From: BrendaSueCook (brenda@math.missouri.edu)
Date: Tue May 08 2007 - 09:14:38 CDT
Ph.D. DEFENSE
Department of Mathematics
Pei Yin
University of Missouri-Columbia
Volatility Estimation and Price Prediction Using a Hidden Markov Model
with Empirical Study
Abstract: This work provides a solid development of a hidden Markov
model (HMM) from the economic insight to the mathematic formulation. In
this model, we assume both drift and volatility of the security return
process are driven by certain underlying economic forces which evolve
together as a finite-state, time-invariant Markov chain. Unfortunately,
this chain is unobservable.
Through stochastic filtering techniques and EM algorithm with modified
iteration steps, we estimate the state space and transition matrix of
the Markov chain, as well as the state spaces of the drift and
volatility. With these estimates we can smooth and predict the drift and
volatility processes and apply them to the security price prediction.
On an empirical level, we first use Monte Carlo simulation to show the
robustness of our estimates, and then implement HMM on various data sets
of historical prices including: major indices, bonds, mutual funds,
common stocks, and ETFs to back test the predicability of the model.
Moreover, we compare the applicability of HMM with the well established
GARCH(1,1) model, as far as the prediction performance is concerned, our
results indicate HMM outperforms GARCH(1,1).
Dissertation Advisor: Allanus Tsoi
Tuesday, May 8
2:00 p.m.
117 General Classroom Building
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