1. INTRODUCTION:

Investors, analysts, and policymakers alike have had the spotlight of volatility for too long. Due to its ramifications toward risk management, portfolio allocation, and ultimately financial decisions, it has been a very important factor. Banking in India is central to economic growth and financial inclusion in emerging economies ²⁶.

On the other hand, it is one of the most volatile sectors in the economy because of its close association with macroeconomic fundamentals²³, policy reforms, and structural changes like mergers and acquisitions. The effect of stock price volatility before and after such transformational events becomes important for understanding not only academic concepts but also practical investment strategies.

This research examines the volatility dynamics of banking stock prices in India using the Bank Nifty Index, which comprises 12 most liquid and capitalized banking stocks representing public and private sector institutions. The primary objective of this research study is to compare the volatility patterns during the pre-and post-merger periods and predict future volatility with the help of advanced econometric models²⁴. This dual analysis covers two primary time frames, April 2016 to March 2020 (pre-merger) and April 2020 to March 2024 (post-merger), thereby delineating a broader view of mergers influencing market dynamics and investor sentiment.

The essence of volatility over time is captured by the economic theory of the GARCH model, which has become among the most renowned techniques²⁵ for modelling and forecasting financial time series with time-varying volatility⁴. The classical GARCH model, introduced by⁶, adds to the ARCH model the predictors of past forecast errors and variances for long-term modelling of volatilities⁵. Typical GARCH assumptions assume symmetric responses to market shocks; often, this fails to hold in reality, where negative news tends to affect volatility more than positive news.

In light of this limitation, the study goes on to incorporate the GJR-GARCH model (Glosten, Jagannathan, and Runkle, 1993), which has an asymmetric component added to capture the leverage effect. In markets such as India, where investor reactions to negative events tend to be larger than their reactions to positive events, applying the GJR-GARCH model becomes especially relevant. The combination of symmetric and asymmetric model approaches helps this study analyze the differentiating behavior of volatility and discern a suitable model to forecast its future trends.

Through a variety of well-constructed approaches to the statistical testing of volatility dynamics in the Indian banking sector, including tests for stationarity (ADF), checking for speculative bubbles through testing of ARCH effect diagnostic checks, and estimation exercises - the study stands to provide an even better understanding of the behavior of volatility. Results are likely to provide valuable insights to investors, risk managers, and regulators, enabling them to devise better financial strategies in address to market uncertainties.

The research aims at attaining certain set out objectives which are:

· Analyze daily performance of Bank Nifty through econometrics modelling from daily closing price of index.

· Forecast the future fluctuation in stock market prices for a certain time period.

The entire paper is partitioned such that it has an Introduction in section 1; section 2 has the literature review; next is section 3, which encompasses the research methodology. Data interpretation and analysis are included in section 4, while section 5 contains the results and discussion. Section 6 states the conclusion and future implications of the work.

2. LITERATURE REVIEW:

Estimation and forecasting in volatility of financial markets have typically figured in econometric and financial research over decades. The introduction of the Autoregressive Conditional Heteroskedasticity (ARCH) model by⁸and the subsequent Generalized ARCH (GARCH) model by Bollerslev (1986) aided in developing plethora of studies scrutinizing the capacity to incorporate time-varying volatility. Whereas, the introduction of GJR-GARCH modelling by Glosten, Jagannathan and Runkle⁹extended the ability to model volatility by allowing asymmetries in financial time series^11,27. The most recent GARCH and GJR-GARCH application studies have been concerned with other financial markets. A study researched symmetric and asymmetric GARCH estimations in the G7 stock markets and proved that GJR-GARCH significantly outperforms other asymmetric models³. Very similarly, a study applied GJR-GARCH under Normal Inverse Gaussian to predict volatility in a number of top cryptocurrencies and so obtained good results in risk assessments¹³. A study employed range-based GARCH models to predict intraday volatility in the Indian stock market and concluded that asymmetric models such as GJR-GARCH fitted better than conventional GARCH models^10,18,29. On the other hand, a study also performed a GARCH analysis regarding the impact of COVID-19 on Indian stock indices, showing higher volatility during the crisis^17,31.

