Polynomial Chaos Expansion approach to Financial Modeling
Speaker: Luca Di Persio, Department of Computer Science, University of Verona, Italy
Abstract: The Polynomial Chaos Expansion (PCE) technique allows to recover the finite second order moment of a random variable exploiting suitable linear combinations of orthogonal polynomials, functions of a given stochastic quantity, acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigorous Uncertainty Quantification (UQ) method aiming at providing reliable numerical estimates for given uncertain physical quantities characterizing specific engineering simulations. We exploit the PCE approach to analyze some simple and well known financial models, as, e.g., the ones based on the Geometric Brownian Motion, the Vasicek model and the CIR model. In particular we present theoretical, as well as related concrete numerical approximations results, providing both an efficiency and an accuracy study of our approach by comparing its outputs with the ones obtained by mean of the Monte Carlo technique in its standard as well as in its enhanced version. Latter comparisons show how the PCE outperforms the Monte Carlo based simulations.
Room Reservation Information
Room Number: 114 McAllister
Time: 12:20pm - 1:10pm