Volatility Behaviour and Spillover Effect: Evidence from Indian Foreign Exchange Market

Abstract

The study aims to analyze the volatility behaviour and its spillover effect on Indian foreign exchange rates Indian Rupee (INR), specifically against the Euro (EUR), British Pound (GBP), Japanese Yen (JPY) and US Dollar (USD). The study is based on the Reserve Bank of India (RBI) data from January 2019 to June 2023. A statistical approach suitable for capturing the dynamics of volatility over time, allowing for both short-term and long-term effects, is used. Additionally, a method designed to examine returns, shocks and volatility spillover effects, due to its flexibility in capturing asymmetry in volatility among foreign exchange rates, is employed. The empirical findings show that USD/INR is the most volatile and JPY/INR is the least volatile. As for the spillover effect, it is found that there is a bidirectional volatility linkage between the USD and EUR, suggesting that both currencies have a significant impact on the volatility of the INR exchange rate. This study’s impact goes beyond academic circles, directly influencing real-world practices of hedgers, arbitrators and other market players.

Keywords

Foreign exchange rates volatility volatility spillover generalized autoregressive conditional heteroskedasticity Indian foreign exchange market

1. Introduction

The foreign exchange rate reflects the relative strength or weakness of a nation’s currency, influencing trade, tourism and the prices of imports and exports (Donnelly, 2019). Understanding its fluctuations will undoubtedly provide answers to more general macroeconomic issues (Saglam & Uzun, 2020). Exchange rate fluctuations have a strong detrimental impact on both foreign direct investment (FDI) and international commerce (Latief & Lefen, 2018). There is a debate on the impact of exchange rates on economic growth (Barguellil et al., 2018). The crucial element of India’s financial system is the foreign exchange market. This platform plays a pivotal role in fostering international economic activity through efficient currency exchange. Indian foreign currency rates are significantly influenced by the monetary policy goals expressed by the bank rate of the Reserve Bank of India (RBI), both short- and long-term national interest variations, and the pace of fluctuations in foreign exchange reserves (Suthar, 2008). The selection of an anchor currency or basket of currencies for a country’s exchange rate regime holds substantial weight in influencing economic growth across varying income levels, and this selection process is not inconsequential, as it can significantly impact a nation’s development trajectory (Jamil, 2022). The foreign currency market in India is not inefficient in any way (Das & Roy, 2023). However, this may be connected to the fact that during times of crashes and crises, the economy is affected by a liquidity crisis, financial panic and chaotic market circumstances, which may result in predicting irregularities in markets and, as a consequence, cause periods of inefficiency. The introduction of LPG in India, together with an increase in FDI, tourism, growing incomes, international financial activities and many other factors, has increased demand for Indian foreign exchange. Continuous FDI inflows into the economy aid in the local build-up of capital and offer stability to the global exchange market (Panda & Mohanty, 2015). Also, FDI inflows show negative consequences over time that extend to currency rate volatility (Raghutla & Chittedi, 2020). The country’s exchange rate policies had a considerable influence on international commerce, as evidenced by the causal relationship between the real exchange rate and exports and imports (Azhar et al., 2015). In countries where currencies freely fluctuate (floating exchange rates), sudden changes in monetary policy tend to make exchange rate volatility linger for longer (increase long memory). However, this effect is not seen in China, where the exchange rate is more controlled (managed floating) (Wang et al., 2023).

Firms may be exposed to exchange risk, since there are actual flaws in the markets for both financial assets and tangible products and services (Qamaruzzaman et al., 2021). Traditionally, a rising domestic currency is seen as positive, promoting exports and making the tradable sector more profitable. This, in turn, expands its share of the economy. However, some economists argue the opposite for developing economies, suggesting a rise in domestic currency can hinder growth (Karahan, 2020). Market efficiency is a dynamic factor that changes with varying market conditions. Consequently, the recommendation emerged for currency traders to consider embracing active portfolio management strategies (Khuntia & Pattanayak, 2020).

The Indian Rupee (INR) has displayed significant volatility throughout time (Kumar, 2018). Shifting exchange rates can significantly impact the global economy. They influence the cost of imported and exported goods, potentially altering trade patterns. Additionally, currency fluctuations can discourage international investment due to uncertainty. This interplay between exchange rates, trade and investment ultimately shapes economic growth (Alper, 2017). Financial openness amplifies the negative effects of exchange rate volatility on economic growth (Barguellil et al., 2018).

While fluctuations in India’s exchange rate can impact trade in the short term and in the long run, these volatilities significantly hinder exports to major partners like the USA, Germany and China, and also dampen imports from the USA and China, while the impact of exchange rate volatility on India’s trade with major partners like Japan and Germany seems to be influenced by financial crises (Sharma & Pal, 2018). In calmer times, the effects are more balanced, with both positive and negative fluctuations impacting exports. However, during financial crises, the relationship becomes more complex. India’s exports to certain countries, like Germany, post-crisis, become more sensitive to exchange rate swings, suggesting a potentially larger impact (Hashmi et al., 2020). The fluctuations in the value of the rupee against the dollar impact both Indian exports and foreign investment (Jamal & Bhat, 2023). The periodic predictability of Indian currency rate returns depends on the occurrence of significant macroeconomic events (Azhar et al., 2015).

