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Defense: Volatility and Correlation Analysis of Financial Market Data

Speaker Name: 
Georgi Dinolov
Speaker Title: 
PhD Candidate (Advisor: Abel Rodriguez)
Speaker Organization: 
Statistical Science
Start Time: 
Monday, March 11, 2019 - 10:30am
End Time: 
Monday, March 11, 2019 - 10:30am
Engineering 2, Room 280
Abel Rodriguez

Abstract:  Statistical models of price volatility most commonly use low-frequency (daily, weekly, or monthly) returns. However, despite their availability, two types of financial data have not been extensively studied: high-frequency data where sampling periods are on the order of seconds; and open, close, high, and low (OCHL) data which incorporate intraperiod extremes. We formulate a discrete-time Bayesian stochastic volatility model for high-frequency stock-market data that directly accounts for microstructure noise, and outline a Markov chain Monte Carlo algorithm for parameter estimation. The method described is designed to be coherent across all sampling timescales, with the goal of estimating the latent log-volatility signal from data collected at arbitrarily short sampling periods. We also present and motivate the bivariate OCHL problem, enumerate the fundamental limitations of some common out-of-the-box approaches, and present a semidiscrete Galerkin numerical solver for computing the likelihood of the observed data. In addition, we prove the consistency of maximum likelihood estimates under the approximate density given by the solver. Finally, we develop a closed-form, analytic solution to the OCHL likelihood problem in parameter ranges where the Galerkin solver requires near-infinite compute time and memory to produce numerically accurate results. A matching solution is also proposed to interpolate between parameter regions where neither the Galerkin nor analytic solutions are applicable. Thus, we present a method for producing likelihoods based on OCHL data over all model parameter ranges, which is a key requirement in statistical estimation algorithms.