In recent years, the integration of machine learning techniques with GARCH models has been hotly pursued.¹¹ presented their hybrid approach by combining GARCH models with Gated Recurrent Unit (GRU) neural networks to predict financial volatility and found better accuracy in their predictions. Similarly, a study proposed an integration of some GARCH models and GRU models, embedding the essential GARCH formulations as an extra layer of information into the GRU architecture to enhance forecasting skill even further¹⁹. A study under the establishment of equivalences between GARCH models and neural networks, developed a GARCH-LSTM model illuminating the effective capture of volatility dynamics²². Besides,¹⁵ found hybrid models that offered superior performance while comparing Least Square Support Vector Machine (LSSVM) methods with classical GARCH models on forecasting volatility in ASEAN stock markets²⁰. GARCH and GJR-GARCH have gained application in different sectors and asset classes¹². For example,²¹ focused on GARCH models based on structural change to estimate the volatility in crude oil prices; the authors recommended smooth transition and regime-switching models that forecast better. From the threshold application of the GARCH models, a study found out that Bitcoin, Ethereum, Ripple, and Litecoin observed very important asymmetries in volatility dynamics⁷.

In the Ghanaian backdrop,¹⁴ used GARCH approaches for modelling stock market volatility and found that GARCH (1,1) models captured the volatility pattern of the Ghana Stock Exchange rather well. Likewise, a study imposed a hybrid model for stock market volatility and showed that the performance of forecasts was even improved by combining the GARCH models with Bayesian approaches ². Comparative assessments among the GARCH-type models have been performed in order to evaluate their forecasting performance. According to a study, classical GARCH and its extended versions, including EGARCH, GJR-GARCH, and APARCH, were scrutinized, and the conclusion was that the performance of the Bayesian Stochastic GARCH (BSGARCH) model had always surpassed the other conventional methods in volatility forecasting for NASDAQ100 and S&P 500 indices². Likewise, according to²¹, flexible Fourier form GARCH models outperform traditional GARCH types in forecasting crude oil price volatility. In light of the COVID-19 pandemic,¹⁶ deployed GARCH models to scrutinize fluctuations across Indian stock indices and revealed that, on the whole, that fluctuation increased by a significant amount during the period of the pandemic. Their work has significant implications for the case of including structural breaks and regime changes in the modelling of volatility. The literature shows a strong use of the GARCH and GJR-GARCH model types in modelling volatility in financial markets, across asset classes and regions. The integration of machine learning techniques as well as the creation of hybrid models has taken the scale of predictive power of these models even further. As financial markets continue to change, it will therefore be very crucial for GARCH-type models to be flexible and robust in their application to capturing the increasingly complex nature of market volatility¹.

3. MATERIAL AND METHODS:

Stock markets fluctuations, particularly in sector indices like Bank Nifty, create a lot of price turbulence, which generates difficulty for investors in spotting patterns and taking rational decisions with regard to investments. To tackle the problem, the present study employs advanced econometric techniques for modelling and forecasting volatility specifically in the Bank Nifty returns during periods of structural transition caused by the merger of major public sector banks in India. The dataset on Bank Nifty comprises daily closing prices from 1^st April 2016 to 31^st March 2024, divided into two distinctly defined periods of pre-merger (2016-2020) and post-merger (2020-2024). Thereby, an analysis of the volatility behaviour can be drawn with comparisons made before and after the consolidation in the banking sector. The choice of Bank Nifty , which consists of India's most liquid and large-cap banking stocks—makes it a relevant benchmark for analysing sectorial volatilities. To quantitatively analyse and forecast this volatility, the study uses the Generalized Autoregressive Conditional Heteroskedasticity model (GARCH) family. It was first introduced by⁶ and further extended the earlier ARCH model, which predicted future variances based only on past error terms, while the GARCH model extended this definition to include past errors and variances to predict future variances. While ARCH models provide a reasonable model for volatility prediction in the short run, on the contrary, GARCH models are mainly useful for capturing the long-run persistence of volatility, which makes it a suitable model for the longer horizon of this study of five years. The progressive technique, particularly symmetric, implies that positive and negative shocks of equal magnitudes have an identical impact on volatility. However, in reality, financial market data—especially post-merger stock returns—manifests asymmetric patterning, whereby negative news or shocks usually have greater impact than positive ones. The Bank Nifty has a clustering pattern called volatility clustering, where periods of time when volatility is high tend to cluster together. For this reason, GJR-GARCH modelling will be adapted since it can be used well to account for asymmetric effects of high volatility events clustering. That is why, presently, it was applied in this research to evaluate how investor sentiment and market responses vary during the pre- and post-merger phases. These models could be employed in finding structural changes in volatility behaviour and ascertaining how volatility has possibly changed in the investor confidence- and reaction-patterns as a consequence of the internal reforms inflicted on the banking sector recently.

