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We propose a fast algorithm for computing the economic capital, Value at Riskand Greeks in the Gaussian factor model. The algorithm proposed here is muchfaster than brute force Monte Carlo simulations or Fourier transform basedmethods \cite{MD}. While the algorithm of Hull-White \cite{HW} is comparablyfast, it assumes that all the loans in the portfolio have equal notionals andrecovery rates. This is a very restrictive assumption which is unrealistic formany portfolios encountered in practice. Our algorithm makes no assumptionsabout the homogeneity of the portfolio. Additionally, it is easier to implementthan the algorithm of Hull-White. We use the implicit function theorem toderive analytic expressions for the Greeks.

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