The Financial Crisis: Warnings, Guilt and a Mathematical ... fileThe Financial Crisis: Warnings, Guilt and a Mathematical Theorem Paul Embrechts Department of Mathematics . Director
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The Financial Crisis: Warnings, Guilt and a
Mathematical Theorem
Paul EmbrechtsDepartment of Mathematics
Director of RiskLab, ETH Zurich Senior SFI Chair
www.math.ethz.ch/~embrechts
This talk is very much based on the following RiskLab publications:
Catherine Donnelly and Paul Embrechts, The devil is in the tails: actuarial mathematics and
the subprime crisis Astin Bulletin 2010, to appear
Guus Balkema, Paul Embrechts, Natalia Nolde Meta densities and the shape of their sample clouds
Several papers, submitted, 2009-2010
Mathematics and Financial Crises
• 1987: (October 19, Black Monday) electronic/algorithmic trading, portfolio insurance, Value-at-Risk (VaR), …
• 1995: (Barings Bank) Financial Enginee- ring, off-balance products (derivatives), …
• 1998: (LTCM disaster) normal-based risk management systems (VaR again), leverage, personalities, too big to fail, …
• 2007 - ???: (Subprime Crisis) numerous accusations, main content of this talk!
The Great Hanshin (Kobe) earthquake of January 17, 1995
Prime example for Operational Risk (later),external event (on top of all else)
How Kobe earthquake and a straddle position finally broke the back of Barings bank
Straddle = Short Call and Short Put on Common Strike
Volume of Nikkei Futures
Example 2: The Black-Scholes Formula(s)
TdT
TrKSd
TTrKSd
dNSdNeKp
dNeKdNScrT
rT
10
2
01
102
210
)2/2()/ln(
)2/2()/ln(
)()(
)()(
where
Conditions
And then indeed disaster struck in September 1998
Nobel Prize 1997
March 1998!
But first
By that time we should have learned about:
• (I)liquidity• Leverage• Model Uncertainty• Non-normality, Extreme Events• Regulatory Arbitrage• Off-Balance Positions• Greed, Non-rationality, Human Factors • Accounting Deficiencies• Global Financial Networks• Etc …
Well we didn’t, previous events were justpeanuts compared to the Perfect Stormthat came to us around late 2007, and isstill going on!
“Blame the mathematicians!” (*)
For some it was however clear:
Here are some examples:
(*) financial engineers, quants, …
Recipe for Disaster: The Formula That Killed Wall Street
By Felix Salmon 23 February, 2009 Wired Magazine
Error, )
The Financial Times:
Of couples and copulas by Sam Jones (April 24, 2009)
In the autumn of 1987, the man who would become the world’s most influential actuary landed in Canada on a flight from China.He could apply the broken hearts maths to broken companies.Li, it seemed, had found the final piece of a risk ma-nagement jigsaw that banks had been slowly piecingtogether since quants arrived on Wall Street.
Why did no one notice the formula’s Achilles heel? Johnny Cash and June Carter
These are rather serious allegations, so let us look at some examples of financial products (*) and
investigate where the mathematics “went wrong”
(*) Credit Derivatives
As examples of credit derivatives:
CDS = Credit Default SwapA relatively simple instrument
CDO = Collateralized Dept ObligationA rather complex instrument
And the “new” RM-paradigm of securitization
Economists’ Voice: www.bwpress.com/ev 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 tech-nologies, or an unfounded reduction in concern about the importance of scree-ning loan applications? … we should at least entertain the possibility that it isthe latter rather than the former.”
At the very least, the banks have demonstratedan ignorance of two very basic aspects of risk:(a) the importance of correlation, and(b) the possibility of price decline.
So according to Stiglitz (1992!) the issues to concentrate on are:
• Downside risk: extremes• Correlation: dependence
And let me add as an Intermezzo:
Chapter on Extreme Value Theorybeyond Normality
Chapter on Dependence Modellingbeyond Linear Correlation
… (2005) contains
and much more …
In order to understand the CDO-mispricing issue, consider the following stylized
example very clearly showing that extremes and dependence matter very much:
Two results from the 1998 RiskLab report
Remark 1: See Figure 1 next page
Remark 2: In the above paper it is shown that
A very early warning!
1960
Indeed we did warn about the Achilles heel!
Some comments by mathematicians:
• (L.C.G. Rogers) The problem is not that mathematics was used by the banking industry, the problem was that it was abused by the banking industry. Quants were instructed to build models which fitted the market prices. Now if the market prices were way out of line, the calibrated models would just faithfully reproduce those wacky values, and the bad prices get reinforced by an overlay of scientific respectability!
A further example of an early warning by academics that was dismissed as
“that’s academic” and one by a concerned risk manager
that was totally ignored! (and there are more examples)
Charles Ponzi1910
Harry Markopolos
Embrechts, P. et al. (2001): An academic response to Basel II. Financial Markets Group, London School of Economics. (Mailed to the Basel Committee)
(Critical on VaR, procyclicality, systemic risk)
Markopolos, H. (2005): The world’s largest hedge fund is a fraud. (Mailed to the SEC)
(Madoff runs a Ponzi scheme)
Bernard Madoff
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)
Here is an example from joint workwith Guus Balkema and Natalia Nolde:
A mathematical theorem on copula-basedmodels like the Gaussian copula model for CDO pricing.
Numerous further results:
• Other examples• More specific convergence properties• (non-)Robustness/sensitivity results• An alternative approach to MEVT• Interplay Geometry – Probability• Statistical estimation• …
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