Estimating continuous-time stochastic volatility models of the short-term interest rate: a comparison of the generalized method of moments and the Kalman filter

2009 ◽  
Vol 33 (4) ◽  
pp. 303-326 ◽  
Author(s):  
Travis R. A. Sapp
Keyword(s):  
Kalman Filter ◽  
Interest Rate ◽  
Stochastic Volatility ◽  
Method Of Moments ◽  
Continuous Time ◽  
Generalized Method Of Moments ◽  
Stochastic Volatility Models ◽  
Short Term ◽  
Volatility Models

METHOD OF MOMENTS ESTIMATION FOR LÉVY-DRIVEN ORNSTEIN–UHLENBECK STOCHASTIC VOLATILITY MODELS

2020 ◽  
pp. 1-30
Author(s):  
Xiangyu Yang ◽  
Yanfeng Wu ◽  
Zeyu Zheng ◽  
Jian-Qiang Hu
Keyword(s):  
Stochastic Volatility ◽  
Method Of Moments ◽  
Model Misspecification ◽  
Analytical Framework ◽  
Model Parameters ◽  
Computationally Efficient ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Form Representation ◽  
Method Of Moments Estimation

This paper studies the parameter estimation for Ornstein–Uhlenbeck stochastic volatility models driven by Lévy processes. We propose computationally efficient estimators based on the method of moments that are robust to model misspecification. We develop an analytical framework that enables closed-form representation of model parameters in terms of the moments and autocorrelations of observed underlying processes. Under moderate assumptions, which are typically much weaker than those for likelihood methods, we prove large-sample behaviors for our proposed estimators, including strong consistency and asymptotic normality. Our estimators obtain the canonical square-root convergence rate and are shown through numerical experiments to outperform likelihood-based methods.

ESTIMATION IN CONTINUOUS-TIME STOCHASTIC VOLATILITY MODELS USING NONLINEAR FILTERS

2000 ◽  
Vol 03 (02) ◽  
pp. 279-308 ◽  
Author(s):  
JAN NYGAARD NIELSEN ◽  
MARTIN VESTERGAARD
Keyword(s):  
Differential Equations ◽  
Stochastic Volatility ◽  
Stock Prices ◽  
Continuous Time ◽  
Stock Price ◽  
Estimation Method ◽  
Small Sample ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Filtering Problem

The stylized facts of stock prices, interest and exchange rates have led econometricians to propose stochastic volatility models in both discrete and continuous time. However, the volatility as a measure of economic uncertainty is not directly observable in the financial markets. The objective of the continuous-discrete filtering problem considered here is to obtain estimates of the stock price and, in particular, the volatility using discrete-time observations of the stock price. Furthermore, the nonlinear filter acts as an important part of a proposed method for maximum likelihood for estimating embedded parameters in stochastic differential equations. In general, only approximate solutions to the continuous-discrete filtering problem exist in the form of a set of ordinary differential equations for the mean and covariance of the state variables. In the present paper the small-sample properties of a second order filter is examined for some bivariate stochastic volatility models and the new combined parameter and state estimation method is applied to US stock market data.

Sign in / Sign up

Export Citation Format

Share Document