Vanna-Volga and Karasinski Risk Correction Methods

Thesis

The Vanna-Volga (VV) method has been in wide use as one of the major tools for several years among foreign exchange (FX) trading desks. Despite its popularity, the properties of the VV method are not well studied and understood. This thesis attempts to understand better why and when the VV method makes sense, and how to use it better. Often under practical circumstances the state of calibration can be described as being frequent but imperfect. To take advantage of this level of calibration, we studied the properties and benefits of the Karasinski method, and extended this method to a few useful applications. We have found that the Karasinski method, if used with a reasonably calibrated model, can provide significant performance improvement over the VV method.The VV and Karasinski chapters contain most of the original research in this thesis; there are a wealth of discoveries made in these chapters. Novel methods and applications related to the VV and Karasinski methods are proposed, and some of which can be readily applied to the practical trading environment. To make the VV and Karasinski methods work well in practice, the numerical issues for computing the price and Greeks have been carefully addressed with finite difference schemes that are second-order convergent and fast to compute. As an example of easy-to-compute but difficult-to-calibrate model candidates for the Karasinski method, the Multi-Heston model has been discussed too. A sound computational preparation enables the VV and in particular Karasinski methods to enjoy high viability as being fast, efficient and practical. This thesis is tailored to the purpose of making a detailed study on these useful methods whose great potential has not been adequately understood and fully realised.

Authors: Tao, M

• Publication date: 2009
• DOI: 10.5287/ora-obdnj2zvq
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: Finite Difference; Finance; FX; Volatility; PDE; Calibration; Greeks; Correction; Numerical; Vanna-Volga
• Subjects: Finance; Mathematical finance