This book develops alternative methods to estimate the unknown
parameters in stochastic volatility models, offering a new approach
to test model accuracy. While there is ample research to document
stochastic differential equation models driven by Brownian motion
based on discrete observations of the underlying diffusion process,
these traditional methods often fail to estimate the unknown
parameters in the unobserved volatility processes. This text
studies the second order rate of weak convergence to normality to
obtain refined inference results like confidence interval, as well
as nontraditional continuous time stochastic volatility models
driven by fractional Levy processes. By incorporating jumps and
long memory into the volatility process, these new methods will
help better predict option pricing and stock market crash risk.
Some simulation algorithms for numerical experiments are provided.
General
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