- Hardcover: 512 pages
- Publisher: Wiley; 1 edition (April 2, 2004)
- Language: English
- ISBN-10: 0470861541
- ISBN-13: 978-0470861547
- Product Dimensions: 7 x 1.3 x 9.9 inches
- Shipping Weight: 2.3 pounds (View shipping rates and policies)
- Average Customer Review: 4.0 out of 5 stars See all reviews (1 customer review)
- Amazon Best Sellers Rank: #2,202,473 in Books (See Top 100 in Books)
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Risk Measures for the 21st Century 1st Edition
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“…excellent..provides detailed and up-to-date reference material…written by someone at the top of his field” (Accounting Technician, Sep 2004)
From the Back Cover
The last five years have witnessed a great momentum in the research into measures of financial risk. After many years of ad-hoc and non-consistent measures, now the problem is finally well formulated and some useful and very user-friendly solutions have been proposed. These new measures of risk should be of great interest for investors, financial institutions as well as for regulators.
Under the editorship of Professor Giorgio Szego of the University of Rome "La Sapienza", this book is a collection of the revised and updated papers from prestigious international specialists who are leaders in their field, amongst whom is Robert Engle, a newly-announced Nobel prize-winner in finance. These authors bring a broad perspective across a wide selection of topics, ranging from the critique of some currently used methods, like Value at Risk, to the presentation of some correct risk measures and of some advanced application
The book provides a detailed and up-to-date reference for researchers within academia, and risk managers or financial engineers.
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Financial modelers have also been criticized recently for their use of `copula functions'. Indeed, one article in the press described copulas as a "recipe for disaster" and their use is held to be responsible for the "killing of Wall street." To counter these claims, a few articles and books have appeared in recent months, and this book contains an article that addresses the use of copulas in finance. The authors introduce copulas as a method for dealing with the aggregation of individual risks that goes beyond the Gaussian assumption.
If one begins with a vector of uniform random variables, a copula is their joint distribution, and is effectively a function that can be written as a product if the variables are independent. It also must satisfy certain properties dealing with how it increases and how it operators on the boundary of an n-dimensional hypercube. The authors believe that copulas are useful in finance in that they can quantify risk in terms of individual risk variables and the dependences between them without having to have an explicit characterization of the individual risks.
With all the press about stress testing of banks and the failure of (Gaussian) VAR models in risk management, the author detail how to use copulas in these two areas. A non-Gaussian VAR model is constructed using two different choices of copula functions and compared with the historical Gaussian VAR. The latter is show to underestimate the risk for a confidence level greater than 95%. This situation is the "tail" risk of the Gaussian assumption that has been widely discussed in the financial press in the last couple of years.
Bank stress testing, especially for European banks, is of great interest at the present time and the authors. As the name implies, stress testing deals with how resilient a bank's portfolio is to extreme shocks of the type that might be "rare" or "extreme". Regulatory requirements force the world's major banks to do this (the famous `Basel Accords'). The authors construct `extreme value' copulas to build multivariate stress scenarios. An elementary example for the bivariate case is given that deals with the DowJones and the French CAC40 risk factors. It would have been helpful if the authors would have included at least one more example in order to compare differences.
The authors also present a toy model for pricing basket (equity) derivatives that illustrates the issues in modeling the dependences in risk factors in this case. An explicit real-world example would have been helpful here, or a reference to such an example, in order that readers can see what can go wrong in a realistic scenario from an investment house or hedge fund. They do the same for credit derivatives in another section, wherein they give an interesting graph that illustrates the dependence of the loss distribution and VAR on the choice of copula function. One part of this discussion which may be new to some readers is the notion of `derivatives at risk', which the author write in terms of a conditional expectation and explain how to estimate it with Monte Carlo simulation. Readers will need to know what a `risk-neutral' probability measure to follow the discussion.