Parameter Estimation in Stochastic Volatility Models

Contents
Basic Notations
Preface
Introduction
Chapter 1 Stochastic Volatility Models: Methods of Pricing, Hedgingand Estimation
	1.1 Introduction
	1.2 Stochastic Derivative and Malliavin Calculus for Stochastic Volatility Models
	1.3 Pricing European Options
	1.4 Hedging and Greek Estimation
	1.5 Bootstrap Method for Volatility Estimation
	1.6 Stochastic Gradient Descent Algorithm for American Option
	1.7 Peacock Process and Indian Option
	1.8 Brownian Excursion and Volatility Estimation inLimit Order Book
	1.9 Rate of Cauchy Convergence of Brownian Winding and Asian Options
	1.10 Bond Pricing for the Fractional Vasicek Model
	1.11 Extreme Value Theory in Finance
	1.12 Epsilon-Markov Processes
Chapter 2 Sequential Monte Carlo Methods
	2.1 Introduction
	2.2 Stochastic Volatility Models and SMC Methods
	2.3 Spline Method in Volatility Estimation
	2.4 Multilevel Monte Carlo Method for Nonlinear SPDE
	2.5 Third Order Composition Scheme for Diffusions
Chapter 3 Parameter Estimation in the Heston Model
	3.1 Introduction
	3.2 Continuous Observation
	3.3 Discrete Observations
	3.4 Estimators in the Supercritical CIR Process
	3.5 Sequential Estimation in CIR Process
	3.6 Berry–Esseen Bound for Heston Model
	3.7 Method of Moments Estimation in Heston Model
Chapter 4 Fractional Ornstein–Uhlenbeck Processes,Levy–Ornstein–UhlenbeckProcesses, and FractionalLevy–Ornstein–Uhlenbeck Processes
	4.1 Introduction
	4.2 Continuous Sampling
	4.3 Discrete Sampling
	4.4 Ornstein–Uhlenbeck–Gamma Process
	4.5 Fractional Levy–Ornstein–Uhlenbeck Process
	4.6 FIECOGARCH Process
	4.7 Fractional Gamma and Fractional Inverse Gaussian Ornstein–Uhlenbeck Process
Chapter 5 Inference for General Semimartingales and Self-similarProcesses
	5.1 Introduction
	5.2 Continuous Sampling of Semimartingales
	5.3 Discrete Sampling of Semimartingales
	5.4 Asymptotics of the Log-likelihood Function
	5.5 Random Observation Period: Sequential Inference
	5.6 Fractional and Sub-Fractional Levy O-U Process
Chapter 6 Estimation in Gamma-Ornstein–Uhlenbeck StochasticVolatility Model
	6.1 Introduction
	6.2 Gamma-Ornstein–Uhlenbeck Model
	6.3 Method of Moments Estimators
	6.4 Fractional MS-OU and OU-MS Processes
	6.5 Fractional Hermite OU Processes
Chapter 7 Berry–Esseen Inequalities for the FunctionalOrnstein–Uhlenbeck-Inverse-Gamma Process
	7.1 Introduction
	7.2 Approximate Maximum Likelihood Estimators
	7.3 Berry–Esseen Bounds for AMLE1
	7.4 Berry–Esseen Bounds for AMLE2
	7.5 Berry–Esseen Bounds for AMCEs
	7.6 Geometric Mean Reversion Process: Black-Karasinski Model
Chapter 8 Maximum Quasi-Likelihood Estimation in FractionalLevy Stochastic Volatility Model
	8.1 Introduction
	8.2 Fractional Levy Process
	8.3 Quasi-Maximum Likelihood Estimator
	8.4 Conclusion
Chapter 9 Estimation in Barndorff Nielsen-ShephardOrnstein–Uhlenbeck Stochastic Volatility Models
	9.1 Introduction
	9.2 Modified Tempered Stable Models
	9.3 Method of Moments Estimators
	9.4 Robust Estimation in Inverse Gaussian Ornstein- Uhlenbeck Stochastic Volatility Model
	9.5 Quasi-Maximum Likelihood Estimation in Stable-OU Process
	9.6 Empirical Characteristic Function Estimator
Chapter 10 Parameter Estimation in Student Ornstein–UhlenbeckProcess
	10.1 Introduction
	10.2 Student O–U Process
	10.3 Speed of Convergence for the Cauchy Approximation
	10.4 Berry–Esseen Type Bounds
Chapter 11 Berry–Esseen Asymptotics for Pearson Diffusions
	11.1 Introduction
	11.2 Pearson Diffusions
	11.3 Fractional Student Ornstein–Uhlenbeck Process
	11.4 Estimators
Chapter 12 Bayesian Maximum Likelihood Estimation in FractionalStochastic Volatility Model
	12.1 Introduction
	12.2 Fractional Stochastic Volatility Model
	12.3 Bayesian Maximum Likelihood Estimation
	12.4 Fractional Heston Model
Chapter 13 Berry–Esseen–Stein–Malliavin Theory for FractionalOrnstein–Uhlenbeck Process
	13.1 Introduction
	13.2 Exact Berry–Esseen Bounds
	13.3 Continuous Sampling
	13.4 Discrete Sampling
	13.5 Approximate Minimum Contrast Estimator
	13.6 Higher Order Estimators
	13.7 Fractional Discrete Sampling
Chapter 14 Approximate Maximum Likelihood Estimationin Sub-fractional Hybrid Stochastic Volatility Model
	14.1 Introduction
	14.2 Term Structure Models and Derivative Pricing
	14.3 Newton–Cotes Distribution and Drift Estimators
	14.4 Test Function Estimator of Elasticity of Volatility and Stochastic Elasticity Model
	14.5 Conclusion
Appendix
	A Time Series Regression and Discrete Financial Models
	B Stochastic Calculus
Bibliography
Index