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Fast Computation of the Economic Capital, the Value at Risk and the Greeks of a Loan Portfolio in the Gaussian Factor Model

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  • Pavel Okunev

    (Lawrence Berkeley National Laboratory)

Abstract

We propose a fast algorithm for computing the economic capital, Value at Risk and Greeks in the Gaussian factor model. The algorithm proposed here is much faster than brute force Monte Carlo simulations or Fourier transform based methods. While the algorithm of Hull-White is comparably fast, it assumes that all the loans in the portfolio have equal notionals and recovery rates. This is a very restrictive assumption which is unrealistic for many portfolios encountered in practice. Our algorithm makes no assumptions about the homogeneity of the portfolio. Additionally, it is easier to implement than the algorithm of Hull- White. We use the implicit function theorem to derive analytic expressions for the Greeks

Suggested Citation

  • Pavel Okunev, 2005. "Fast Computation of the Economic Capital, the Value at Risk and the Greeks of a Loan Portfolio in the Gaussian Factor Model," Risk and Insurance 0507004, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpri:0507004
    Note: Type of Document - pdf; pages: 9
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ri/papers/0507/0507004.pdf
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    References listed on IDEAS

    as
    1. Pavel Okunev, 2005. "Using Hermite Expansions for Fast and Arbitrarily Accurate Computation of the Expected Loss of a Loan Portfolio Tranche in the Gaussian Factor Model," Finance 0506015, University Library of Munich, Germany.
    2. Pavel Okunev, 2005. "A Fast Algorithm for Computing Expected Loan Portfolio Tranche Loss in the Gaussian Factor Model," Risk and Insurance 0506002, University Library of Munich, Germany.
    3. P. Okunev, 2005. "Fast Computation of the Expected Loss of a Loan Portfolio Tranche in the Gaussian Factor Model: Using Hermite Expansions for Higher Accuracy," Papers math/0506378, arXiv.org.
    4. Pavel Okunev, 2005. "A Fast Algorithm for Computing Expected Loan Portfolio Tranche Loss in the Gaussian Factor Model," Papers math/0506125, arXiv.org, revised Jun 2005.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Economic capital; gaussian factor model; value at risk; unexpected loss; fast algorithm;
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