1.1. Motivation

India is ranked 18th among the leading merchandise exporters in the world and third among Asian countries. Also, as a leading exporter of commercial services, India is in the seventh rank in the world according to the World Trade Organization (2023). While India ranks among the top eight global recipients of FDI, its exchange rate fluctuations can impact international trade (UNCTAD, 2023). A recent report revealed that India dominated the global remittance landscape in 2022, becoming the first country to surpass the significant threshold of $100 billion received. Mexico, China, the Philippines and France followed behind, receiving substantially smaller remittance inflows (IOM UN Migration, 2024). RBI data reveal a positive trend in Non-Resident Indian (NRI) deposits. Compared to the previous year’s 10.6 trillion rupees, NRI deposits have grown to 11.4 trillion rupees, signifying increased confidence in the Indian economy among overseas Indians. And also, foreign exchange earnings due to tourism have increased to 13.5 million rupees from the previous year of 6.5 million rupees, as per Ministry of Tourism, GOI (2023).

Additionally, India’s economic trajectory is on an upward trend. It is projected to achieve a robust real gross domestic product (GDP) growth of 8.2% in the fiscal year 2023–2024, solidifying its position as the fastest-growing major economy globally (World Bank Group, 2024). Moreover, India has advanced to the fifth-largest economy worldwide in terms of GDP in 2023, up from its sixth-place ranking in 2019 (International Monetary Fund, 2024). This upward momentum marks India as a significant player in the global economic landscape, steadily gaining prominence and contributing to the world’s economic growth. Due to which there is aforementioned multiple exposures of Indian foreign exchange rates, therefore, it has become necessary to research the volatility behaviour of the various Indian exchange rates traded on the Indian foreign exchange market while identifying the events affecting volatility and the analysis of volatility spillover among the traded Indian foreign exchange rates to evaluate risk, make wise investment decisions by the various stakeholders, and comprehend the interconnectedness of various exchange rates.

The article is organized as follows: Section 2 gives an overview of existing literature. Section 3 analyses the data, and Section 4 discusses the empirical results, while Section 5 outlines practical implications derived from the study’s findings, and lastly, Section 6 provides the conclusion, highlights the study’s limitations and proposes directions for future research.

2. Literature Review

The INR has exhibited tremendous volatility throughout the years, and several macroeconomic factors, including capital inflow, interest rates, inflation rates, and GDP of the country, are to blame (Mirchandani, 2013). Interventions by central banks in the foreign exchange market have a substantial impact on the degree to which businesses in emerging economies are affected by currency fluctuations (Sikarwar, 2020). Therefore, measures like monetary policy that maintain stable exchange rates and rate-variability are necessary to draw in additional investment. Research revealed a robust correlation between the Wholesale Price Index (WPI) and Consumer Price Index (CPI) with major hard currencies like US Dollar (USD), Euro (EUR) and Japanese Yen (JPY) (Aravind, 2023). Additionally, an elevation in interest rates has the potential to lead to depreciation in the exchange rate of the INR.

The researcher looked at how volatility spillovers changed across the foreign exchange markets of five specific Central and Eastern European (CEE) nations—Poland, the Czech Republic, Hungary and the Czech Republic—during and after the 2007 financial crisis (Hung, 2021). They discovered that positive shocks produce more volatility spillovers than negative shocks of the same size. Das and Roy (2023) analyzed the volatility spillover among Brazil, Russia, India, China and South Africa (BRICS) countries and found that India, China and South Africa receive volatility from their developed counterparts, that is, Brazil and Russia. Researchers also assert that imports and exports have a sizable, favourable influence on economic growth in the five developing countries that make up the BRICS (India being one of the nations). Yadav et al. (2023) examined how energy commodity prices (carbon emissions, natural gas and crude oil) affect the Shanghai and European stock markets. It found that volatility and connectedness increase over longer periods, with natural gas being a significant shock transmitter and crude oil as a major receiver. Hameed et al. (2021) investigated how oil price volatility affects exchange rates in major oil-importing and exporting countries while using the Diebold and Yilmaz (2012) methodology. Notably, oil-exporting countries experience greater volatility spillover from oil prices compared to oil-importing countries.

McMillan and Speight (2010) investigated the interdependence and spillover effects of returns and volatility among the USD, JPY and British Pound (GBP) exchange rates against the EUR. It finds significant contemporaneous relationships and market-specific spillovers, with the USD dominating in both return and volatility transmission. Mohammed (2021) examined how returns and volatility move between 23 global currencies (developed and developing) against the USD. He found that volatility, but not returns, flows from developed to developing countries. Within Europe, there are strong two-way volatility flows, with the GBP and EUR being key transmitters. The research underscores the importance of monitoring volatility spillovers for financial regulators. Huynh et al. (2023) examined how trade policy uncertainty impacts the return and volatility of major global currency exchange rates against the USD. It reveals asymmetric spillover effects, meaning the impact is not uniform and that volatility is more sensitive to trade policy uncertainty than returns. Albrecht and Kočenda (2024) and Kocenda and Moravcova (2019) analyzed volatility transmission among Central European currencies (Czech Koruna (CZK)/EUR, Hungarian Forint (HUF)/EUR, PLN/EUR) and their relationship with the USD. The CZK is identified as a minor net transmitter of volatility, showing increased sensitivity to economic distress. The HUF generally acts as a volatility receiver, especially during global shocks, with volatility largely coming from Czech and Polish currencies.

Movements in foreign exchange rates, particularly for major currencies like USD, EUR, GBP, CNY and JPY, ripple through different segments of the Indian stock market. This means the performance of sectors like auto, banking and energy can be influenced by these currency fluctuations (Mohapatra et al., 2024). Stocks and commodities play the role of volatility generators, while bonds, currencies and gold act as volatility sinks in India (Roy & Roy, 2017). Arora et al. (2024) analyzed the interconnectedness of India’s stock, forex, oil and gold markets, revealing long-term relationships and significant lag effects. It finds that West Texas Intermediate (WTI) futures strongly drive oil prices, while gold acts as a stable asset. The Bombay Stock Exchange (BSE) index shows complex interdependence with exchange rates, gold and oil, highlighting the impact of economic growth indicators and investor sentiment. Mohanty et al. (2023) investigated how fluctuations in five key exchange rates (USD/INR, EUR/INR, GBP/INR, CNY/INR, JPY/INR) affect the volatility of India’s National Stock Exchange (NSE) Nifty large-cap, mid-cap and small-cap indices. Using generalized autoregressive conditional heteroskedasticity (GARCH) and dynamic conditional correlation (DCC)-GARCH models, it reveals that exchange rate volatility positively impacts stock market volatility, with varying degrees of influence across different market capitalization indices. Specifically, it finds significant short-term and long-term volatility spillovers, with the long-term impact being most pronounced on the large-cap index.

