10.6 Further Reading – Transformation Procedures
The mathematics of quadratic transformation procedures is well established except with regard to calculating quantiles of 1P. Two approaches are discussed in this book—the Cornish-Fisher expansion and the trapezoidal rule—but there are others. See, for example, Mina and Ulmer (1999). Jaschke (2001) provides an in-depth discussion of the Cornish-Fisher expansion and its use with quadratic transformations. Jaschke and Mathé (2004) compare two alternative methods, Fourier transforms and a method they propose based on the Monte Carlo method. They find the latter to be superior. Pichler and Selitsch (2000) compare several methods using simulated return data. See also Fuglsbjerg (2000).
Glasserman, Heidelberger and Shahabuddin (2000) describe alternative techniques of variance reduction for value-at-risk. In side-by-side testing, your author found these to be inferior to the methods of Cárdenas et al. (1999) described in Section 10.5. Glasserman (2003) describes other methods of variance reduction, which your author has not tested.