Sebastian Baldivieso PhD Mathematical Sciences Dissertation Defense
Friday, January 31, 2020 - 3:00pm

Ph.D. in Mathematical Sciences Dissertation Defense

Sebastian Baldivieso

Sensitivity Diagnostics and Adaptive Tuning of the Multivariate Stochastic Volatility Model

Sebastian BaldiviesoMS Economics, Portland State University, 2016
BS Mathematics, Portland State University, 2014

Defense Date: Friday, January 31, 2020
Time: 3:00PM
Location: Fariborz Maseeh Hall room 462
1855 SW Broadway, Portland

Committee Chair:    Dacian Daescu, PhD
Committee Members:    Steven Bleiler, PhD
                                     Daniel Taylor-Rodriguez, PhD
                                     Bin Jiang, PhD
                                     Rossitza Wooster, PhD
Graduate Office Representative:   John Gallup, PhD

Abstract: New methodologies for diagnostic analysis and adaptive tuning based on sensitivity information of the Multivariate Stochastic Volatility (MSV) model are established in this dissertation. The main focus is on obtaining optimal conditional volatilities from a time series set of financial data observed in the market by specifying a State-Space model with error covariance adaptive tuning of the MSV model. Variational Data Assimilation methods are used in this research as tools for obtaining the optimal a posteriori estimates of the multivariate series of volatilities. Calculus of Variations techniques are then applied to a forecast score function to derive the sensitivities of the forecasted volatilities in terms of the input parameters. In summary, this dissertation achieves the development of these new methodologies by
•     Developing the sensitivity information of the multivariate conditional volatilities to observations, covariance specifications and prior estimates,
•    Developing tools for assessing multivariate volatility forecasts diagnostics and performance,
•    Developing an adaptive tuning procedure based on the multivariate volatility sensitivity information to provide improved results online. 
Applications of the new sensitivity diagnostics and adaptive tuning procedures of the MSV model are explored in two experiments. The first experiment is a proof-of-concept experiment where a multivariate series of volatilities is simulated through the specification of a MSV model. Then, adaptive tuning procedure is performed on the calibrated model to demonstrate superior estimation results over the current literature methodologies. In the second experiment, a time series set of Foreign Exchange (FX) rate data is used to calibrate the MSV model to provide a time series of conditional volatilities of each FX rate. The sensitivity information of each FX rate's conditional volatility forecasts is implemented to derive model performance diagnostics, while the adaptive tuning procedure is implemented to provide improved conditional volatility estimates.