Mishra et al. (2020) analyzed volatility spillovers between the INR and four major currencies (USD, GBP, EUR, JPY) from 1999 to 2018 using Glosten–Jagannathan–Runkle (GJR)-GARCH and connectedness methodologies, where the EUR and the Pound Sterling are identified as net transmitters of volatility, while the USD and JPY are net receivers. Evidence of significant Indian foreign exchange rates volatility spillover effect from USD to GBP, EUR and JPY, and from GBP and EUR to USD was found in Kumar (2014). Kumar (2011) investigated how the INR exchange rates with the USD, EUR and GBP are interconnected, focusing on return and volatility spillovers. Using the Diebold and Yilmaz method, it finds strong contemporaneous relationships among these exchange rates. The INR–EUR rate significantly influences the INR–Pound rate, while the INR–USD rate remains relatively isolated. Economic shocks are shown to impact both the returns and volatility across these exchange rates. Rajamani et al. (2024) investigated the volatility and volatility transmission of currencies between 2008 and 2023, focusing on EUR/INR, USD/INR, GBP/INR and JPY/INR. It analyzed the volatility transmission of current volatility with previous volatility, which means the lagged volatility spillover.

The main benefit of the GARCH model is that it effectively captures volatility clustering in financial rates of return and provides evidence for volatility clustering (Black, 1976). GARCH exchange rate models are found in Engle and Bollerslev (1986). In the multivariate GARCH model, the two most popular models for conditional covariances and conditional correlations are BEKK (Baba, Engle, Kraft and Kroner) and DCC. A direct connection to the Indirect DCC Model proposed by Caporin and McAleer (2009), which shows that BEKK could be utilized to provide reliable estimates of DCCs. Also, studies have shown that the vector autoregression (VAR)-BEKK-GARCH model is a good choice for analyzing connections between different markets (spillover effects) because it needs fewer variables to estimate in comparison to other models (Carpantier, 2013). Several studies have also considered the spillover index value, which focuses on measuring the interconnectedness and spillover effects between a system of variables, primarily through variance decomposition. It provides a broad overview of spillover effects in a large system (McMillan & Speight, 2010; Mishra et al., 2020).

2.1. Research Gaps and Rationale of the Study

A rigorous review of prior studies makes evident a critical void concerning volatility and spillover effects in the Indian foreign exchange market. Several studies have examined the impact of foreign exchange, particularly USD/INR, on other Indian financial assets (such as bonds, stock, commodities and so on) and spillover effects among currencies against EUR and USD, but there is a lack of research focusing specifically on the volatility and spillover dynamics among various exchange rates within the Indian context (EUR, GBP, JPY, USD against INR). Moreover, in the existing literature, the methodologies often rely on spillover index methods, provide a general overview, but fail to offer the detailed analysis necessary to fully comprehend the intricate interrelationships between these exchange rates. Additionally, highlights of several domestic and global events affecting the volatility of exchange rates are also lacking.

Mishra et al. (2020) studied all four currencies traded in India with data till 2018, but used the Diebold and Yilmaz spillover index for analysis. Kumar (2011) studied three currencies, avoiding JPY in the analysis with the Diebold and Yilmaz spillover index. Rajamani et al. (2024) studied the spillover effect of all four currencies, but only the past volatility spillover, ignoring the cross-currency spillover effect, which is very much crucial for the spillover analysis. Kumar (2014) studied the spillover of all four currencies with the DCC-GARCH model, which requires more parameters for analysis, and also in the study, the data considered were around 15 years back, limiting the recent data analysis and the flexible GARCH model, such as the BEKK model.

Therefore, this study aims to bridge the identified gaps in existing research by examining the volatility of Indian foreign exchange rates and their spillover effects through a contemporary lens. To achieve this, the analysis utilizes a recent data set spanning 2019–2023, employs the VAR-BEKK GARCH model—a methodology recognized for its capacity in capturing both time-varying volatility and the dynamic correlations—and explicitly highlights significant global and domestic events that have contributed to observed fluctuations, thereby providing a more current and nuanced understanding of the Indian forex market’s dynamics.

By analyzing the volatility of Indian foreign exchange rates and subsequently examining the volatility spillover effects among them, this research aims to provide critical insights for risk management, the formulation of informed trading and investment strategies, and a deeper understanding of the interconnectedness within the Indian forex market. Ultimately, the findings are intended to assist corporations and investors in making more informed and timely decisions regarding foreign transactions and asset allocation.

3. Materials and Methods

3.1. Model Specification

3.1.1. GARCH Model

The GARCH (1,1) model is employed for the analysis of exchange rate return volatility, selected for its parsimonious nature, which ensures a robust fit to the data while mitigating the risk of overfitting. This model, GARCH of order (p,q), is a widely utilized framework for capturing conditional volatility within time series data. It extends the fundamental autoregressive conditional heteroskedasticity (ARCH) model by incorporating a lagged squared residual term alongside the lagged conditional variance term. The GARCH model is particularly suitable for characterizing the dynamic nature of volatility over time, accommodating both short-term and long-term influences.

