Putting the smile back on the face of derivatives

Cross-asset quadratic Gaussian models have been limited in the scale of their implementation by the difficulty in ensuring the correct drift conditions to omit arbitrage. Here, Paul McCloud shows how to exploit the symmetries of the functional form to solve this, and implements the model to price cliquets in the presence of significant skew in the smile

This article considers the exponential-quadratic Gaussian model, an extension of the familiar quadratic Gaussian model with application in the pricing of hybrid exotics. The principal attraction of the approach is its capacity to provide flexible smile behaviour in a multi-factor cross-asset term-structure setting, while retaining simple closed-form analytic expressions for the financial variables