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Saddlepoint methods in portfolio theory

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  • Richard J Martin

Abstract

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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  • Richard J Martin, 2011. "Saddlepoint methods in portfolio theory," Papers 1201.0106, arXiv.org.
    • Handle: RePEc:arx:papers:1201.0106
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    References listed on IDEAS

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    1. 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.
    2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    3. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    4. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

    1. Richard J. Martin, 2021. "Design and analysis of momentum trading strategies," Papers 2101.01006, arXiv.org, revised Jan 2023.
    2. Herbertsson, Alexander, 2022. "Saddlepoint approximations for credit portfolios with stochastic recoveries," Working Papers in Economics 823, University of Gothenburg, Department of Economics.
    3. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
    4. Richard J. Martin, 2020. "Fixed income portfolio optimisation: Interest rates, credit, and the efficient frontier," Papers 2004.02312, arXiv.org.

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