σ_{t}^{2} = α_{0} + α_{1} u_{t - 1}^{2} + α_{2} σ_{t - 1}^{2}

(1)

The left-hand side (LHS) of Equation (1) represents the conditional variance, also known as volatility. Within this specification:

$α_{0}$ is the constant term or intercept.

$α_{1}$ is the coefficient for the squared residuals at lag (t–1), which captures the short-term impact of shocks on volatility.

$α_{2}$ is the coefficient associated with the conditional variance at lag (t–1), reflecting the long-term influence of past volatility on the current volatility.

The constraints $α_{1}; α_{2} > 0$ are imposed to ensure that the conditional variance remains positive.

H₀: The time series data adhere to a homoscedastic process, implying that the conditional variance remains constant over time.

H₁: The time-series data follow a heteroskedastic process, indicating that the conditional variance is time-varying.

3.1.2. BEKK-GARCH Model

The BEKK-GARCH model represents an extension of the traditional GARCH framework, specifically designed for the modelling and forecasting of conditional variance and covariance within multivariate time series data. Introduced by Engle and Kenneth (1995), the BEKK-GARCH model facilitates the investigation of volatility interdependence between multiple time series data sets. The primary advantage of the BEKK-GARCH model lies in its capacity to capture both time-varying volatility and the dynamic correlations existing between multiple variables concurrently (Maharana et al., 2024; Yong Fu et al., 2011). The GARCH-BEKK model offers richer dynamics in the variance-covariance structure by directly modelling spillover effects through lagged squared residuals, thereby capturing interactions between the volatilities of different assets.

In contrast, the vector error correction heteroskedasticity (VECH) model, which utilizes a VEC matrix, assumes constant correlations and lacks the flexibility to model time-varying spillover effects. The construction of the GARCH-BEKK model inherently maintains the positive definiteness of the conditional variance–covariance matrix, whereas the DCC model relies on additional constraints or transformations to achieve this property. Furthermore, the GARCH-BEKK model requires fewer parameters for estimation compared to the DCC model, rendering it more parsimonious, particularly when dealing with larger data sets. This characteristic reduces the risk of overfitting and enhances its performance with limited observational data.

The conditional mean equation is modelled based on the VAR model.

The mean Equation (2) is defined as

{lnR}_{t} = μ + Σ_{i = 1}^{k} γ_{i} {lnR}_{t - i} + u_{t}

(2)

Where ${lnR}_{t}$ means log returns for one of the exchange rates, $μ$ means the constant term, and $u_{t}$ is the error term for one of the exchange rate returns.

For the conditional variance-covariance matrix of the BEKK model, $H_{t}$ is expressed in Equation (3) as follows

H_{t} = C C' + A' u_{t - 1} u_{t - 1} A + B' H_{t - 1} B + D' δ_{t - 1} δ_{t - 1} D

(3)

$H_{t}$ indicates the time-varying variance and covariance matrix, and $u_{t - 1}$ denotes the matrix of the residuals from the mean equations. Moreover, A, B, C and D indicate coefficient matrices, and δ represents the asymmetric effect. Equation (3) states that the variance and conditional covariance matrix depend upon four types of parameters, that is, C = constant, A = ARCH effect, B = GARCH effect, and D = asymmetric effect.

3.2. Data

The study has considered the daily spot exchange rate for the four pairs of currency rates traded (i.e., EUR/INR, GBP/INR, JPY/INR, USD/INR) in the Indian foreign exchange market, for which data are taken from the official website of the RBI. The sample period of the study, as per the availability of data, is from 1st January 2019 to 30th June 2023, having 4,340 observations. Initially, the study computed the daily log returns on day ‘t’ to measure the returns in the exchange rate between two consecutive trading days. To examine the volatility clustering of the exchange rate in India, the equation is as follows:

{lnR}_{t} = ln (E_{t} / E_{t - 1})

(4)

Where ${lnR}_{t}$ is the log returns of the exchange rate on day t, $E_{t}$ represents the exchange rate on day t, and $E_{t - 1}$ represents the exchange rate on the previous day, ‘t–1’. A positive return indicates an appreciation of the currency, while a negative return indicates a depreciation.

Figure 1 depicts EUR/INR, GBP/INR, JPY/INR and USD/INR trends. EUR and GBP moved closely, with the EUR peaking above ₹100 in 2021 before moderating. The GBP showed mild appreciation. The JPY depreciated sharply post-2022 due to rate differentials and accommodative policy, while the USD maintained a steady appreciation against the INR.

Figures 2 –5 represent a graphical depiction of volatility clustering across four currency exchange rate pairs: EUR, GBP, JPY and USD, respectively. An examination of the USD/INR graph indicates significant volatility clustering, evidenced by prolonged periods of consistently high market volatility. The volatility clustering of EUR/INR also demonstrates a high degree of clustering, whereas the GBP/INR and JPY/INR exhibit low volatility clustering. In conclusion, a general assessment suggests that the USD and EUR exchange rates are associated with high volatility clustering, while the JPY and GBP exchange rates are associated with lower volatility clustering.

4. Results and Discussions

4.1. Descriptive Statistics

The study presents the descriptive statistics of all the return series in Table 1. According to Table 1, all the return series are both positive and negative for the sample periods. The highest returns are provided by GBP/INR, and the lowest returns are provided by JPY/INR. As per the standard error data, JPY/INR is highly volatile compared to other exchange rate returns. Every exchange rate return exhibits positive skewness except for GBP/INR. The null hypothesis of the normality test, that is, the returns of time series data are not normal, is strongly rejected, as per the Jarque–Bera (JB) normality test. It can also be interpreted from kurtosis (excess), that is, >0 (standard value) for every exchange return, indicating heavier tails and a more peaked distribution compared to a normal distribution, which means the distribution has a higher probability of extreme values (outliers) than a normal distribution. The probability mass is concentrated around the mean, resulting in a more pronounced and peaked shape in the centre.

