scholarly journals A New Class of Discrete-Time Stochastic Volatility Model with Correlated Errors

2017 ◽  
Author(s):  
Sujay Mukhoti ◽  
Pritam Ranjan
Keyword(s):  
Stochastic Volatility ◽  
Discrete Time ◽  
Stochastic Volatility Model ◽  
Correlated Errors ◽  
New Class ◽  
Volatility Model

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.

STOCHASTIC VOLATILITY MODEL WITH CORRELATED JUMP SIZES AND INDEPENDENT ARRIVALS

2020 ◽  
pp. 1-19
Author(s):  
Pengzhan Chen ◽  
Wuyi Ye
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stochastic Volatility Models ◽  
Period Analysis ◽  
New Class ◽  
Volatility Models ◽  
Volatility Model ◽  
Article Study ◽  
Jump Sizes

In light of recent empirical research on jump activity, this article study the calibration of a new class of stochastic volatility models that include both jumps in return and volatility. Specifically, we consider correlated jump sizes and both contemporaneous and independent arrival of jumps in return and volatility. Based on the specifications of this model, we derive a closed-form relationship between the VIX index and latent volatility. Also, we propose a closed-form logarithmic likelihood formula by using the link to the VIX index. By estimating alternative models, we find that the general counting processes setting lead to better capturing of return jump behaviors. That is, the part where the return and volatility jump simultaneously and the part that jump independently can both be captured. In addition, the size of the jumps in volatility is, on average, positive for both contemporaneous and independent arrivals. However, contemporaneous jumps in the return are negative, but independent return jumps are positive. The sub-period analysis further supports above insight, and we find that the jumps in return and volatility increased significantly during the two recent economic crises.

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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