Author: Kai LiPublisher:
ISBN:
Category : Rate of return
Languages : en
Pages : 35
Book Description
On Estimation, Diagnostic Testing and Smoothing of Long Memory Stochastic Volatility Models
Author: Kai LiPublisher:
ISBN:
Category : Rate of return
Languages : en
Pages : 35
Book Description
Estimation and identification in long-memory stochastic volatility models
Author: Ana Perez EsparteroParameter Estimation in Stochastic Volatility Models
Author: Jaya P. N. BishwalPublisher: Springer Nature
ISBN: 3031038614
Category : Mathematics
Languages : en
Pages : 634
Book Description
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Bias-Reduced Estimation of Long Memory Stochastic Volatility
Author: Per Skaarup FrederiksenPublisher:
ISBN:
Category :
Languages : en
Pages : 17
Book Description
We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long memory stochastic volatility models with potential nonstationarity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining bias reduction as well as a rate of convergence arbitrarily close to the parametric rate, n1=2. A Monte Carlo study is conducted to support the theoretical results, and an analysis of daily exchange rates demonstrates the empirical usefulness of the estimators.
Univariate and Multivariate Stochastic Volatility Models
Author: Roman LiesenfeldPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
A Maximum Likelihood (ML) approach based upon an Efficient Importance Sampling (EIS) procedure is used to estimate several extensions of the standard Stochastic Volatility (SV) model for daily financial return series. EIS provides a highly generic procedure for a very accurate Monte Carlo evaluation of the marginal likelihood which depends upon high-dimensional interdependent integrals. Extensions of the standard SV model being analyzed only require minor modifications in the ML-EIS procedure. Furthermore, EIS can also be applied for filtering which provides the basis for several diagnostic tests. Our empirical analysis indicates that extensions such as a semi-nonparametric specification of the error term distribution in the return equation dominate the standard SV model. Finally, we also apply the ML-EIS approach to a multivariate factor model with stochastic volatility.
Estimation of the Long-Memory Stochastic Volatility Model Parameters that is Robust to Level Shifts and Deterministic Trends
Author: Adam McCloskeyPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
I provide conditions under which the trimmed FDQML estimator, advanced by McCloskey (2010) in the context of fully parametric short-memory models, can be used to estimate the long-memory stochastic volatility model parameters in the presence of additive low-frequency contamination in log-squared returns. The types of low-frequency contamination covered include level shifts as well as deterministic trends. I establish consistency and asymptotic normality in the presence or absence of such low-frequency contamination under certain conditions on the growth rate of the trimming parameter. I also provide theoretical guidance on the choice of trimming parameter by heuristically obtaining its asymptotic MSE-optimal rate under certain types of low-frequency contamination. A simulation study examines the finite sample properties of the robust estimator, showing substantial gains from its use in the presence of level shifts. The finite sample analysis also explores how different levels of trimming affect the parameter estimates in the presence and absence of low-frequency contamination and long-memory.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
Author: Shelton PeirisOn the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models
Author: Rohit DeoPublisher:
ISBN:
Category :
Languages : en
Pages : 25
Book Description
We consider semiparametric estimation of the memory parameter in a long memorystochastic volatility model. We study the estimator based on a log periodogramregression as originally proposed by Geweke and Porter-Hudak (1983,Journal of Time Series Analysis 4, 221 238). Expressions for the asymptotic biasand variance of the estimator are obtained, and the asymptotic distribution is shownto be the same as that obtained in recent literature for a Gaussian long memoryseries. The theoretical result does not require omission of a block of frequenciesnear the origin. We show that this ability to use the lowest frequencies is particularlydesirable in the context of the long memory stochastic volatility model.
Stochastic Volatility and Realized Stochastic Volatility Models
Author: Makoto TakahashiPublisher: Springer Nature
ISBN: 981990935X
Category : Business & Economics
Languages : en
Pages : 120
Book Description
This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.
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