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

9 Pages Posted: 20 Jul 2005

See all articles by Pavel Okunev

Pavel Okunev

Lawrence Berkeley National Laboratory

Date Written: July 1, 2005

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.

Keywords: Economic capital, gaussian factor model, value at risk, unexpected loss, fast algorithm

Suggested Citation

Okunev, Pavel, Fast Computation of the Economic Capital, the Value at Risk and the Greeks of a Loan Portfolio in the Gaussian Factor Model (July 1, 2005). Available at SSRN: https://ssrn.com/abstract=758505 or http://dx.doi.org/10.2139/ssrn.758505

Pavel Okunev (Contact Author)

Lawrence Berkeley National Laboratory ( email )

310 Barrows Hall
Berkeley, CA 94720
United States

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