bayesian methods

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.

Due to the strategic role of volatility and instability of crude oil prices and its effects on all countries of the world, different methods of modeling and forecasting are necessary. Over the past two decades, extensive literature has emerged on various approaches to empirically modeling volatility in the crude oil market. In this research, WTI crude oil price volatility modeling, which is one of the most important types of crude oil in the market of this strategic commodity, is examined with six flexible stochastic volatility (SV) models. Then the experimental performance of these models is compared with each other using Bayesian methods. The findings of this study show that adding jump in efficiency and leverage effect to the stochastic volatility (SVLJ) model greatly improves its performance compared to other models. According to the findings of this model, the stability of volatility in the WTI market is very high and on average one jump occurs in this market every year. However, this model shows that in 2020, two jumps in WTI returns occurred in April and May, which is a unique event. In addition, the correlation between the return jump component and the volatility jump (Merton correlation jump) is not confirmed in the WTI data. Also, due to the negative leverage effect, negative shocks have stronger volatility effects than positive shocks in the crude oil market.

Forecasting is an essential and growing component of financial theories and applications. Forecasts are expressed in three ways: point, interval, and probability distribution. The largest amount of information a forecast can provide is in the form of a probability distribution. For example, in addition to the mean and conditional variance of other torques including kurtosis and skewness, the probability distribution can also be calculated. This form of forecasting is very important in the financial economy, which is a fundamental risk assessment and uncertainty. Because the sum of all possible events is estimated and the future events may not be missed. Therefore, estimating uncertainty in this case is much more accurate than other forms of forecasting. In the present study, based on the Geometric Brownian Model (GBM), the probability of future stock price index values of Tehran Stock Exchange is calculated. Bayesian parametric approach and MCMC sampling algorithm are used for this purpose. The results show the growth rate of the stock price index at an average rate of 4% in the year 1398 (forecast year) and the probability of limiting events such as the index falling to below the 1397 average is very low (about 7%). The results also show that the probability of falling stock price index in the forecast year is lower than the minimum of the previous year is only 0.0017. Therefore, investing in the stock market is very safe. This information is only available in the manner of predicting the probability of future stock price indexes.