"Everything should be made as simple as possible, but not simpler." - Albert Einstein

Seminar Announcement

Parameter Estimation in Stochastic Volatility Models with Jumps
and Long Memory

Jaya Bishwal, University of North Carolina, Charlotte

Monday, March 22, 2010

4:00 p.m., Weber 223

ABSTRACT

Stochastic volatility has both long memory and jumps. Models driven by fractional
Brownian motion contain long memory. Fractional Levy process is a generalization
of fractional Brownian motion to include jumps. By replacing the Brownain motion
with fractional Levy process in the classical Ornstein-Uhlenbeck process one obtains
the fractional Levy-Ornstein-Uhlenbeck (FLOU) process. Thus the model generalizes
Barndorff-Neilsen and Shephard stochastic volatility model. Stochastic leverage and
stochastic volatility of volatility models will also be discussed. Stochastic volatility
being not observed, estimation of the parameters in the FLOU process based on asset
price data is hidden epsilon-Markov fractional-martingale type problem. We study
minimum contrast estimators of the mean reversion speed parameter of the volatility
process and study their asymptotic behavior. We study method of moments estimation
in pure jump FLOU process: the Ornstein-Uhlenbeck-Gamma process. We also study
minimum contrast estimation in Heston model.