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Journal of Probability and Statistics
Volume 2015, Article ID 369053, 24 pages
http://dx.doi.org/10.1155/2015/369053
Research Article

Polynomial Chaos Expansion Approach to Interest Rate Models

1Department of Computer Science, University of Verona, Strada le Grazie 15, 37134 Verona, Italy
2Iason Ltd., Milan, Italy
3IMT Lucca, Piazza San Francesco 19, 55100 Lucca, Italy

Received 30 June 2015; Accepted 19 October 2015

Academic Editor: Z. D. Bai

Copyright © 2015 Luca Di Persio et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantity , hence acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigorous Uncertainty Quantification (UQ) method which aims at providing reliable numerical estimates for some uncertain physical quantities defining the dynamic of certain engineering models and their related simulations. In the present paper, we use the PCE approach in order to analyze some equity and interest rate models. In particular, we take into consideration those models which are based on, for example, the Geometric Brownian Motion, the Vasicek model, and the CIR model. We present theoretical as well as related concrete numerical approximation results considering, without loss of generality, the one-dimensional case. We also provide both an efficiency study and an accuracy study of our approach by comparing its outputs with the ones obtained adopting the Monte Carlo approach, both in its standard and its enhanced version.