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.

### Polynomial Chaos Expansion Approach to Interest Rate Models

#### 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 \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.
##### Scheda breve Scheda completa Scheda completa (DC)
Polynomial chaos expansion, Geometric Brownian Motion, Cox-Ingersoll-Ross model, Vasicek model, Interest rates models, Uncertainty Quantification, Orthogonal Polynomials, numerical methods
File in questo prodotto:
File
Polynomial Chaos Expansion Approach to Interest Rate Models Di Persio Bonollo Pellegrini.pdf

solo utenti autorizzati

Tipologia: Versione dell'editore
Licenza: Dominio pubblico
Dimensione 3.63 MB
Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/930233