The methodology adopted in this study which reflects GJR-GARCH modelling technique is shown in step-by-step procedure below:

Step 1: Data Stationarity Testing

Given the high degree of daily stock return volatilities, the first thing to check is the properties of the data before applying models such as GARCH, which is derived from the ARCH framework. In principle, this requires the data to be stationary, i.e., even though the data is highly volatile, its statistical properties such as mean and variance are constant over time. This test checks whether or not there exists a unit root, which indicates non-stationarity. Data is stationary if the test produces a negative statistic and a value of p less than 0.05, thus the data is of non-stationarity type. If the first ADF test produces a p-value of greater than 0.05 indicating non-stationarity of data, then we proceed to apply logarithmic transformation to the dataset and again perform the ADF test, hoping to bring the p-value below 0.05. The transformed values are:

Augmented Dickey-Fuller Test

(Pre-merger 2016-2020)

Dickey-Fuller = -7.7652, Lag order = 9, p-value = 0.01

Since, p-value is less than 0.05 thus the alternative hypothesis is accepted. This signifies that the data is converted to stationary.

(Post-merger 2020-2024)

Dickey-Fuller = -10.714, Lag order = 9, p-value = 0.01

Since, p-value is less than 0.05 thus the alternative hypothesis is accepted. This signifies that the data is converted to stationary.

Step 2: Checking for Volatility Clustering

In assessing stock returns, one aspect to be concerned with would be any signs of volatility clustering, whereby stretches of high volatility tend to be, more often than not, followed by even higher volatility, while stretches of low volatility would be following each other as well. This daily closing price pattern indicates a main feature of financial time series. Observing this phenomenon would be very useful if the data were plotted, as visualization would help show the clustering behaviour more distinctly. This is done in the chart below:

Figure 1 showing plot of volatility clustering of the daily stock returns of closing prices of Banking index for Pre-merger Data (2016-2020)

Source: Generated through RStudio

Figure 2 showing plot of volatility clustering of the daily stock returns of closing prices of Banking index for Pre-merger Data (2020-2024)

Source: Generated through RStudio

The above shows that the big changes are followed by big changes and small changes are followed by small changes. This is volatility clustering.

Step 3: Checking for ARCH Effects

Before applying the GARCH model, it is first necessary to check if the stock returns data exhibits ARCH (Autoregressive Conditional Heteroskedasticity) effects. In the absence of such effects, GARCH would not be appropriate. The presence of ARCH effects implies that the variance of a time series changes at different points in time-even at very short intervals-showing how volatile the time series is, which is the characteristic that GARCH is supposed to explain.

The presence of these ARCH effects will be tested according to the following equation:

The following are the results from the ARCH test:

ARCH LM-test;

(Pre-merger 2016-2020)

Chi-squared = 473.88, df = 12, p-value < 2.2e-16

(Post-merger 2020-2024)

Chi-squared = 148.3, df = 12, p-value < 2.2e-16

The p-value which is much below the 0.05 level shows that the null hypothesis is rejected proving that there are ARCH effects within the data. Thus, the pre-conditions to conduct the GARCH test have been fulfilled signifying the data is ready to be tested with GARCH test.

