Introduction
Alexander McNeil, an expert on financial risk management, believes the reason that most European banks entered the recent credit crisis dangerously undercapitalized was because they failed to adopt an integrated, or “economic capital,” approach to assessing risk. This left them vulnerable once the crisis erupted and left many needing state support.
McNeil is Maxwell Professor of Mathematics in the Department of Actuarial Mathematics and Statistics at Heriot-Watt University, Edinburgh, and is a former assistant professor in the Department of Mathematics at ETH Zurich. He has a BSc from Imperial College, London, and a PhD in mathematical statistics from Cambridge University. His interests include the development of mathematical and statistical methodologies for integrated financial risk management. He has published papers in leading academic journals and is a regular speaker at international risk-management conferences. Together with Rüdiger Frey and Paul Embrechts he is joint author of Quantitative Risk Management: Concepts, Techniques, Tools, published by Princeton University Press in 2005. In 2010 he founded the Scottish Financial Risk Academy with support from the Scottish government and private sector backers. The SFRA runs a series of knowledge exchange activities designed to improve the interaction between the academic sector and the financial services industry.
When did mathematics first become an integral part of banking and finance?
It was largely a post-war phenomenon. In the 1950s Harry Markowitz started applying mathematical ideas to portfolio selection and introduced the idea of mean–variance portfolio optimization. Further mathematical finance theories were developed and applied after that, including the capital asset pricing model and arbitrage pricing theory. But the biggest breakthrough was the Black–Scholes model in 1973.
Did that permit derivatives to be more accurately priced?
The Black–Scholes model quickly became indispensable to all participants in derivatives trading, since the no-arbitrage arguments provided valuations that were, supposedly, consistent with those of other quoted instruments. However, the model never pretended to describe the market 100% accurately and most users would recognize that it has deficiencies.
Did mathematicians become more sought after by Wall Street firms after that?
Yes. In order to properly derive the Black–Scholes formula, you need to engage in quite sophisticated mathematics—which implies a need for more mathematicians.
In her book Fool’s Gold, the Financial Times journalist Gillian Tett focuses on value-at-risk. How did that concept come about?
VaR can trace its origins back to the “4.15 pm report” of former JP Morgan CEO Dennis Weatherstone. In that report, he requested a means of measuring how the value of the bank’s trading book might change in a 24-hour period—how much it could fall in value. The risk metrics methodology JP Morgan developed to do that basically follows VaR.
But wasn’t the VaR model seriously flawed?
No, I wouldn’t say flawed. VaR is a measure for calculating the risk of changes to the value of a portfolio over a 24-hour period. One of its possible flaws is that its properties are weak under aggregation, making it difficult to deliver an aggregate calculation of the total possible losses across an organization using VaR. The other weakness is that VaR is a theoretical concept; to translate it into reality, you need to use data to estimate it. And although there are good statistical or econometric models, there are also bad ones.
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