Table 1.

Descriptive Statistics.

Statistics	USD_R	GBP_R	EUR_R	JPY_R
Mean	0.000155	0.000157	0.000111	−0.000087
Minimum	−0.0133	−0.0472	−0.0176	−0.0214
Maximum	0.0138	0.0290	0.0198	0.0359
Standard error	0.003148	0.005896	0.004609	0.005940
t-statistics	1.622190	0.876219	0.792832	−0.480745
Skewness	0.081560	−0.338513*	0.313682*	0.748854*
Kurtosis (excess)	2.057537*	6.163821*	1.350069*	3.875242*
Variance	0.000010	0.000035	0.000021	0.000035
Jarque–Bera	192.590442*	1,738.307982*	100.193907*	780.324360*
Observation	1,085	1,085	1,085	1,085

Note: * indicates the value to be significant at the 1% level of significance.

4.2. Stationary Test

To ensure the reliability of the data analysis, it is imperative to verify the stationarity of the time series. This is achieved through the application of both the augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests. From Table 2, it can be concluded that the t-statistics of all the time series data (exchange rate returns) in both ADF and PP tests are > (greater than) critical values at the 1% level of significance, which means it fails to accept the null hypothesis. Hence, the time series data are stationary at the level.

Table 2.

Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) Stationary Test.

Variable	Level (t-statistics)
Variable	ADF	PP
USD_R	−33.3223*	−33.4176*
GBP_R	−31.1285*	−31.1745*
EUR_R	−31.9544*	−32.0025*
JPY_R	−32.7724*	−32.8026*

Note: * represents the 1% level of significance.

4.3. Heteroscedasticity Test (ARCH Effects)

The estimation of ARCH models necessitates a preliminary diagnostic procedure to ascertain the existence of ARCH(q) effects. Consequently, to assess the presence of these effects within the residual series, a generalized autoregressive (AR) representation of the squared residuals, as delineated in Equation (5):

u_{t}^{2} = β_{0} + β_{1} u_{t - 1}^{2} + β_{2} u_{t - 2}^{2} + \dots + β_{q} u_{t - q}^{2} + e_{t}

(5)

Evidence of conditional volatility (ARCH effects) is inferred from the statistical significance of the $β_{i}$ parameters, under the assumption of a null hypothesis of no ARCH effect. The results of the Lagrange multiplier (LM) statistic are presented in Table 3.

β_{1} = β_{2} = β_{3} = \dots = β_{q} = 0

Table 3.

Autoregressive Conditional Heteroskedasticity (ARCH) Effects Lagrange Multiplier (LM).

USD_R	ARCH-LM test statistics	19.69889
	Probability chi-square (1)	0.00
GBP_R	ARCH-LM test statistics	33.60689
	Probability chi-square (1)	0.00
EUR_R	ARCH-LM test statistics	16.46196
	Probability chi-square (1)	0.00
JPY_R	ARCH-LM test statistics	88.63233
	Probability chi-square (1)	0.00

The LM statistic exhibits evidence of heteroskedasticity in the series, as it is statistically significant at the 1% level with p values less than .01 for all series, indicating the existence of ARCH effects by rejecting the null hypothesis of no ARCH effects. This suggests that employing an ARCH model will yield more accurate results for all four exchange rate pairs.

4.4. Volatility Behaviour of Indian Foreign Exchange

The empirical results of the t-GARCH (1,1) model are shown in Table 4. The results are for all four Indian foreign exchange rates (i.e., EUR/INR, GBP/INR, JPY/INR, USD/INR). Conventionally, the error distribution in GARCH models is assumed to be Gaussian. However, in the context of financial returns, it is often observed that the residuals deviate from a normal distribution, exhibiting heavier tails and excess kurtosis. Empirical evidence, as depicted in Table 1, supports this observation for the exchange rate returns under consideration, where non-normality and positive excess kurtosis are evident. Consequently, this study incorporates the Student’s t-distribution to account for the heavy-tailed nature of the return distribution, thereby enhancing the model’s robustness to extreme events and outliers present in the data.

Table 4.

Conditional Variance of the Four-exchange Rate Returns Through t-Generalized Autoregressive Conditional Heteroskedasticity (GARCH) (1,1) Model.

Variable	Mean Equation		Variance Equation
Variable	Constant	Lagged Values	Constant	ARCH Effects	GARCH
EUR_R	0.0000766 (0.000147)	0.026252 (0.030753)	0.00000136** (0.00000057)	0.083566* (0.022972)	0.875406* (0.031957)
GBP_R	−0.0000697 (0.000123)	0.023663* (0.029507)	0.000000555** (0.000000265)	0.064324* (0.016813)	0.910018* (0.023954)
JPY_R	−0.000407* (0.000142)	0.004568 (0.030833)	0.00000295* (0.00000103)	0.122663* (0.033608)	0.805675* (0.043632)
USD_R	0.000072 (0.0000793)	−0.010773 (0.032692)	0.00000107* (0.000000331)	0.185508* (0.042365)	0.715713* (0.055635)

Notes: Values without parentheses represent the coefficient, and those with parentheses indicate standard error. * and ** represent the 1% and 5% levels of significance, respectively.

4.4.1. Mean Equation

Empirical evidence suggests the presence of significant AR behaviour in the GBP/INR exchange rate series. Specifically, analysis reveals that lagged returns of the GBP/INR exhibit statistically significant predictive power for future returns. This observation contrasts with the findings for other currency pairs examined, where no discernible serial correlation in returns was detected. These results imply that incorporating lagged return information into forecasting models may enhance predictive accuracy for the GBP/INR exchange rate.

