Saddlepoint methods in portfolio theory
We discuss the use of saddlepoint methods in the analysis of portfolios, with particular reference to credit portfolios. The objective is to proceed from a model of the loss distribution, given through probabilities, correlations and the like, to an analytical approximation of the distribution. Once this is done we show how to derive the so-called risk contributions which are the derivatives of risk measures, such as a given quantile (VaR) or expected shortfall, to the allocations in the underlying assets. These show, informally, where the risk is coming from, and also indicate how to go about optimising the portfolio.
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- Acerbi, Carlo & Tasche, Dirk, 2002.
"On the coherence of expected shortfall,"
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Elsevier, vol. 26(7), pages 1487-1503, July.
- Michael B. Gordy, 2002.
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Finance and Economics Discussion Series
2002-55, Board of Governors of the Federal Reserve System (U.S.).
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- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
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