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New Methods For Performing Efficient Inference For Linear And Log Normal Stochastic Volatility Models
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Book Synopsis New Methods for Performing Efficient Inference for Linear and Log-normal Stochastic Volatility Models by : Chak Kei Jack Wong
Download or read book New Methods for Performing Efficient Inference for Linear and Log-normal Stochastic Volatility Models written by Chak Kei Jack Wong and published by . This book was released on 1999 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Volatility by : Neil Shephard
Download or read book Stochastic Volatility written by Neil Shephard and published by Oxford University Press, USA. This book was released on 2005 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This work brings together some of the main papers that have influenced this field, andshows that the development of this subject has been highly multidisciplinary.
Book Synopsis Parameter Estimation in Stochastic Volatility Models by : Jaya P. N. Bishwal
Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Long-memory Stochastic Volatility Models by : Libo Xie
Download or read book Long-memory Stochastic Volatility Models written by Libo Xie and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Estimation and Inference with the Efficient Method of Moment by : Pieter Jelle van der Sluis
Download or read book Estimation and Inference with the Efficient Method of Moment written by Pieter Jelle van der Sluis and published by . This book was released on 1999 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Lognormal Type Stochastic Volatility Model With Quadratic Drift by : Peter Carr
Download or read book A Lognormal Type Stochastic Volatility Model With Quadratic Drift written by Peter Carr and published by . This book was released on 2019 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant level, with a speed of mean reversion that is affine in the instantaneous volatility level. The steady-state distribution of the instantaneous volatility belongs to the class of Generalized Inverse Gaussian distributions. We show that the quadratic term in the drift is crucial to avoid moment explosions and to preserve the martingale property of the stock price process. Using a conveniently chosen change of measure, we relate the model to the class of polynomial diffusions. This remarkable relation allows us to develop a highly accurate option price approximation technique based on orthogonal polynomial expansions.
Author :D. Alistair Steyn-Ross Publisher :Springer Science & Business Media ISBN 13 :1441907963 Total Pages :325 pages Book Rating :4.4/5 (419 download)
Book Synopsis Modeling Phase Transitions in the Brain by : D. Alistair Steyn-Ross
Download or read book Modeling Phase Transitions in the Brain written by D. Alistair Steyn-Ross and published by Springer Science & Business Media. This book was released on 2010-03-14 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foreword by Walter J. Freeman. The induction of unconsciousness using anesthetic agents demonstrates that the cerebral cortex can operate in two very different behavioral modes: alert and responsive vs. unaware and quiescent. But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts. Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle. The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states. Modeling Phase Transitions in the Brain contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band Hopf oscillations, gap-junction-moderated Turing structures, and Hopf-Turing interactions leading to cortical waves.
Book Synopsis Log-Normal Stochastic Volatility Model by : Artur Sepp
Download or read book Log-Normal Stochastic Volatility Model written by Artur Sepp and published by . This book was released on 2016 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: While empirical studies have established that the log-normal stochastic volatility (SV) model is superior to its alternatives, the model does not allow for the analytical solutions available for affine models. To circumvent this, we show that the joint moment generating function (MGF) of the log-price and the quadratic variance (QV) under the log-normal SV model can be decomposed into a leading term, which is given by an exponential-affine form, and a residual term, whose estimate depends on the higher order moments of the volatility process. We prove that the second-order leading term is theoretically consistent with the expected values and covariance matrix of the log-price and the quadratic variance. We further extend this approach to the log-normal SV model with jumps. We use Fourier inversion techniques to value vanilla options on the equity and the QV and, by comparison to Monte Carlo simulations, we show that the second-order leading term is precise for the valuation of vanilla options. We generalize the affine decomposition to other non-affine stochastic volatility models with polynomial drift and volatility functions, and with jumps in the volatility process.
Book Synopsis Computationally Efficient Multi-asset Stochastic Volatility Modeling by : Yizhou Fang
Download or read book Computationally Efficient Multi-asset Stochastic Volatility Modeling written by Yizhou Fang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility (SV) models are popular in financial modeling, because they capture the inherent uncertainty of the asset volatility. Since assets are observed to co-move together, multi-asset SV (mSV) models are more appealing than combining single-asset SV models in portfolio analysis and risk management. However, the latent volatility process renders the observed data likelihood intractable. Therefore, parameter inference typically requires computationally intensive methods to integrate the latent volatilities out, so that it is computationally challenging to estimate the model parameters. This three-part thesis is concerned with mSV modeling that is both conceptually and computationally scalable to large financial portfolios. In Part I, we explore the potential of substituting the latent volatility by an observable market proxy. For more than 20 years of out-of-sample predictions, we find that modeling the Standard and Poor's 500 (SPX) index by a simple framework of Seemingly Unrelated Regressions (SUR) with VIX volatility proxy is comparable to the benchmark Heston model with latent volatility, at a fraction of the computational cost. In Part II, we propose a new mSV model structured around a common volatility factor, which also can be proxied by an observable process. Unlike existing mSV models, the number of parameters in ours scales linearly instead of quadratically in the number of assets -- a desirable property for parameter inference of high-dimensional portfolios. Empirical evidence suggests that the common-factor volatility structure has considerable benefits for option pricing compared to a richer class of unconstrained models. In Part III, we propose an approximate method of parameter inference for mSV models based on the Kalman filter. A large-scale simulation study indicates that the approximation is orders of magnitude faster than exact inference methods, while retaining comparable accuracy.