4.4.2. Variance Equation

The empirical results from the ARCH-GARCH model exhibit statistically significant (p < .01) positive coefficients for the constant variance, ARCH, and GARCH terms. This signifies a substantial impact of past volatility shocks on future market fluctuations. The model adheres to stability conditions: 0 < $α_{1}$ <1; 0 < $α_{2}$ <1; and ( $α_{1} + α_{2}$ ) < 1, ensuring the reliability of the generated forecasts. Notably, the sum of ARCH and GARCH parameters ( $α_{1} + α_{2}$ ), approaches unity, indicating high persistence in volatility shocks. This implies that current market volatility fluctuations will exert a prolonged influence on predicted variance over an extended period, suggesting that the effects of past shocks will continue to exert a significant influence on market behaviour over an extended horizon.

The following graphs (Figures 6 –9) indicate the conditional variance (volatility) of the exchange rate returns of four pairs of currencies (i.e., EUR/INR, GBP/INR, JPY/INR, USD/INR, respectively) along with the annotations indicating several events impacting the fluctuation in the volatility. It can be interpreted that USD/INR is highly volatile (Figure 9) and JPY/INR is the least volatile (Figure 8). The period from 2019 to 2023 is likely to see increased volatility in the USD/INR exchange rate due to a confluence of global and domestic factors. Global economic events like the COVID-19 pandemic, US–China trade war, and Russia–Ukraine war have created widespread uncertainty, making investors risk-averse and pushing them towards safe-haven currencies like the USD, which has also been concluded in Le Thi Thuy et al. (2024). This increased demand for USD would naturally put downward pressure on the INR. And domestic events such as the presidential election, early signs of rising inflation, federal rate hikes, and the debt ceiling crisis also impacted the volatility of the USD/INR. Oil prices also play a role, as India relies heavily on oil imports. Fluctuations in global oil prices cause an energy crisis in the economy, impacting India’s current account deficit and influencing the INR’s exchange rate (Ben Salem et al., 2024). Furthermore, sudden surges or dips in foreign investment flows can affect the demand for INR, as was seen during the pandemic period, when there was a sudden decline in FDI inflow, followed by a gradual increase in FDI inflow in developing nations (UNCTAD, 2023). The JPY/INR exchange rate is relatively stable compared to USD/INR during 2019–2023, which can be attributed to a few reasons, as highlighted in Figure 8. First, in times of global economic uncertainty, investors seek JPY (Feder-Sempach et al., 2024), which reduces volatility in its exchange rate compared to other currencies like INR. Second, the trade relationship between India and Japan is less significant compared to the USA–India trade ties. This means that fluctuations in trade flows between the two nations have a potentially smaller impact on the JPY/INR rate. However, several economic and environmental events have impacted the rise and fall of volatility of JPY/INR, such as COVID-19 and Omicron COVID-19, early signs of inflation rising, Japan’s investment of $42 billion in India during March 2022, typhoon Hagibis cyclone, and the Russia–Ukraine war.

Figure 6 depicts the volatility of the EUR/INR exchange rate, where, notably, the sharp spike in volatility around late Q1 2020 coincides with the onset of the COVID-19 pandemic, underscoring the profound impact of the global crisis on currency markets. Subsequent periods of relatively lower volatility with several events like the presidential election and early signs of inflation rising suggest a return to stability until late 2022, when another significant surge occurs, potentially influenced by factors such as the peak of inflation, the global energy crisis, and the ongoing Russia–Ukraine war. The annotations highlight specific events like Belarus–EU border situations, Brexit, and the EU–Ukraine summit, which likely contributed to the fluctuations in between. The conditional variance of the GBP/INR exchange rate effectively depicts its volatility over time and contextualizes it with significant global and regional events in Figure 7. Notably, the first major volatility spike in late 2019 coincides with political turmoil and Brexit, highlighting the market’s sensitivity to political uncertainty. The subsequent sharp rise in volatility around early 2020 aligns with the onset of the COVID-19 pandemic and the early rise of inflation, emphasizing the profound impact of global crises on currency markets. Further fluctuations are observed, with events such as the debt crisis in 2020 contributing to the volatility. The most significant surge in volatility occurred in late 2022 and early 2023, attributed to a confluence of factors including the Russia–Ukraine war, energy crisis, inflation hike, and Bank of England raising interest rates. These events collectively underscore the interconnectedness of currency markets with geopolitical tensions, inflation and monetary policy decisions.

4.5. Volatility Spillover Among the Four Currency Pairs: EUR/INR, GBP/INR, JPY/INR, USD/INR

4.5.1. Mean Equation

Table 5 represents the mean equation of returns spillover effects of four pairs of exchange rates: USD_R, GBP_R, EUR_R and JPY_R, indexed as 1, 2, 3 and 4, respectively. In the mean equation, the parameters $γ_{i j}$ in the table indicate the directional relationship in terms of returns across these exchange rates. The diagonal parameters $γ_{11} γ_{22} γ_{33} and γ_{44}$ are statistically insignificant, which means that the returns of the exchange rates do not depend on their immediate previous lag. In the cross-market returns linkage, it can be evidently seen that there is a unidirectional spillover returns effect from USD to GBP and JPY to USD, and bidirectional returns spillover between GBP and EUR, which is implied from the statistically significant value of $γ_{23}, γ_{32}$ .

Table 5.

Estimated Coefficients from Mean Equation.