Step 6: Develop GJR-GARCH model

GJR-GARCH (Glosten–Jagannathan–Runkle GARCH) model, named after the mathematicians who gave it. The advantage of this model is that the variance is directly modelled and does not use natural logarithm like EGARCH model. Previous studies have agreed that GJR-GARCH is the most sufficient in forecasting the volatility and VaR estimation²⁵.

The GJR-GARCH (1,1) model is stated in below stated equation:

Where, is the conditional forecasted variance

ω is the intercept for the variance

is the variance that depends on previous lag terms

is the scale of asymmetric volatility

is a dummy variable

β is the coefficient for yesterday’s forecasted variance

is the yesterday’s forecasted variance

is the dummy variable that is only activated if the previous shock is negative (), allowing the GJR-GARCH to take the leverage effect into consideration⁹.

It shows that in the case of = 0 the GJR-GARCH becomes a regular symmetric GARCH (1,1) model. A negative shock is captured by ( and a positive shock is captured by . The sign of the leverage effect is the opposite compared to the EGARCH Dutta, 2014).

If = 0, symmetry that is, no asymmetric volatility.

If > 0, negative shocks will increase volatility more than positive shocks.

If < 0, positive shocks will increase volatility more than negative shocks.

Here, a necessary condition needs to be satisfied for the GJR-GARCH model fitness, that is:

1. There should be volatility clustering.

2. There should be ARCH effect within the dataset.

3. There should be leverage effect.

The below shown tables show the estimates of optimal parameters and their significance values of the GJR-GARCH model

Table 1 showing GJR-GARCH Model fit for Pre-merger 2016-2020

Optimal Parameters
	Estimate	Std. Error	t value	Pr(>\|t\|)
mu	0.000752	0.000083	9.0322	0
ar1	0.994359	0.002441	407.3663	0
ma1	-1.000000	0.000012	-86062.6509	0
omega	0.000005	0.000001	7.3365	0
alpha1	0.012302	0.000586	20.9766	0
beta1	0.876864	0.010052	87.2363	0
gamma1	0.154798	0.023217	6.6673	0

Source: Generated through RStudio

Table 2 showing GJR-GARCH Model fit Post-merger 2020-2024

Optimal Parameters
	Estimate	Std. Error	t value	Pr(>\|t\|)
mu	0.000436	0.000391	1.11496	0.264868
ar1	-0.092942	0.216732	-0.42883	0.668045
ma1	0.195381	0.211842	0.92230	0.356373
omega	0.000003	0.000002	1.24857	0.211822
alpha1	0.038762	0.014021	2.76450	0.005701
beta1	0.900786	0.018322	49.16395	0.000000
gamma1	0.091782	0.032312	2.84052	0.004504

Source: Generated through RStudio

Table 3 showing Sign Bias Test Pre-merger 2016-2020

	t-value	prob sig
Sign Bias	2.286	0.02249
Negative Sign Bias	1.521	0.12858
Positive Sign Bias	1.972	0.04885
Joint Effect	7.040	0.07065

Source: Generated through RStudio

Table 4 showing Sign Bias Test (Post-merger 2020-2024)

	t-value	prob sig
Sign Bias	0.02735	0.97818
Negative Sign Bias	1.86587	0.06236
Positive Sign Bias	1.03674	0.30011
Joint Effect	8.15798	0.04286

Source: Generated through RStudio

For example, if α₂ = zero, then the model turns out to be A GJR-GARCH model with only symmetric GARCH (1, 1) implications. A negative shock could, therefore, be represented as that of the following, (α₁ + α₂) where a positive shock is represented by αt. Asgharian (2016). But interestingly, direction of the leverage effect is opposite from that given in the view of the EGARCH model (Dutta, 2014). If α₂ = 0, symmetry that is, no asymmetric volatility.

As per the previous table, parameter selection was made for the GJR-GARCH model on an appropriate basis. The Mu parameter, which is tested statistically, shows significance, thus giving a meaningful constant. The AR term, being negative yet statistically insignificant, indicates that this term does not contribute meaningfully to the model definition. The MA term is positive yet statistically insignificant.

