarial mathematics and the subprime crisis Astin Bulletin 2010, to appear (*) It contains more technical details

6 Recipe for Disaster: The Formula That Killed Wall Street By Felix Salmon 23 February, 2009 Wired Magazine Error, )

7 A stylized Credit Default Swap Set-Up 1 bio USD 1%/year PF1 IC-AA Insurance on F-BB s debt 10%/year rating F-BB RA rating PF2/F2 PF3/F3 PFn/Fn HF1 HFk Betting on default, no link

8 CDOs Complexity, Opacity, Distance, Greed, Economic and Political Stupidity, Regulatory Blindness, Academic Naivity, and Arrogance We are all to blame!

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10 Was it really A Brave New World for Valuation Methodologies (Mary Meeker) and a time to be rationally reckless (*)? The four most expensive words in investment are This time it s different. (xyz) Mr Greenspan so described this New World in 2002(!): The use of a growing array of derivatives and the related application of more sophisticated methods for measuring and managing risk are key factors underpinning the enhanced resilience of our largest financial institutions. As a result, not only have individual financial institutions become less vulnerable to shocks from underlying risk factors, but also the financial system as a whole has become more stable. (*) John Kay (FT, 28/12/09), chiding Mr Greenspan

11 Exhibit 2.9: The conventional wisdom 2006 (!!!!!) There is growing recognition that the dispersion of credit risk by banks to a broader and more diverse group of investors, rather than warehousing such risk on their balance sheets, has helped make the banking and overall financial system more resilient. The improved resilience may be seen in fewer bank failures and more consistent credit provision. Consequently the commercial banks may be less vulnerable today to credit or economic shocks IMF Global Financial Stability Report, April 2006

12 Before we say something about pricing, let us first reflect about volume(*), in particular what order of magnitude are we talking about for these markets? (*) Where is all the credit risk hiding? (+/- 2005)

13 $ * CDS is almost a brand new investment vehicle, but the market is already 20 times its size in The principal amount of CDS outstanding equals $50 trillion, or more than three times the U.S. Gross Domestic Product and bigger than all the U.S. credit markets put together. And the CDS has been a huge source of "financial engineering" profits, both for Wall Street and the hedge fund community over the last few years. World GDP is about $66 trillion. First CDS about Total nominal volume of OTC derivatives 550 Tri. $ * 3.7 Tri. $ after netting

14 micro- The normal distribution Extremes matter Correlation matters

15 Economists Voice: November, 2008 I went on to explain how securitization can give rise to perverse incentives Has the growth in securitization been result of more efficient transactions technologies, or an unfounded reduction in concern about the importance of screening loan applications? we should at least entertain the possibility that it is the latter rather than the former. At the very least, the banks have demonstrated an ignorance of two very basic aspects of risk: (a) the importance of correlation, and (b) the possibility of price decline.

16 So according to Stiglitz (1992!) the issues to concentrate on are: Downside risk: extremes Correlation: dependence And let me add as an Intermezzo:

17 (2005) contains Chapter on Extreme Value Theory beyond Normality Chapter on Dependence Modelling beyond Linear Correlation and much more

18 The AIG-story: AIGFP sold protection on super-senior tranches of CDOs, where the underlying portfolio consisted of loans, debt securities, asset-backed securities and mortgage-backed securities. The likelihood of any payment obligation by AIGFP under each transaction is remote, even in severe recessionary market scenarios (2006, AR) It is hard for us, without being flippant, to even see a scenario within any kind of realm of reason that would see us losing one dollar in any of those transactions. (8/2007, CEO of AIGFP)

19 And yet: AIG, a company of around 100,000 employees brought to its knees by a small subsidiary of 400 employees, is an example of a failure of risk management, both at the division and the group level. AIG almost went bankrupt because it ran out of cash. As at December , AIG had assets of $1,000 billion dollars. Problems with collateral posting and securities lending program also affecting its credit rating, etc On September , the Federal Reserve Board, with the support of the U.S. Department of the Treasury, announced that it had authorized the Federal Reserve Bank of New York to lend up to $85 billion to AIG. Liquidity Speed Size

20 Mathematical Finance Financial Mathematics is of key importance for understanding and clarifying models used in economics making heuristic methods mathematically precise highlighting model conditions and restrictions on applicability working out numerous explicit examples leading the way for stress testing and robustness properties a relevant mathematical theory on its own (Hans Föllmer)

21 Thank you!