Returns	USD_R		GBP_R		EUR_R		JPY_R
Returns	Coefficients	p Value	Coefficients	p Value	Coefficients	p Value	Coefficients	p Value
γ(i, 1)	−0.0146	.66	−0.0839	.18	−0.0457	.35	−0.1402	.02**
γ(i, 2)	0.0567	.00*	0.0385	.30	0.0854	.00*	0.0366	.33
γ(i, 3)	−0.0155	.58	0.0917	.08***	−0.0225	.58	0.0492	.35
γ(i, 4)	−0.0029	.88	−0.0626	.08	−0.0059	.83	0.0032	.92

Notes: *, **, *** represent the 1%, 5% and 10% significance level, respectively. i = 1, 2, 3 and 4 stands for USD_R, GBP_R, EUR_R and JPY_R, respectively.

4.5.2. Variance Equation

The estimated results of time-varying variance-covariance are reported in Table 6. By examining the diagonal elements of matrices A, B and D presented in Table 6, we can delve into the relationship between different factors and volatility. The ARCH effect, represented by the diagonal element in A, reveals how recent volatility shocks impact future volatility. Meanwhile, the GARCH effect, captured by the diagonal element in B, measures the influence of past volatility on future volatility. And the diagonal element in D represents the asymmetric effect of negative shocks.

Table 6.

Estimated Coefficients for Four Variable Asymmetric Baba, Engle, Kraft and Kroner (BEKK)-Generalized Autoregressive Conditional Heteroskedasticity (GARCH).

Variable	USD_R (i = 1)	GBP_R (i = 2)	EUR_R (i = 3)	JPY_R (i = 4)
A_i ₁	0.3258*	−0.0144	0.0151	0.0337***
A_i2	0.0277	0.059	0.206*	−0.033
A_i3	0.1292*	−0.0825**	0.1837*	0.0205
A_i4	0.1507**	−0.0265	0.0882***	0.1839*
B_i1	0.8757*	−0.0055	−0.0145*	−0.0102
B_i2	0.0275	0.9039*	0.0443**	0.0306**
B_i3	−0.0712*	0.0064	0.9677	−0.0158*
B_i4	−0.1172*	−0.0123	−0.0107	0.9621*
D_i1	0.1694**	0.0518	−0.135**	0.0587***
D_i2	0.2796*	−0.3266*	−0.1075	0.0709
D_i3	0.3641*	0.0555	−0.155**	−0.1118*
D_i4	0.3185*	−0.0029	0.0478	−0.1384**

Notes: *, ** and *** represent that the coefficient is significant at the level 1%, 5% and 10%, respectively. Coefficients A, B and D capture ARCH, GARCH, and asymmetric GARCH effects. i = 1, 2, 3 and 4 stands for USD_R, GBP_R, EUR_R and JPY_R, respectively.

Table 6 reveals statistically significant ARCH effects in the USD/INR, EUR/INR and JPY/INR exchange rates, as evidenced by the significance of elements $A_{1, 1}, A_{3, 3} and A_{4, 4}$ . Furthermore, the statistical significance of elements $B_{1, 1}, B_{2, 2} and B_{4, 4}$ indicates the presence of a robust GARCH (1,1) process driving the conditional variances of the USD/INR, GBP/INR and JPY/INR exchange rates. The magnitude of own volatility, as represented by the GARCH parameter, is observed to be highest for the JPY/INR exchange rate, followed by the EUR/INR and USD/INR exchange rates, suggesting a substantial influence of own volatility on their respective conditional variances.

The off-diagonal elements of matrices A and B quantify cross-market effects, specifically shock and volatility spillovers, respectively, among the four exchange rates. The analysis demonstrates statistically significant bidirectional shock spillover effects between the USD and JPY exchange rates and between the EUR and GBP exchange rates $A_{1, 4}, A_{4, 1}, A_{2, 3}, A_{3, 2})$ . This bidirectional spillover suggests a strong interconnectedness between these pairs, wherein shock-related information in one exchange rate significantly impacts the volatility of the other and vice versa. And unidirectional shock spillover from USD to EUR and from EUR to JPY.

This effect can be due to the economic relations between the nations, as the economic relationship between the United States and Japan is multifaceted and has evolved over time, impacted by various global and domestic factors. While not a free trade agreement (FTA) partner, the USA and Japan engaged in substantial trade. In 2022, Japan was the fifth largest USA trading partner for exports and imports, and the USA was the second largest trading partner for exports and imports for Japan (World Trade Organization, 2022). In 2022, Japan remained the top investor in the USA (U.S. Bureau of Economic Analysis, 2022), and the USA also has major investments in Japan (Japan External Trade Organization, 2024). Both economies were significantly impacted by global events like the COVID-19 pandemic, the rise of inflation, and the Russia–Ukraine war. While trade frictions and macroeconomic differences arose, both countries actively sought ways to strengthen their economic ties through measures like digital trade agreements and bilateral dialogues.

The economic relationship between Europe and the UK has been complex and evolving, marked by both continuity and significant change due to Brexit. Both the UK and EU economies have rebounded from the COVID-19 pandemic, but growth rates have diverged. The UK’s GDP is estimated to be slightly lower than pre-pandemic levels, while the EU is closer to exceeding them. Both regions face rising inflation, fuelled by global factors like the war in Ukraine and supply chain disruptions. However, the UK’s inflation rate is currently higher than the EU’s average.

Second, there are unidirectional volatility linkages from USD to JPY, EUR to GBP, JPY to GBP, JPY to EUR, GBP to JPY $B_{14}, B_{32}, B_{42}, B_{43} and B_{24}$ , which are statistically significant. And, also, the evidence of significant volatility spillover effect from USD to GBP, EUR and JPY, and from GBP and EUR to USD was found by Kumar (2014). Own volatility spillovers in USD, GBP and JPY markets are large and significant. The overall persistence of exchange rate volatility is highest for EUR/INR and lowest for JPY/INR, similar to the findings of Dua and Suri (2019). We also find the bidirectional volatility linkage between USD and EUR, $B_{13}, B_{31}$ . This interconnectedness means that economic events or policy changes affecting one currency can have ripple effects on the other, leading to increased market uncertainty and potentially higher volatility in both currencies. Also, bidirectional volatility spillovers were found between all exchange rate markets (USD, EUR, JPY, GBP) in Dua and Suri (2019).