Book Synopsis Bayesian Analysis of a Stochastic Volatility Model with Leverage Effect and Fat Tails by : Eric Jacquier
Download or read book Bayesian Analysis of a Stochastic Volatility Model with Leverage Effect and Fat Tails written by Eric Jacquier and published by . This book was released on 2001 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic univariate stochastic volatility model specifies that conditional volatility follows a log-normal auto-regressive model with innovations assumed to be independent of the innovations in the conditional mean equation. Since the introduction of practical methods for inference in the basic volatility model (JPR-(1994)), it has been observed that the basic model is too restrictive for many financial series. We extend the basic SVOL to allow for a so-called quot;Leverage effectquot; via correlation between the volatility and mean innovations, and for fat-tails in the mean equation innovation. A Bayesian Markov Chain Monte Carlo algorithm is developed for the extended volatility model. Thus far, likelihood-based inference for the correlated SVOL model has not appeared in the literature. We develop Bayes Factors to assess the importance of the leverage and fat-tail extensions. Sampling experiments reveal little loss in precision from adding the model extensions but a large loss from using the basic model in the presence of mis-specification. For both equity and exchange rate data, there is overwhelming evidence in favor of models with fat-tailed volatility innovations, and for a leverage effect in the case of equity indices. We also find that volatility estimates from the extended model are markedly different from those produced by the basic SVOL.
Book Synopsis Robust Inference with Quantile Regression in Stochastic Volatility Models with Application to Value at Risk Calculation by :
Download or read book Robust Inference with Quantile Regression in Stochastic Volatility Models with Application to Value at Risk Calculation written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Volatility (SV) models play an integral role in modeling time varying volatility, with widespread application in finance. Due to the absence of a closed form likelihood function, estimation is a challenging problem. In the presence of outliers, and the high kurtosis prevalent in financial data, robust estimation techniques are desirable. Also, in the context of risk assessment when the underlying model is SV, computing the one step ahead predictive return densities for Value at Risk (VaR) calculation entails a numerically indirect procedure. The Quantile Regression (QR) estimation is an increasingly important tool for analysis, which helps in fitting parsimonious models in lieu of full conditional distributions. We propose two methods (i) Regression Quantile Method of Moments (RQMM) and (ii) Regression Quantile - Kalman Filtering method (RQ-KF) based on the QR approach that can be used to obtain robust SV model parameter estimates as well as VaR estimates. The RQMM is a simulation based indirect inference procedure where auxiliary recursive quantile models are used, with gradients of the RQ objective function providing the moment conditions. This was motivated by the Efficient Method of Moments (EMM) approach used in SV model estimation and the Conditional Autoregressive Value at Risk (CAViaR) method. An optimal linear quantile model based on the underlying SV assumption is derived. This is used along with other CAViaR specifications for the auxiliary models. The RQ-KF is a computationally simplified procedure combining the QML and QR methodologies. Based on a recursive model under the SV framework, quantile estimates are produced by the Kalman filtering scheme and are further refined using the RQ objective function, yielding robust estimates. For illustration purposes, comparison of the RQMM method with EMM under different data scenarios show that RQMM is stable under model misspecification, presence of outliers and heavy-tailedness. Comparison of the RQ.
