高斯因子模型下贷款组合的经济资本、风险价值和Greeks的快速计算
Fast Computation Of the Economic Capital, the Value at Risk and the Greeks of a Loan Portfolio in the Gaussian Factor Model
摘要：
本文提出了一种计算高斯因子模型中经济资本、风险价值和希腊数的快速算法。这里提出的算法比蛮力蒙特卡罗模拟或基于傅里叶变换的方法\cite{MD}快得多。虽然Hull-White \cite{HW}的算法非常快，但它假设投资组合中的所有贷款都具有相同的名义利率和回收率。这是一个非常严格的假设，对于实践中遇到的许多投资组合来说是不现实的。我们的算法没有假设投资组合的同质性。此外，它比Hull-White算法更容易实现。我们使用隐函数定理来推导希腊人的解析表达式。
英文摘要：
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 \cite{MD}. While the algorithm of Hull-White \cite{HW} 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.
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