GaussHermite Quadrature in Financial Risk （在金融风险GaussHermite正交）.pdf

Submitted version of article published in GARP Risk Review with additional section to prove high-order accuracy of Gauss-Hermite Quadrature Gauss-Hermite Quadrature in Financial Risk Analysis Joe Pimbley* Introduction Financial risk analysis often focuses on calculating the probability of loss or expected loss of a given risky transaction or portfolio of transactions. In structured finance applications, these calculations may include the presence of a loss buffer (otherwise known as “equity”) when the calculations pertain to a risk position that is not the first loss. The analyst compiles the PDF (probability density function) for the loss process and integrates this PDF with the desired risk measure to give a loss probability or expected loss with or without the presence of an equity loss buffer. While this process may seem straightforward, there are many, many practical obstacles. The analyst must make many simplifying assumptions to the point that the problem that is “solved” may bear little resemblance to the true problem. The greatest challenge, then, is to possess the judgment to interpret what meaning the solution to the approximate problem has for the true problem. Two lesser but significant problems are solution complexity (including calculation time) and difficulty of explaining results (and uncertainty of results) to colleagues. We‟ve stumbled across Gauss-Hermite Quadrature (GHQ) as a contribution to these two “lesser but significant problems” of financial analysis. GHQ permits us to use traditional “risk management stress tests” to determine approximations of the PDF integrations n