A NONLINEAR FILTERING APPROACH TO VOLATILITY ESTIMATION WITH A VIEW TOWARDS HIGH FREQUENCY DATA

2001 ◽  
Vol 04 (02) ◽  
pp. 199-210 ◽  
Author(s):  
RÜDIGER FREY ◽  
WOLFGANG J. RUNGGALDIER
Keyword(s):  
Point Process ◽  
High Frequency ◽  
Nonlinear Filtering ◽  
Marked Point ◽  
Asset Price ◽  
Price Volatility ◽  
High Frequency Data ◽  
Marked Point Process ◽  
Frequency Data ◽  
State Variable

In this paper we consider a nonlinear filtering approach to the estimation of asset price volatility. We are particularly interested in models which are suitable for high frequency data. In order to describe some of the typical features of high frequency data we consider marked point process models for the asset price dynamics. Both jump-intensity and jump-size distribution of this marked point process depend on a hidden state variable which is closely related to asset price volatility. In our setup volatility estimation can therefore be viewed as a nonlinear filtering problem with marked point process observations. We develop efficient recursive methods to compute approximations to the conditional distribution of this state variable using the so-called reference probability approach to nonlinear filtering.

The dependence structure in volatility between Shanghai and Shenzhen stock market in China

2016 ◽  
Vol 6 (3) ◽  
pp. 264-283 ◽  
Author(s):  
Mingyuan Guo ◽  
Xu Wang
Keyword(s):  
Stock Market ◽  
High Frequency ◽  
Estimation Method ◽  
Garch Model ◽  
Price Volatility ◽  
Market Volatility ◽  
High Frequency Data ◽  
Dependence Structure ◽  
Frequency Data ◽  
Content Type

Purpose – The purpose of this paper is to analyse the dependence structure in volatility between Shanghai and Shenzhen stock market in China based on high-frequency data. Design/methodology/approach – Using a multiplicative error model (hereinafter MEM) to describe the margins in volatility of China’s Shanghai and Shenzhen stock market, this study adopts static and time-varying copulas, respectively, estimated by maximum likelihood estimation method to describe the dependence structure in volatility between Shanghai and Shenzhen stock market in China. Findings – This paper has identified the asymmetrical dependence structure in financial market volatility more precisely. Gumbel copula could best fit the empirical distribution as it can capture the relatively high dependence degree in the upper tail part corresponding to the period of volatile price fluctuation in both static and dynamic view. Originality/value – Previous scholars mostly use GARCH model to describe the margins for price volatility. As MEM can efficiently characterize the volatility estimators, this paper uses MEM to model the margins for the market volatility directly based on high-frequency data, and proposes a proper distribution for the innovation in the marginal models. Then we could use copula-MEM other than copula-GARCH model to study on the dependence structure in volatility between Shanghai and Shenzhen stock market in China from a microstructural perspective.

A MODEL FOR HIGH FREQUENCY DATA UNDER PARTIAL INFORMATION: A FILTERING APPROACH

2006 ◽  
Vol 09 (04) ◽  
pp. 555-576 ◽  
Author(s):  
CLAUDIA CECI ◽  
ANNA GERARDI
Keyword(s):  
Point Process ◽  
Stock Price ◽  
Asset Prices ◽  
Partial Information ◽  
Marked Point ◽  
Recursive Algorithm ◽  
Asset Price ◽  
Linearization Method ◽  
Marked Point Process ◽  
Jump Intensity

A general model for intraday stock price movements is studied. The asset price dynamics is described by a marked point process Y, whose local characteristics (in particular the jump-intensity) depend on some unobservable hidden state variable X. The dynamics of Y and X may be strongly dependent. In particular the two processes may have common jump times, which means that the actual trading activity may affect the law of X and could be also related to the possibility of catastrophic events. The agents, in this model, are restricted to observing past asset prices. This leads to a filtering problem with marked point process observations. The conditional law of X given the past asset prices (the filter) is characterized as the unique weak solution of the Kushner–Stratonovich equation. An explicit representation of the filter is obtained by the Feyman–Kac formula using a linearization method. This representation allows us to provide a recursive algorithm for the filter computation.

scholarly journals Modeling Financial Intraday Jump Tail Contagion with High Frequency Data Using Mutually Exciting Hawkes Process

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Chao Yu ◽  
Jianxin Bi ◽  
Xujie Zhao
Keyword(s):  
Stock Market ◽  
Stock Markets ◽  
High Frequency ◽  
Asset Price ◽  
High Frequency Data ◽  
Background Intensity ◽  
Chinese Stock Market ◽  
Hawkes Process ◽  
Frequency Data ◽  
The Stability

Financial extreme jumps in asset price may propagate across stock markets and lead to the market-wide crashes, which severely threatens the stability of the financial system. In order to analyzing the contagion features of jump tail risk, this paper proposes a mutually exciting contagion model based on Hawkes process with intraday high frequency data. We use a simple two-stage method that first extracts the jump component nonparametrically from the high frequency data and then models the intraday jump tail using mutually exciting Hawkes process. Moreover, we take both the occurrence time and magnitude of jump into account in modeling the conditional intensity of Hawkes process. The proposed method is applied to the five-minute high frequency data of the Chinese stock market. The empirical results show that, for the two main Chinese stock markets, only background intensity is significant in the Shanghai stock market, while mutually exciting effect is significant in the Shenzhen stock market. Both the location and size of jump in the Shanghai stock market have significant stimulation to the next occurrences of jump in the Shenzhen stock market. Furthermore, the proposed model performs very well in predicting the future jump tail events.

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