# David X. Li

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Not to be confused with Li Xianglin (footballer).

David X. Li (born in Nanjing, China, in the 1960s as Chinese: 李祥林; pinyin: Lǐ Xiánglín[1]) is a quantitative analyst and a qualified actuary who in the early 2000s pioneered the use of Gaussian copula models for the pricing of collateralized debt obligations (CDOs).[2][3] The Financial Times called him "the world’s most influential actuary",[1] while in the aftermath of the global financial crisis of 2008–2009, to which Li's model has been credited partly to blame,[1][2] his model has been called a "recipe for disaster".[2]

## Biography

Li was born as Li Xianglin and raised in a rural part of China during the 1960s;[2] his family had been relocated during the Cultural Revolution to a rural village in southern China for "re-education".[1] Li was talented and with hard work he received a master's degree in economics from Nankai University, one of the country’s most prestigious universities.[1] After leaving China in 1987 at the behest of the Chinese government to learn more about capitalism from the west,[1] he earned an MBA from Laval University in Quebec, and an MMath in Actuarial Science and PhD in statistics from the University of Waterloo in Ontario[2] in 1995 with thesis title An estimating function approach to credibility theory under the supervision of Harry H. Panjer.[4] At this point he changed his name to David X. Li.[1] His financial career began in 1997 at Canadian Imperial Bank of Commerce World Markets division.[2] He eventually moved to New York City and in 2000, he was a partner in J.P. Morgan's RiskMetrics unit.[5] By 2003 he was director and global head of credit derivatives research at Citigroup.[1] In 2004 he moved to Barclays Capital and headed up the credit quantitative analytics team.[2] In 2008 Li moved to Beijing where he works for China International Capital Corporation as head of the risk management department.[2]

## CDOs and Gaussian copula

Li's paper "On Default Correlation: A Copula Function Approach"[3] (2000) was the first appearance of the Gaussian copula applied to CDOs, which quickly became a tool for financial institutions to correlate associations between multiple securities.[2] This allowed for CDOs to be supposedly accurately priced for a wide range of investments that were previously too complex to price, such as mortgages. However, in the aftermath of the Global financial crisis of 2008–2009 the model has been seen as fundamentally flawed and a "recipe for disaster".[2] According to Nassim Nicholas Taleb, "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked. Co-association between securities is not measurable using correlation"; in other words, because history is not predictive of the future, "[a]nything that relies on correlation is charlatanism."[2]

Li himself apparently understood the fallacy of his model, in 2005 saying "Very few people understand the essence of the model."[6] Li also wrote that "The current copula framework gains its popularity owing to its simplicity....However, there is little theoretical justification of the current framework from financial economics....We essentially have a credit portfolio model without solid credit portfolio theory."[7] Kai Gilkes of CreditSights says "Li can't be blamed", although he invented the model, it was the bankers who misinterpreted and misused it.[2]

### Li's paper

Li's paper is called "On Default Correlation: A Copula Function Approach" (2000), published in Journal of Fixed Income, Vol. 9, Issue 4, pages 43–54.[3]

In section 1 through 5.3, Li describes actuarial math that sets the stage for his theory. The mathematics are from established statistical theory, actuarial models, and probability theory.

In section 5.4, he uses Gaussian Copula to measure event relationships, or mathematically, correlations, between random economic events, expressed as:

${\displaystyle C_{\rho }(u,v)=\Phi _{\rho }\left(\Phi ^{-1}(u),\Phi ^{-1}(v)\right)}$

In layman's terms, he proposes there is a relationship between 2 different but related events i.e. "House A" defaulting and "House B" defaulting are measurable using correlation. While under some scenarios (such as real estate) this correlation appeared to work most of the time, the underlying problem is that history ultimately cannot predict the future.

From 6.0 onward, the paper presents experimental results using the Gaussian Copula. The results are favorable to Li's proposal.

## References

1. Jones, Sam (April 24, 2009). "The formula that felled Wall St". Financial Times. Financial Times.
2. Salmon, Felix (March 2009). "Recipe for Disaster: The Formula That Killed Wall Street". Wired Magazine. Wired (magazine). 17 (3).
3. ^ a b c Li, David X. (2000). "On Default Correlation: A Copula Function Approach". Journal of Fixed Income. 9 (4): 43–54. doi:10.3905/jfi.2000.319253. Archived from the original on 2008-04-30.
4. ^ Li, Xianglin. "An estimating function approach to credibility theory". ProQuest.
5. ^ The Star. Toronto http://www.thestar.com/business/2009/03/18/meet_the_man_whose_big_idea_felled_wall_street.html. Missing or empty |title= (help)
6. ^ "Slices of Risk", Mark Whitehouse, The Wall Street Journal, September 12, 2005
7. ^ The Definitive Guide to CDOs, Edited by Gunter Meissner, pg. 71, 2008, Risk Books