Estimation of continuous-time stochastic volatility models with jumps using high-frequency data

2009 ◽  
Vol 148 (2) ◽  
pp. 131-148 ◽  
Author(s):  
Viktor Todorov
Keyword(s):  
Stochastic Volatility ◽  
Continuous Time ◽  
High Frequency ◽  
High Frequency Data ◽  
Frequency Data ◽  
Stochastic Volatility Models ◽  
Volatility Models

COMPUTATION OF VOLATILITY IN STOCHASTIC VOLATILITY MODELS WITH HIGH FREQUENCY DATA

2010 ◽  
Vol 13 (05) ◽  
pp. 767-787 ◽  
Author(s):  
EMILIO BARUCCI ◽  
MARIA ELVIRA MANCINO
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
Asset Price ◽  
Heston Model ◽  
High Frequency Data ◽  
Monte Carlo Experiment ◽  
Price Model ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Correlation Parameters

We consider general stochastic volatility models driven by continuous Brownian semimartingales, we show that the volatility of the variance and the leverage component (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying parametrically the asset price model we show that the method allows us to compute the parameters of the model. We provide a Monte Carlo experiment to recover the volatility and correlation parameters of the Heston model.

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.

Noncausality in Continuous Time Models

1996 ◽  
Vol 12 (2) ◽  
pp. 215-256 ◽  
Author(s):  
F. Comte ◽  
E. Renault
Keyword(s):  
Stochastic Volatility ◽  
Continuous Time ◽  
Moving Average ◽  
Sufficient Conditions ◽  
Stochastic Volatility Models ◽  
Discrete Sample ◽  
Volatility Models ◽  
Moving Average Representation ◽  
Canonical Representations ◽  
Average Representation

In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as properties of interest for structural interpretations. In particular, we examine the example of processes solutions of stochastic differential equations, for which we study the links between continuous and discrete time definitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a discrete sample of observations. Finally, we illustrate a possible generalization of definitions and characterizations that can be applied to continuous time fractional ARMA processes.

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