On the contrary, Omega and Beta were both significant from a statistical point of view and have been positively estimated, thus asserting their meaningfulness in volatility definition. One parameter, Alpha, was found to be statistically insignificant, although, with a positive estimate, it is relevant for short-term volatility. Alpha is important for measuring the ARCH-type model's reaction to news—both negative and positive—whereas Beta concerns the persistence of volatility.

The model becomes GJR-GARCH if the sum of parameters (typically Alpha + Beta + any additional terms, such as Gamma) is less than 1, <1, which means that volatility persistence with asymmetry is emphasized—that is, negative shocks affect volatility more than positive shocks.

The following plots demonstrate the GJR-GARCH model outputs:

The above graphs indicate the presence of asymmetrical volatility in the dataset indicating that negative shocks have stronger impacts than positive ones. This is strong evidence in favour of the similar outcomes arising from the GJR-GARCH models applied for both sets of data considered, which yield impressively close results in every statistical test. These two models and their consistent results enhance the model and reinforce the principle that negative news induces more market volatility than positive news, which fits with the general behaviour of investors as negative information elicits stronger reactions.

Step 7: Forecasting Volatility

Given that the GJR-GARCH model performs brilliantly for capturing volatility shocks, it is therefore suitable for forecasting future volatility³⁰. Accordingly, the table shows the volatility forecasts of the index during the pre-merger period (2016-2020) obtained through RStudio below:

Table 5 showing forecast of volatility of the index through GJR-GARCH model (Pre-merger 2016-2020 and post merger 2020-2024)

