The Financial Crisis: Warnings, Guilt and a Mathematical ... fileThe Financial Crisis: Warnings, Guilt and a Mathematical Theorem Paul Embrechts Department of Mathematics . Director

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!

And since our memory is so short:

Example 1: February 1995

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

The Black-Scholes Model and Model Uncertainty

Just waiting for disaster to strike!

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!

And many more!!!

“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:

The normal distribution

Extremes matter

Correlation matters

Credit Default Swaps Securitisationconstruction

The investors

(Synthetic)

?Eq. Mez. Sen.

The waterfall principle

Why did no one notice the formula’s Achilles heel?

We did, but nobodylistened!

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!

Standard - model Stress - model(3) (12)

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.

d

(d, ,

Numerous further results:

• Other examples• More specific convergence properties• (non-)Robustness/sensitivity results• An alternative approach to MEVT• Interplay Geometry – Probability• Statistical estimation• …

Thank You!