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. The analysis combines the potential models originating in the work of Rogers (1997) with results from the theory of quadratic Gaussian models, particularly from Assefa (2007), and is explored in more detail (with extensions to semi-martingales) in McCloud (2008). Recent publications such as the paper by Piterbarg (2009) indicate that the approach is increasing in popularity.
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