Analysis of matrix D reveals statistically significant evidence of asymmetric responses to negative shocks within each individual exchange rate, as indicated by the significance of the diagonal elements, that is, $D_{11}, D_{22}, D_{33}, and D_{44}$ . Furthermore, the study identifies bidirectional cross-market asymmetric responses between USD and EUR and between USD and JPY, as their d parameters are statistically significant. Additionally, unidirectional cross-market asymmetric response spillover is observed from JPY to EUR and from USD to GBP.

5. Practical Implications

The analysis culminates in several recommendations directed towards regulatory bodies, notably the RBI, and market participants, including exporters/importers, investors and businesses, to facilitate informed decision-making. Specifically, the observed relative stability of the JPY/INR exchange rate suggests its potential utility as a stable reference or transaction currency for entities prioritizing long-term predictability, albeit within specific trade contexts. Conversely, given the high volatility associated with the USD/INR pair, the adoption of robust risk management strategies, such as the utilization of futures, options and swaps, is imperative for businesses engaged in international trade. The RBI is advised to enhance its monitoring of global economic developments, capital flows, and market indicators through the development of a sophisticated early warning system (EWS) as incorporated by the International Monetary Fund (IMF) and the Bank for International Settlements (BIS) to anticipate and mitigate potential spillover effects. Further, the identified interconnectedness of major currency pairs, such as USD/JPY, EUR/GBP and USD/EUR, evidenced by shock and volatility spillover effects, necessitates that investors and businesses acknowledge this interdependence when formulating diversification and investment strategies, such as Global Tactical Asset Allocation (GTAA) with currency overlay. And RBI is encouraged to engage in dialogue and coordination with international counterparts to address global imbalances, promote the rupee’s internationalization, and conduct regular stress tests and scenario analysis to assess financial system resilience against exchange rate shocks.

6. Conclusion

India’s foreign exchange reserves are a key pillar of economic resilience, ensuring stability, trade support, investment inflows and protection against shocks. Given the rupee’s sensitivity to both domestic and global factors, analyzing its volatility is crucial for policymakers and investors. Such volatility stems from fundamentals, speculative activity and external disturbances, with events like financial crises, oil price shocks and policy shifts in advanced economies often driving sharp fluctuations. Spillover effects, where shocks in one market transmit to others, further amplify risks by influencing capital markets and investor sentiment, thereby affecting economic growth trajectories. Despite extensive research on advanced economies, limited focus has been given to India’s distinct forex market. Moreover, the growing integration of India with global financial systems underscores the need to examine how domestic volatility interacts with external shocks and transmits across markets.

This study extends the existing literature on exchange rate dynamics by focusing on volatility and spillover effects in the Indian foreign exchange market (against the USD, EUR, GBP, JPY) from 2019 to 2023. Unlike previous studies, it employs the advanced VAR-BEKK GARCH model for a detailed analysis of time-varying volatility and dynamic correlations, explicitly linking findings to significant global and domestic events for risk management and investment strategies. The study found USD/INR to be highly volatile and JPY/INR as the least volatile. Volatility was seen as high during COVID-19, Russia–Ukraine war, and during the early rise of inflation. Several other geopolitical and environmental factors affected the fluctuations of the conditional variance of the exchange rates, such as political turmoil, US–China trade war, presidential election, typhoon cyclone, rate hike and Brexit.

Furthermore, to know more insights into the movements of volatility, it was found that the magnitude of own volatility is highest in JPY/INR, which means that the volatility of the exchange rate is influenced by its own previous volatility. And as far as shocks spillover effects are concerned, there are bidirectional effects between USD and JPY and between EUR and GBP. Also, the results found a bidirectional volatility linkage between USD and EUR, which means both nations have strong links in the volatility of the exchange rates.

In a nutshell, crises and external shocks exert a substantial influence on the volatility and spillover effects of the Indian foreign exchange market, with notable implications for exports and economic growth, as highlighted in prior studies (Barguellil et al., 2018; Hashmi et al., 2020; Sharma & Pal, 2018; Qamaruzzaman et al., 2021). This underscores the need for effective portfolio management strategies (Khuntia & Pattanayak, 2020). The study recommends that the RBI and market participants utilize JPY/INR’s stability for predictable transactions and adopt stronger risk management for the volatile USD/INR. It also advises implementing an EWS, fostering international collaboration, and urging investors to account for the interconnectedness of major currency pairs.

Limitations include the short four-and-a-half-year timeframe, which may not capture long-term dynamics, and the India-focused scope, which restricts global applicability. Future studies should broaden the data set and incorporate cross-country comparisons to yield a more holistic understanding of global exchange rate interdependencies.

Acknowledgements

The authors would like to express their sincere gratitude to their family and friends for their encouragement and support throughout this research journey. Their unwavering belief in us helped us to persevere through challenges and achieve our goals.

Authors Contribution

Dixita Barai: Contributed to the conceptualization of the study, designed the methodology, carried out the formal analysis and prepared the initial draft of the manuscript.

Gouri Prava Samal: Validated the methodology and results, revised and edited the manuscript for clarity, provided insights on policy implications and refined the conclusion.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Ethical Declaration

The authors abide by all the ethics involved in this academic work and have not submitted it to any other journal.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Dixita Barai

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