BAYESIAN UNIT-ROOT TESTING IN STOCHASTIC VOLATILITY MODELS WITH CORRELATED ERRORS

Date

2013-12-01

Author

Kalaylıoğlu Akyıldız, Zeynep Işıl
Ghosh, Sujit K.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

205
views

0
downloads

A series of returns are often modeled using stochastic volatility models. Many observed financial series exhibit unit-root non-stationary behavior in the latent AR(1) volatility process and tests for a unit-root become necessary, especially when the error process of the returns is correlated with the error terms of the AR(1) process. In this paper, we develop a class of priors that assigns positive prior probability on the non-stationary region, employ credible interval for the test, and show that Markov Chain Monte Carlo methods can be implemented using standard software. Several practical scenarios and real examples are explored to investigate the performance of our method.

Subject Keywords

Financial data, WinBUGS, Unit-root test, Gibbs sampling, Markov chain Monte Carlo, Contemporaneous financial correlation

URI

https://hdl.handle.net/11511/54469

Journal

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

Analysis of stochastic and non-stochastic volatility models. Özkan, Pelin; Ayhan, Hüseyin Öztaş; Department of Statistics (2004) Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order...
Computation of Malliavin Greeks in Hybrid StochasticVolatility Models Yılmaz, Bilgi; Yolcu Okur, Yeliz (2015-05-16) Contrary to Black-Scholes model in stochastic volatility models, the stock price’s volatility assumed to be a stochastic process and the Brownian motions of volatility and stock price process are correlated with each other. Moreover, in some models, called hybrid stochastic volatility models, the interest rate also assumed to be a stochastic process. Because of the stochastic volatility, stochastic interest rate and correlated Brownian motions, a closed form solution for the Greeks of the options usually do...
Application of stochastic volatility models with jumps to BIST options Rahiminejat, Monireh; Sezer, Ali Devin; Department of Financial Mathematics (2017) This thesis gives a derivation of call and put option pricing formulas under stochastic volatility models with jumps; the precise model is a combination of Merton and Heston models. The derivation is based on the computation of the characteristic function of the underlying process. We use the derived formulas to fit the model to options written on two stocks in the BIST30 index covering the first two months of 2017. The fit is done by minimizing a weighted $L_2$ distance between the observed prices and the ...
Nonlinear and dynamic programming models for an inventory problem in a partially observable environment Darendeliler, Alp; Serin, Yaşar Yasemin; Department of Industrial Engineering (2016) In this study, a single-item periodic-review inventory system is considered in a partially observable environment with finite capacity, random yield and Markov modulated demand and supply processes for finite-horizon. The exact state of the real process, which determines the distribution of the demand and supply, is unobservable so the decisions must be made according to the limited observations called observed process. Partially Observable Markov Decision Process is used to model this problem. As an altern...
Maximum likelihood estimation of transition probabilities of jump Markov linear systems Orguner, Umut (Institute of Electrical and Electronics Engineers (IEEE), 2008-10-01) This paper describes an online maximum likelihood estimator for the transition probabilities associated with a jump Markov linear system (JMLS). The maximum likelihood estimator is derived using the reference probability method, which exploits an hypothetical probability measure to find recursions for complex expectations. Expectation maximization (EM) procedure is utilized for maximizing the likelihood function. In order to avoid the exponential increase in the number of statistics of the optimal EM algori...

Citation Formats

Z. I. Kalaylıoğlu Akyıldız and S. K. Ghosh, “BAYESIAN UNIT-ROOT TESTING IN STOCHASTIC VOLATILITY MODELS WITH CORRELATED ERRORS,” HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, pp. 659–669, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54469.