T	Pre-Merger Series	Pre-Merger Sigma	Post-Merger Series	Post-Merger Sigma
T+1	0.003992	0.06750	0.003992	0.06750
T+2	0.003974	0.06640	0.003974	0.06640
T+3	0.003956	0.06532	0.003956	0.06532
T+4	0.003938	0.06425	0.003938	0.06425
T+5	0.003920	0.06321	0.003920	0.06321
T+6	0.003902	0.06218	0.003902	0.06218
T+7	0.003884	0.06117	0.003884	0.06117
T+8	0.003866	0.06018	0.003866	0.06018
T+9	0.003849	0.05921	0.003849	0.05921
T+10	0.003831	0.05825	0.003831	0.05825
T+11	0.003814	0.05731	0.003814	0.05731
T+12	0.003797	0.05639	0.003797	0.05639
T+13	0.003780	0.05548	0.003780	0.05548
T+14	0.003762	0.05459	0.003762	0.05459
T+15	0.003745	0.05372	0.003745	0.05372
T+16	0.003729	0.05286	0.003729	0.05286
T+17	0.003712	0.05201	0.003712	0.05201
T+18	0.003695	0.05118	0.003695	0.05118
T+19	0.003678	0.05037	0.003678	0.05037
T+20	0.003662	0.04957	0.003662	0.04957
T+21	0.003646	0.04878	0.003646	0.04878
T+22	0.003629	0.04801	0.003629	0.04801
T+23	0.003613	0.04725	0.003613	0.04725
T+24	0.003597	0.04651	0.003597	0.04651
T+25	0.003581	0.04578	0.003581	0.04578
T+26	0.003565	0.04506	0.003565	0.04506
T+27	0.003549	0.04436	0.003549	0.04436
T+28	0.003533	0.04367	0.003533	0.04367
T+29	0.003518	0.04299	0.003518	0.04299
T+30	0.003502	0.04232	0.003502	0.04232
T+31	0.003486	0.04166	0.003486	0.04166
T+32	0.003471	0.04102	0.003471	0.04102
T+33	0.003456	0.04039	0.003456	0.04039
T+34	0.003440	0.03977	0.003440	0.03977
T+35	0.003425	0.03916	0.003425	0.03916
T+36	0.003410	0.03856	0.003410	0.03856
T+37	0.003395	0.03798	0.003395	0.03798
T+38	0.003380	0.03740	0.003380	0.03740
T+39	0.003365	0.03684	0.003365	0.03684
T+40	0.003351	0.03629	0.003351	0.03629
T+41	0.003336	0.03574	0.003336	0.03574
T+42	0.003321	0.03521	0.003321	0.03521
T+43	0.003307	0.03468	0.003307	0.03468
T+44	0.003293	0.03417	0.003293	0.03417
T+45	0.003278	0.03367	0.003278	0.03367
T+46	0.003264	0.03317	0.003264	0.03317
T+47	0.003250	0.03269	0.003250	0.03269
T+48	0.003236	0.03221	0.003236	0.03221
T+49	0.003222	0.03175	0.003222	0.03175
T+50	0.003208	0.03129	0.003208	0.03129
T+51	0.003194	0.03084	0.003194	0.03084
T+52	0.003180	0.03040	0.003180	0.03040
T+53	0.003166	0.02997	0.003166	0.02997
T+54	0.003153	0.02955	0.003153	0.02955
T+55	0.003139	0.02913	0.003139	0.02913
T+56	0.003126	0.02873	0.003126	0.02873
T+57	0.003112	0.02833	0.003112	0.02833
T+58	0.003099	0.02794	0.003099	0.02794
T+59	0.003086	0.02756	0.003086	0.02756
T+60	0.003073	0.02718	0.003073	0.02718
T+61	0.003060	0.02681	0.003060	0.02681
T+62	0.003047	0.02645	0.003047	0.02645
T+63	0.003034	0.02610	0.003034	0.02610
T+64	0.003021	0.02576	0.003021	0.02576
T+65	0.003008	0.02542	0.003008	0.02542
T+66	0.002995	0.02509	0.002995	0.02509
T+67	0.002983	0.02476	0.002983	0.02476
T+68	0.002970	0.02445	0.002970	0.02445
T+69	0.002958	0.02413	0.002958	0.02413
T+70	0.002945	0.02383	0.002945	0.02383
T+71	0.002933	0.02353	0.002933	0.02353
T+72	0.002920	0.02324	0.002920	0.02324
T+73	0.002908	0.02295	0.002908	0.02295
T+74	0.002896	0.02268	0.002896	0.02268
T+75	0.002884	0.02240	0.002884	0.02240
T+76	0.002872	0.02213	0.002872	0.02213
T+77	0.002860	0.02187	0.002860	0.02187
T+78	0.002848	0.02162	0.002848	0.02162
T+79	0.002836	0.02137	0.002836	0.02137
T+80	0.002824	0.02112	0.002824	0.02112
T+81	0.002813	0.02088	0.002813	0.02088
T+82	0.002801	0.02065	0.002801	0.02065
T+83	0.002790	0.02042	0.002790	0.02042
T+84	0.002778	0.02020	0.002778	0.02020
T+85	0.002767	0.01998	0.002767	0.01998
T+86	0.002755	0.01977	0.002755	0.01977
T+87	0.002744	0.01956	0.002744	0.01956
T+88	0.002733	0.01935	0.002733	0.01935
T+89	0.002722	0.01916	0.002722	0.01916
T+90	0.002710	0.01896	0.002710	0.01896

Source: Generated through RStudio

A 90-day forecast on the series and sigma values concerning the index under consideration is presented in the table. These forecasts speak volumes of altering patterns with time beneath changing dimensions of volatility. The series values, indicative of financial stock price returns from the Bank Nifty Index, remain significantly stable over the forecast period. Of course, these series values form a direct contrast with the sigma values-the conditionally standard deviation values measuring time-varying volatility-which exhibit a persistent downward incline. The decline in sigma over the 90-day period clearly indicates that there has been a decline in volatility, which, in turn, could mean that investors feel confident about their investments concerning Bank Nifty.

4. RESULTS AND DISCUSSION:

Stock markets, especially in dynamic economies like India, are continuously shaped by a mix of economic reforms, structural changes, and investor sentiments. In the case of the Bank Nifty index, which represents the performance of major banking stocks, volatility is not just a reflection of market sentiment but often stems from deeper shifts—such as bank mergers and policy interventions. The study was conducted to measure and model Bank Nifty volatility patterns before and after the major banking sector consolidation in India in 2020 ²⁴, with particular emphasis on the pre-merger phase of 2016-2020 and the post-merger phase 2020-2024.

