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On the structure of Gaussian pricing models and Gaussian Markov functional models
[journal article]
Abstract This article investigates the structure of Gaussian pricing models (that is, models in which future returns are normally distributed). Although much is already known about such models, this article differs in that it is based on a formulation of the theory of derivative pricing in which numeraire in... view more
This article investigates the structure of Gaussian pricing models (that is, models in which future returns are normally distributed). Although much is already known about such models, this article differs in that it is based on a formulation of the theory of derivative pricing in which numeraire invariance is manifest, extending earlier work on this subject. The focus on symmetry properties leads to a deeper insight in the structure of these models. The central idea is the construction of the most general class of derived Gaussian tradables given a set of underlying tradables which are themselves Gaussian. These derived tradables are called "generalized power tradables" and they correspond to portfolios in which the fraction of total value invested in each asset is a deterministic function of time. Applying this theory to Gaussian HJM models, the new tradables give an explicit description of the interdependence of bonds implicit in such models. Given this structure, a simple condition is derived under which these models allow a description in terms of an M-factor Markov functional model, as introduced by Hunt, Kennedy and Pelsser. Finally, conditions are derived under which these Gaussian Markov functional models are time homogeneous (bond volatilities depending only on the time to maturity). This result is linked to recent results by Björk and Gombani.... view less
Classification
Economic Statistics, Econometrics, Business Informatics
Basic Research, General Concepts and History of Economics
Method
theory application
Free Keywords
Interest Rate Modelling; LIBOR Market Models; Derivatives Pricing; American Options
Document language
English
Publication Year
2007
Page/Pages
p. 487-496
Journal
Quantitative Finance, 7 (2007) 5
DOI
https://doi.org/10.1080/14697680601146838
Status
Postprint; peer reviewed
Licence
PEER Licence Agreement (applicable only to documents from PEER project)