Book Synopsis Inference in Stochastic Volatility Models for Gaussian and T Data by : Nan Zheng
Download or read book Inference in Stochastic Volatility Models for Gaussian and T Data written by Nan Zheng and published by . This book was released on 2013 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Volatility by : Sangjoon Kim
Download or read book Stochastic Volatility written by Sangjoon Kim and published by . This book was released on 1997 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Inferences in Volatility Models by : Vickneswary Tagore
Download or read book Inferences in Volatility Models written by Vickneswary Tagore and published by . This book was released on 2010 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Volatility Models and Simulated Maximum Likelihood Estimation by : Ji Eun Choi
Download or read book Stochastic Volatility Models and Simulated Maximum Likelihood Estimation written by Ji Eun Choi and published by . This book was released on 2011 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial time series studies indicate that the lognormal assumption for the return of an underlying security is often violated in practice. This is due to the presence of time-varying volatility in the return series. The most common departures are due to a fat left-tail of the return distribution, volatility clustering or persistence, and asymmetry of the volatility. To account for these characteristics of time-varying volatility, many volatility models have been proposed and studied in the financial time series literature. Two main conditional-variance model specifications are the autoregressive conditional heteroscedasticity (ARCH) and the stochastic volatility (SV) models. The SV model, proposed by Taylor (1986), is a useful alternative to the ARCH family (Engle (1982)). It incorporates time-dependency of the volatility through a latent process, which is an autoregressive model of order 1 (AR(1)), and successfully accounts for the stylized facts of the return series implied by the characteristics of time-varying volatility. In this thesis, we review both ARCH and SV models but focus on the SV model and its variations. We consider two modified SV models. One is an autoregressive process with stochastic volatility errors (AR--SV) and the other is the Markov regime switching stochastic volatility (MSSV) model. The AR--SV model consists of two AR processes. The conditional mean process is an AR(p) model, and the conditional variance process is an AR(1) model. One notable advantage of the AR--SV model is that it better captures volatility persistence by considering the AR structure in the conditional mean process. The MSSV model consists of the SV model and a discrete Markov process. In this model, the volatility can switch from a low level to a high level at random points in time, and this feature better captures the volatility movement. We study the moment properties and the likelihood functions associated with these models. In spite of the simple structure of the SV models, it is not easy to estimate parameters by conventional estimation methods such as maximum likelihood estimation (MLE) or the Bayesian method because of the presence of the latent log-variance process. Of the various estimation methods proposed in the SV model literature, we consider the simulated maximum likelihood (SML) method with the efficient importance sampling (EIS) technique, one of the most efficient estimation methods for SV models. In particular, the EIS technique is applied in the SML to reduce the MC sampling error.
Book Synopsis Effective Methods for Generalized Stochastic Volatility Models by : Mike Oliver Felpel
Download or read book Effective Methods for Generalized Stochastic Volatility Models written by Mike Oliver Felpel and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Inference for Stochastic Volatility Models by : Md. Nazmul Ahsan
Download or read book Statistical Inference for Stochastic Volatility Models written by Md. Nazmul Ahsan and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Although stochastic volatility (SV) models have many appealing features, estimation and inference on SV models are challenging problems due to the inherent difficulty of evaluating the likelihood function. The existing methods are either computationally costly and/or inefficient. This thesis studies and contributes to the SV literature from the estimation, inference, and volatility forecasting viewpoints. It consists of three essays, which include both theoretical and empirical contributions. On the whole, the thesis develops easily applicable statistical methods for stochastic volatility models.The first essay proposes computationally simple moment-based estimators for the first-order SV model. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that the proposed estimators match (or exceed) alternative estimators in terms of precision – including Bayesian estimators proposed in this context, which have the best performance among alternative estimators. Using this simple estimator, we study three crucial test problems (no persistence, no latent specification of volatility, and no stochastic volatility hypothesis), and evaluate these null hypotheses in three ways: asymptotic critical values, a parametric bootstrap procedure, and a maximized Monte Carlo procedure. The proposed methods are applied to daily observations on the returns for three major stock prices [Coca-Cola, Walmart, Ford], and the Standard and Poor’s Composite Price Index. The results show the presence of stochastic volatility with strong persistence.The second essay studies the problem of estimating higher-order stochastic volatility [SV(p)] models. The estimation of SV(p) models is even more challenging and rarely considered in the literature. We propose several estimators for higher-order stochastic volatility models. Among these, the simple winsorized ARMA-based estimator is uniformly superior in terms of bias and RMSE to other estimators, including the Bayesian MCMC estimator. The proposed estimators are applied to stock return data, and the usefulness of the proposed estimators is assessed in two ways. First, using daily returns on the S&P 500 index from 1928 to 2016, we find that higher-order SV models – in particular an SV(3) model – are preferable to an SV(1), from the viewpoints of model fit and both asymptotic and finite-sample tests. Second, using different volatility proxies (squared return and realized volatility), we find that higher-order SV models are preferable for out-of-sample volatility forecasting, whether a high volatility period (such as financial crisis) is included in the estimation sample or the forecasted sample. Our results highlight the usefulness of higher-order SV models for volatility forecasting.In the final essay, we introduce a novel class of generalized stochastic volatility (GSV) models which utilize high-frequency (HF) information (realized volatility (RV) measures). GSV models can accommodate nonstationary volatility process, various distributional assumptions, and exogenous regressors in the latent volatility equation. Instrumental variable methods are employed to provide a unified framework for the analysis (estimation and inference) of GSV models. We consider the parameter inference problem in GSV models with nonstationary volatility and develop identification-robust methods for joint hypotheses involving the volatility persistence parameter and the autocorrelation parameter of the composite error (or the noise ratio). For distributional theory, three different sets of assumptions are considered. In simulations, the proposed tests outperform the usual asymptotic test regarding size and exhibit excellent power. We apply our inference methods to IBM price and option data andidentify several empirical relationships"--