The most important thing was to check the suitability of the data for modelling the volatility. The Augmented Dickey-Fuller test gave a p-value of 0.9739, which meant that the raw prices were non-stationary. After taking log returns, setting the lag order to 10, and passing the ADF test, it returned a p-value of 0.01, thus confirming that the modified series is stationary. These results are within respect of pre-merger conditions. With respect to the post-merger conditions, the previous ADF value came out to be 0.3433 and that after converting to logarithm series it comes out to be 0.01. This shows that both the pre and post-merger datasets were non-stationary which were converted to stationary datasets performing log operations and this is confirmed through ADF test. This step was important since GARCH models require a stationary time series to effectively forecast volatility.

The return-series graph demonstrated volatility clustering, where high volatility would be succeeded by even more disturbance and calmness preceded by calmness, thus meeting the second important precondition to apply GARCH-type models. Moreover, the applied ARCH LM test showed a p-value of less than 0.05 for pre-merger and post-merger dataset as well further confirming the presence of ARCH effects in the studied context of modelling variance and thus the appropriateness of GARCH family models for variance modelling.

Among the GARCH models, the best suited model namely, GJR-GARCH model was applied as it captures the negative and positive fluctuations and also can capture the magnitude to which the negative and positive asymmetries impact the volatility in index. Ultimately, the majesty of a GJR-GARCH formulation was found. Not only the model captured asymmetry, but also strong evidence existed for persistency in volatility. All four parameters, ϒ, β, ω, and μ, were under the 0.05 threshold for the model to indicate its significance as an explanation of Bank Nifty's volatility. However, ar1 and ma1 terms were insignificantly statistically tested, suggesting minor effects of the autoregressive and moving average components on volatility in this particular setting.

One of the aspects that can be captured from the GJR-GARCH result is that investors seem to react asymmetrically to news. The coefficient for bad news (α₁ + α₂) came out to be 0.12858, while the coefficient for positive shocks (α_t) was only 0.04885. This is for pre-merger data. Now, for post-merger data, the (α₁ + α₂) is 0.06236 and (α_t) is 0.030011. This shows that with respect to both the pre and post-merger datasets, the negative sign bias is insignificant and the positive sign bias is significant being less than 0.05 which states that the stock market in bank indices are impacted more by positive news than that of negative news. This brings a rather interesting finding that the post-merger period of Bank Nifty reflected stronger investor reactions to positive news as opposed to commonly expected sharper volatility from negative news ²⁸. Such increased reaction may be attributed to the bank mergers that have generally kindled more optimism and confidence about future advantages considered plausible from such mergers.

With condition (α + β + ϒ/2) < 1, model adequacy has been ensured, and it returned 0.966565 just below the critical threshold. This implies that although volatility is persistent, it does not exhibit explosive behaviour, and the model remains reliable for future forecasting.

Consequently, the 90-day out-of-sample volatility forecast showed a downward trend. This gradual decline in predicted volatility indicates a trend toward market stabilization after the merger, which might set investors back towards being confident in the banking space.

5. CONCLUSION AND FUTURE IMPLICATIONS:

Price fluctuations in the stock market due to market volatility hold some of the most unpredictable elements in terms of investing, especially for the everyday investor, who may not fully understand how the market operates. For these investors, past historical prices and trends are often the most helpful technique for trying to understand the current and future trend. In such a scenario the GARCH models are very useful to investors. Since it not only shows the present trend but also predicts the future trend.

The GARCH model has been identified as the most representative of the volatility of the Bank Nifty Index. Because of this property, this model is expected to give volatility forecasts that would be fairly absolute and, thus, facilitate decision-making.

Investors and financial analysts would find these results extremely important in their quest to predict market behaviour and manage risks better³². However, it must be noted that this research used only one index and for a specific time period; scope for further work could include looking at different indices, extending study periods, or comparative studies of markets with the same economic structure between different regions.

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Received on 28.08.2025 Revised on 05.11.2025

Accepted on 23.12.2025 Published on 11.05.2026

Available online from May 14, 2026

Asian Journal of Management. 2026;17(2):112-120.

DOI: 10.52711/2321-5763.2026.00017

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