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Functional modelling of volatility in the Swedish limit order book market
Umeå University, Faculty of Social Sciences, Department of Statistics.
2008 (English)In: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352Article in journal (Refereed) Published
Abstract [en]

The publicly available electronic limit order book at the StockholmStock Exchange consists of five levels of prices and quantities of agiven stock with a bid and ask side. All changes in the book duringone day can be recorded with a time quote. Studying variation of the quoted price returns as function of quantity is discussed. In particular, discovering and modelling dynamic behaviours in thevolatility of prices and liquidity measures are considered. Applying a functional approach, estimation of the volatility dynamics of the spreads, created as differences between the ask and bid prices, is presented through a case study. For thatpurpose  two-step estimation of functional linear models is used, extending this method to atime series context.

Place, publisher, year, edition, pages
2008.
National Category
Computer and Information Science
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-18752DOI: 10.1016/j.csda.2008.01.008OAI: oai:DiVA.org:umu-18752DiVA: diva2:174697
Available from: 2009-02-26 Created: 2009-02-24 Last updated: 2017-12-13Bibliographically approved
In thesis
1. Modeling financial volatility: A functional approach with applications to Swedish limit order book data
Open this publication in new window or tab >>Modeling financial volatility: A functional approach with applications to Swedish limit order book data
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is designed to offer an approach to modeling volatility in the Swedish limit order market. Realized quadratic variation is used as an estimator of the integrated variance, which is a measure of the variability of a stochastic process in continuous time. Moreover, a functional time series model for the realized quadratic variation is introduced. A two-step estimation procedure for such a model is then proposed. Some properties of the proposed two-step estimator are discussed and illustrated through an application to high-frequency financial data and simulated experiments.

In Paper I, the concept of realized quadratic variation, obtained from the bid and ask curves, is presented. In particular, an application to the Swedish limit order book data is performed using signature plots to determine an optimal sampling frequency for the computations. The paper is the first study that introduces realized quadratic variation in a functional context.

Paper II introduces functional time series models and apply them to the modeling of volatility in the Swedish limit order book. More precisely, a functional approach to the estimation of volatility dynamics of the spreads (differences between the bid and ask prices) is presented through a case study. For that purpose, a two-step procedure for the estimation of functional linear models is adapted to the estimation of a functional dynamic time series model.

Paper III studies a two-step estimation procedure for the functional models introduced in Paper II. For that purpose, data is simulated using the Heston stochastic volatility model, thereby obtaining time series of realized quadratic variations as functions of relative quantities of shares. In the first step, a dynamic time series model is fitted to each time series. This results in a set of inefficient raw estimates of the coefficient functions. In the second step, the raw estimates are smoothed. The second step improves on the first step since it yields both smooth and more efficient estimates. In this simulation, the smooth estimates are shown to perform better in terms of mean squared error.

Paper IV introduces an alternative to the two-step estimation procedure mentioned above. This is achieved by taking into account the correlation structure of the error terms obtained in the first step. The proposed estimator is based on seemingly unrelated regression representation. Then, a multivariate generalized least squares estimator is used in a first step and its smooth version in a second step. Some of the asymptotic properties of the resulting two-step procedure are discussed. The new procedure is illustrated with functional high-frequency financial data.

Place, publisher, year, edition, pages
Umeå: , 2009. 18 p.
Series
Statistical studies, ISSN 1100-8989 ; 39
Keyword
Financial data, functional time series, multivariate generalized least squares, seemingly unrelated autoregression
National Category
Computer and Information Science
Research subject
Econometrics
Identifiers
urn:nbn:se:umu:diva-18757 (URN)
Public defence
2009-04-03, Hörsal C, Umeå Universitet, Samhällsvetarhuset, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2009-03-13 Created: 2009-02-24 Last updated: 2009-03-13Bibliographically approved

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