images

Quadratic Gaussian Modelsa

Quadratic Gaussian (QG) models are factor models for the pricing of interest-rate derivatives, where interest rates are quadratic functions of underlying Gaussian factors. The QG model of interest rates was first introduced by Beaglehole and Tenney [3] and by El Karoui et al. [11]. Similar models had been introduced in epidemiology [16]. Jamshidian [14], under restrictive hypothesis on the dynamic of the factors, obtained closed formulas for the prices of vanilla options in the QG model. Durand and El Karoui [10] have detailed some properties and statistical analysis of the QG model. One may refer, for example, to [1, 6] for general studies of quadratic term-structure models.

Quadratic Gaussian Model

Uncertainty is represented by an n-dimensional Brownian motion imagesb on the filtered probability space (Ω, Ft, P), where Ft is the natural augmented filtration of Brownian motion images and P the historical probability. We then add two assumptions:

Hypothesis 1 The asset price processes in all the different markets are regular deterministic functions of n state variables.

Hypothesis 2 The state variables have a Gaussian–Markovian distribution with respect to all the risk-neutral ...

Get Encyclopedia of Quantitative Finance, IV Volume Set now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.