scholarly journals SENSITIVITY ANALYSIS AND DENSITY ESTIMATION FOR THE HOBSON-ROGERS STOCHASTIC VOLATILITY MODEL

2009 ◽  
Vol 12 (03) ◽  
pp. 283-295 ◽  
Author(s):  
REIICHIRO KAWAI
Keyword(s):  
Stochastic Volatility ◽  
Heavy Tails ◽  
Stochastic Volatility Model ◽  
Price Dynamics ◽  
Marginal Density ◽  
The Past ◽  
Sensitivity Indices ◽  
Volatility Model ◽  
Backward Equation ◽  
Volatility Function

Monte Carlo estimators of sensitivity indices and the marginal density of the price dynamics are derived for the Hobson-Rogers stochastic volatility model. Our approach is based mainly upon the Kolmogorov backward equation by making full use of the Markovian property of the dynamics given the past information. Some numerical examples are presented with a GARCH-like volatility function and its extension to illustrate the effectiveness of our formulae together with a clear exhibition of the skewness and the heavy tails of the price dynamics.

scholarly journals Mean-correction and Higher Order Moments for a Stochastic Volatility Model with Correlated Errors

2016 ◽  
Vol 5 (4) ◽  
pp. 102 ◽  
Author(s):  
Sujay Mukhoti ◽  
Pritam Ranjan
Keyword(s):  
Stock Market ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Correlated Errors ◽  
The Past ◽  
Volatility Models ◽  
Volatility Model ◽  
Zero Correlation ◽  
Desirable Feature ◽  
Analytical Expressions

In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by  stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated, which is unrealistic. It turns out that if a non-zero correlation is included in the SVM (e.g., \cite{Shephard05}), then the expected log-return at time $t$ conditional on the past returns is non-zero, which is not a desirable feature of an efficient stock market. In this paper, we propose a mean-correction for such an SVM for discrete-time returns with non-zero correlation. We also find closed form analytical expressions for higher moments of log-return and its lead-lag correlations with the volatility process. We compare the performance of the proposed and classical SVMs on S\&P 500 index returns obtained from NYSE.

Particle Gibbs with ancestor sampling for stochastic volatility models with: heavy tails, in mean effects, leverage, serial dependence and structural breaks

2015 ◽  
Vol 19 (5) ◽  
Author(s):  
Nima Nonejad
Keyword(s):  
Stochastic Volatility ◽  
Structural Breaks ◽  
Sequential Monte Carlo ◽  
Heavy Tails ◽  
Moving Average ◽  
Stochastic Volatility Model ◽  
Stochastic Volatility Models ◽  
Model Framework ◽  
Volatility Models ◽  
Volatility Model

AbstractParticle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of stochastic volatility models with increasing complexity, including leverage and in mean effects. We provide applications that demonstrate the flexibility of PG-AS under these different circumstances and justify applying it in practice. We also combine discrete structural breaks within the stochastic volatility model framework. For instance, we model changing time series characteristics of monthly postwar US core inflation rate using a structural break autoregressive fractionally integrated moving average (ARFIMA) model with stochastic volatility. We allow for structural breaks in the level, long and short-memory parameters with simultaneous breaks in the level, persistence and the conditional volatility of the volatility of inflation.

scholarly journals A CORRELATED STOCHASTIC VOLATILITY MODEL MEASURING LEVERAGE AND OTHER STYLIZED FACTS

2002 ◽  
Vol 05 (05) ◽  
pp. 541-562 ◽  
Author(s):  
JAUME MASOLIVER ◽  
JOSEP PERELLÓ
Keyword(s):  
Stochastic Volatility ◽  
Heavy Tails ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
Leverage Effect ◽  
Stylized Facts ◽  
Uhlenbeck Process ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Negative Skewness

We analyze a stochastic volatility market model in which volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. In the framework of this model we exactly calculate the leverage effect and other stylized facts, such as mean reversion, leptokurtosis and negative skewness. We also obtain a close analytical expression for the characteristic function and study the heavy tails of the probability distribution.

scholarly journals Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects

2021 ◽  
Vol 14 (5) ◽  
pp. 225
Author(s):  
Zhongxian Men ◽  
Tony S. Wirjanto ◽  
Adam W. Kolkiewicz
Keyword(s):  
Stochastic Volatility ◽  
Heavy Tails ◽  
Foreign Currency ◽  
Asset Returns ◽  
Stochastic Volatility Model ◽  
Stochastic Volatility Models ◽  
Asymmetric Effects ◽  
Volatility Models ◽  
Volatility Model ◽  
T Distribution

This paper studies multiscale stochastic volatility models of financial asset returns. It specifies two components in the log-volatility process and allows for leverage/asymmetric effects from both components while return innovation terms follow a heavy/fat tailed Student t distribution. The two components are shown to be important in capturing persistent dependence in return volatility, which is often absent in applications of stochastic volatility models which incorporate leverage/asymmetric effects. The models are applied to asset returns from a foreign currency market and an equity market. The model fits are assessed, and the proposed models are shown to compare favorably to the one-component asymmetric stochastic volatility models with Gaussian and Student t distributed innovation terms.

A non-Gaussian stochastic volatility model

1998 ◽  
Vol 2 (2) ◽  
pp. 33-47 ◽  
Author(s):  
Yuichi Nagahara ◽  
Genshiro Kitagawa
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Non Gaussian
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