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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- Michael B. Gordy, 2002.
"A risk-factor model foundation for ratings-based bank capital rules,"
Finance and Economics Discussion Series
2002-55, Board of Governors of the Federal Reserve System (U.S.).
- Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, vol. 12(3), pages 199-232, July.
- Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
- Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
- Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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