Jump test and Estimate the Size and Probability of Jump in the Stock Market Using Stochastic Volatility Models

Document Type : Original Article

Authors

1 Phd Student of Finance ,Faculty of Administrative Science and Economics, University Isfahan

2 Postdoctoral Researcher, Iran national science found

Abstract

New findings show that volatility models with jump component are more successful than without jumping models in modeling stylized facts about the stock market. This study focuses on the role of jump in the return of the total index of Tehran Stock Exchange from the beginning of the trading day 1396 to the last trading day 1399. The empirical approach used for this purpose is different from the usual procedure for estimating parameters and performing diagnostic tests. In this approach, jump times, jump size and volatility are estimated. These estimates provide a dynamic picture of the role of these factors and are useful for analyzing periods of market pressure. The results of the jump existence test using Bayesian factor show the superiority of the stochastic volatility model with jump component and leverage effect (SVLJ) over other models. The results of estimating the SVLJ model show that only two jumps in the total index yield occurred with a probability between 0.015 and 0.02 in the time interval between the data of this study and six jumps with a probability greater than 0.01 occurred in the return. However, the jump component accounts for up to 15.75% of the efficiency changes, which, if not included in the modeling, will lead to inaccurate results in volatility and risk measurements. This is important because it is important to determine the share of jumps in periods of market stress, as the risk of a jump in returns usually cannot be covered, and investors may need to risk premium to bear these risks.

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