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Full Description
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.
Contents
Stochastic Volatility Models: Methods of Pricing, Hedging and Estimation.- Sequential Monte Carlo Methods.- Parameter Estimation in the Heston Model.- Fractional Ornstein-Uhlenbeck Processes, Levy-Ornstein-Uhlenbeck Processes and Fractional Levy-Ornstein-Uhlenbeck Processes.- Inference for General Semimartingales and Selfsimilar Processes.- Estimation in Gamma-Ornstein-Uhlenbeck Stochastic Volatility Model.- Berry-Esseen Inequalities for the Functional Ornstein-Uhlenbeck-Inverse-Gaussian Process.- Maximum Quasi-likelihood Estimation in Fractional Levy Stochastic Volatility Model.- Estimation in Barndorff-Neilsen-Shephard Ornstein-Uhlenbeck Stochastic Volatility Model.- Parameter Estimation in Student Ornstein-Uhlenbeck Model.- Berry-Esseen Asymptotics for Pearson Diffusions.- Bayesian Maximum Likelihood Estimation in Fractional Stochastic Volatility Models.- Berry-Esseen-Stein-Malliavin Theory for Fractional Ornstein-Uhlenbeck Process.- Approximate Maximum Likelihood Estimation for Sub-fractional Hybrid Stochastic Volatility Model.- Appendix.
