Estimation for Mean-reverting Stochastic Volatility Models with a Leverage Effect
Author : Agnès Grimaud
Publisher :
Page : 16 pages
File Size : 25,65 MB
Release : 2006
Category :
ISBN :
A Threshold Model for Local Volatility
Author : Antoine Lejay
Publisher :
Page : 28 pages
File Size : 26,77 MB
Release : 2019
Category :
ISBN :
Book Description
In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect.We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Tests are performed on the daily prices of 21 assets. They show empirical evidence for leverage and mean-reversion effects, consistent with the results in the literature.
Stochastic Volatility and Realized Stochastic Volatility Models
Author : Makoto Takahashi
Publisher : Springer Nature
Page : 120 pages
File Size : 31,38 MB
Release : 2023-04-18
Category : Business & Economics
ISBN : 981990935X
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.
A Mean-Reverting Stochastic Volatility Option-Pricing Model with an Analytic Solution
Author : Henrik Andersson
Publisher :
Page : 45 pages
File Size : 45,36 MB
Release : 2002
Category :
ISBN :
Book Description
In this paper we derive a closed form approximation to a stochastic volatility option-pricing model and propose a variant of EGARCH for parameter estimation. The model thereby provides a consistent approach to the problem of option pricing and parameter estimation. Using Swedish stocks, the model provides a good fit to the heteroscedasticity prevalent in the time-series. The stochastic volatility model also prices options on the underlying stock more accurately than the traditional Black-Scholes formula. This result holds for both historic and implied volatility. A large part of the volatility smile that is observed for options of different maturity and exercise prices is thereby explained.
Stochastic Volatility and Time Deformation
Author : Joann Jasiak
Publisher :
Page : pages
File Size : 37,15 MB
Release : 2012
Category :
ISBN :
Book Description
In this paper, we study stochastic volatility models with time deformation. Such processes relate to the early work by Mandelbrot and Taylor (1967), Clark (1973), Tauchen and Pitts (1983), among others. In our setup, the latent process of stochastic volatility evolves in an operational time which differs from calendar time. The time deformation can be determined by past volume of trade, past returns, possibly with an asymmetric leverage effect, and other variables setting the pace of information arrival. The econometric specification exploits the state-space approach for stochastic volatility models proposed by Harvey, Ruiz and Shephard (1994) as well as the matching moment estimation procedure using SNP densities of stock returns and trading volume estimated by Gallant, Rossi and Tauchen (1992). Daily data on returns and trading volume of the NYSE are used in the empirical application. Supporting evidence for a time deformation representation is found and its impact on the behavior of returns and volume is analyzed. We find that increases in volume accelerate operational time, resulting in volatility being less persistent and subject to shocks with a higher innovation variance. Downward price movements have similar effects while upward price movements increase the persistence in volatility and decrease the dispersion of shocks by slowing down market time. We present the basic model as well as several extensions; in particular, we formulate and estimate a bivariate return-volume stochastic volatility model with time deformation. The latter is examined through bivariate impulse response profiles following the example of Gallant, Rossi and Tauchen (1993).
Stochastic volatility and the pricing of financial derivatives
Author : Antoine Petrus Cornelius van der Ploeg
Publisher : Rozenberg Publishers
Page : 358 pages
File Size : 10,64 MB
Release : 2006
Category :
ISBN : 9051705778
Book Description
Multiple Time Scales in Volatility and Leverage Correlations
Author : Josep Perelló
Publisher :
Page : 19 pages
File Size : 31,12 MB
Release : 2013
Category :
ISBN :
Book Description
Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or 'leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.
The Estimation of Leverage Effect with High Frequency Data
Author : Dan Christina Wang
Publisher :
Page : 101 pages
File Size : 30,11 MB
Release : 2012
Category :
ISBN : 9781267602435
Book Description
The leverage effect has become an extensively studied phenomenon that describes the (usually) negative correlation between stock returns and volatility. All the previous studies have focused on the origin and properties of the leverage effect. Even though most studies of the leverage effect are based on cross-sectional calibration with parametric models, few of them have carefully studied its estimation. However, estimation of the leverage effect is important because sensible inference is possible only when the leverage effect is estimated reliably. In this thesis, we provide the first nonparametric estimation for a class of stochastic measures of the leverage effect. Unlike most previous work conducted over daily or longer return horizons, we study the estimation of the leverage effect with high frequency data. In order to construct estimators with good statistical properties, we introduce a new stochastic leverage effect parameter, which is usually not specified by other studies. The estimators and their statistical properties are provided in cases both with and without microstructure noise, under the stochastic volatility model. In asymptotics, the consistency and limiting distribution of the estimators are derived and corroborated by simulation results. For consistency, a previously unknown bias correction factor is added to the estimators. In finite samples, we provide two modifications of the estimator to improve its performance. In addition, we explore several applications of the estimators. In one application, we apply the estimators in high frequency regression and discover a novel predictor of volatility that depends on an estimator of the leverage effect. A related study reveals that the leverage effect improves estimation of volatility. In another application, we discover the first theoretical connection between skewness and the leverage effect, which yields a new predictor of skewness.
Range-based Estimation of Stochastic Volatility Models Or Exchange Rate Dynamics are More Interesting Than You Think
Author : Sassan Alizadeh
Publisher :
Page : 28 pages
File Size : 30,59 MB
Release : 2000
Category :
ISBN :
Book Description
Bayesian Analysis of a Stochastic Volatility Model with Leverage Effect and Fat Tails
Author : Eric Jacquier
Publisher :
Page : 31 pages
File Size : 13,23 MB
Release : 2001
Category :
ISBN :
Book Description
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.
