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Essays on ARCH filtering and estimation.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Essays on ARCH filtering and estimation./
Author:	Schwartz, Boaz A.
Description:	1 online resource (191 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 76-02, Section: A.
Contained By:	Dissertations Abstracts International76-02A.
Subject:	Finance. -
Online resource:	click for full text (PQDT)
ISBN:	9798207986456

Essays on ARCH filtering and estimation.
Schwartz, Boaz A.

Essays on ARCH filtering and estimation. - 1 online resource (191 pages)

Source: Dissertations Abstracts International, Volume: 76-02, Section: A.

Thesis (Ph.D.)--The University of Chicago, 1994.

Includes bibliographical references

A large body of literature has recently developed on option pricing in the presence of randomly changing conditional variances. For the past decade an even larger volume of literature has on using ARCH models to estimate time-varying conditional second moments. Nelson and Foster (1994) introduced an asymptotic filtering theory for ARCH models. The first chapter of this dissertation examines the practical relevance of their results using Monte Carlo simulations calibrated to financial data sets. We compare the performance of the theory in the case that both the form and the parameter values of the stochastic volatility data generating process are known as well as in the case that the parameters are estimated. The theory performs well in the former case. In the latter case the theory performs very well and the mean square error of the error in filtering is lower both in and out-of-sample than in the full information setting. These results suggest that in finite samples the quasi-maximum-likelihood procedure "selects" the best parameters for filtering. The second chapter of the dissertation investigates the ability of ARCH models to capture the parameters of stochastic volatility data generating processes. We consider the case in which a stochastic volatility generates the data and a misspecified ARCH model is used to estimate the parameters. We examine both the point estimates and their standard error. We find that all our models estimate the variance of the variance parameter with bias. The bias is a function of the sampling interval rather than of the sample size. It narrows as we move closer to continuous time sampling. The third chapter investigates the properties of MLE and QMLE estimators of AR(1) EGARCH models. The main result of the chapter is to support the common practice among researchers to assume consistency and asymptotic normality of the parameter estimates of AR(1) EGARCH model, except for the mean reversion parameter that behaves like a unit root as the sampling interval shrinks.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798207986456Subjects--Topical Terms:

559073
Finance.
Subjects--Index Terms:

diffusionIndex Terms--Genre/Form:

554714
Electronic books.

Essays on ARCH filtering and estimation.
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500 $a Source: Dissertations Abstracts International, Volume: 76-02, Section: A.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Nelson, Daniel B.
502 $a Thesis (Ph.D.)--The University of Chicago, 1994.
504 $a Includes bibliographical references
520 $a A large body of literature has recently developed on option pricing in the presence of randomly changing conditional variances. For the past decade an even larger volume of literature has on using ARCH models to estimate time-varying conditional second moments. Nelson and Foster (1994) introduced an asymptotic filtering theory for ARCH models. The first chapter of this dissertation examines the practical relevance of their results using Monte Carlo simulations calibrated to financial data sets. We compare the performance of the theory in the case that both the form and the parameter values of the stochastic volatility data generating process are known as well as in the case that the parameters are estimated. The theory performs well in the former case. In the latter case the theory performs very well and the mean square error of the error in filtering is lower both in and out-of-sample than in the full information setting. These results suggest that in finite samples the quasi-maximum-likelihood procedure "selects" the best parameters for filtering. The second chapter of the dissertation investigates the ability of ARCH models to capture the parameters of stochastic volatility data generating processes. We consider the case in which a stochastic volatility generates the data and a misspecified ARCH model is used to estimate the parameters. We examine both the point estimates and their standard error. We find that all our models estimate the variance of the variance parameter with bias. The bias is a function of the sampling interval rather than of the sample size. It narrows as we move closer to continuous time sampling. The third chapter investigates the properties of MLE and QMLE estimators of AR(1) EGARCH models. The main result of the chapter is to support the common practice among researchers to assume consistency and asymptotic normality of the parameter estimates of AR(1) EGARCH model, except for the mean reversion parameter that behaves like a unit root as the sampling interval shrinks.
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538 $a Mode of access: World Wide Web
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