Polynomial chaos expansion approach to interest rate models
type: Item
instance of: scholarly article
title: Polynomial chaos expansion approach to interest rate models
zbMATH Open document ID: 1427.91287
DOI: 10.1155/2015/369053
author: Luca Di Persio
author: Gregorio Pellegrini
author: Michele Bonollo
published in: Journal of Probability and Statistics
publication date: 2018-08-14T00:00:00Z
review text: Summary: 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 \(\xi\), 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.
Mathematics Subject Classification ID: 91G30
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 91G60
zbMATH DE Number: 6917445
Wikidata QID: Q59114211
describes a project that uses: NISP
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/369053
OpenAlex ID: W2190184442
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description: scientific article; zbMATH DE number 6917445