Investment Behavior of Foreign Institutional Investors and Implied Volatility Dynamics: An Empirical Study on the Indian Equity Derivatives Market

Abstract

The aim of this study is to examine the association between the capital flows of foreign institutional investors (FIIs) in the equity derivatives market in India and the implied volatility of options. Previous studies on FIIs and realized volatility in the equity market provide the basis for this study. Covering a period of ten years (2012–2021), this study established the importance of FII capital flows in explaining the implied volatility of options. The Granger causality test confirms the unidirectional flow of causality between FII and implied volatility (VIX) in the Indian stock market. The vector autoregression model developed in the study confirms the dynamic relationship between implied volatility and the investment behavior of foreign institutional investors (FIIs). The outcome of this study will help options traders to understand the mispricing of options because of FII’s buying pressure on implied volatility. The results will also help policymakers understand how institutional investors influence option pricing so that appropriate decisions can be made.

1. Introduction

The expected magnitude of price movements in the underlying asset over the life of the options contract is measured by implied volatility (Ackert et al. 2019). Higher implied volatility suggests a greater range of expected price movements in the underlying asset, which drives up the price of the options contract (Bollen and Whaley 2004). Conversely, lower implied volatility indicates a lower expected range of price movements and a lower premium for the options (Bachmann and Bolliger 2001). Implied volatility is important to both buyers and sellers who trade options contracts (De and Chakrabarty 2016). Buyers use implied volatility to evaluate the potential premium and profitability of an options trade, and sellers use it to evaluate higher-priced option contracts and manage their risk exposure (Duan and Hung 2010). Overall, implied volatility is a key metric in the options market, and it is important to understand its importance for successful options trading, hedging, and risk management in the equity derivatives market (Félix et al. 2020).

Institutional investors, such as pension funds, hedge funds, and mutual funds, are financial organizations that manage large pools of assets on behalf of their clients (Dennis and Strickland 2002). These investors often use options in their portfolios to manage risk and enhance returns (Gong et al. 2022). Institutional investors play an important role in determining implied volatility in the derivatives market (Mall et al. 2014). These investors trade in large volumes, and their trading activity can affect the supply and demand of options, which in turn affects the implied volatility term structure (Pranesh et al. 2017).

If institutional investors are buying options in large quantities, this may increase the demand for option strikes and increase option premiums due to higher implied volatility (Ryu et al. 2023). Conversely, this can increase the supply of options resulting in a push-down of the option premiums (Ryu et al. 2023). Overall, the trading activity of institutional investors can have a significant impact on the level of implied volatility in stock prices (Shiu et al. 2010). The Indian capital market, which is still a semi-efficient capital market, is dominated by Foreign Institutional Investors (FIIs) trading in the equity market, which accounts for about one-third of the total trading volume on each trading day (Ryu et al. 2023). Therefore, the trading behavior of FIIs has a significant role in the movement of asset price in the Indian capital market (Fan and Feng 2022), especially in the derivatives segment where traders rely heavily on expected volatility rather than on asset fundamentals (Vardhan and Sinha 2016). Some of the existing literature has established a significant relationship between institutional investors’ behavior and the expected volatility of the security market from developed economies (Venkatesh et al. 2021).

It is important to note that the relationship between foreign institutional investors and implied volatility is complex and may not always be straightforward (Ryu et al. 2023). Institutional investors may influence volatility through their net buying pressure, but they are also subject to the same market forces that drive volatility (Votano et al. 2004; Shaikh and Padhi 2014), such as changes in market sentiment or economic conditions. Option mispricing, which occurs when the market price of an option is not in line with its true value, can result from implied volatility manipulation (Félix et al. 2020; Nkoro and Uko 2016). This can happen if the underlying volatility of the option has been manipulated to artificially inflate or deflate it (Ackert et al. 2019). The market price of options will be higher than their fair value if implied volatility is artificially inflated, resulting in option buyers overpaying for their contracts (Smales 2016). The market price of options will be lower than their fair value if implied volatility is artificially deflated, on the other hand, option sellers will receive less money for their contracts than they are worth (Doran et al. 2013).

FIIs have become an important source of investment for the Indian securities markets since the introduction of the derivatives segment of the National Stock Exchange of India (Figure 1). Their investments provide much-needed capital to Indian companies and help increase liquidity in the markets (Chadha and Kaur 2017).

Since liberalization in India, the government and regulatory authorities have taken several steps to attract and facilitate FII investments in the country. For example, they have implemented policies to streamline the FII registration process, reduce taxes on FII investments, and liberalize foreign investment limits in various sectors (Tanty and Patjoshi 2016). Despite the benefits of FII investments, there are also concerns about the potential risks associated with such investments. For example, large FII investments can cause volatility in the markets and may exacerbate market downturns (Chadha and Kaur 2017). Additionally, FII investments can be subject to sudden reversals if global economic conditions change or if there are concerns about political or regulatory instability in India (De and Chakrabarty 2016). Overall, FII investments are an important component of the Indian securities markets, and regulatory authorities must balance the benefits of such investments with the potential risks to ensure the stability and integrity of the markets (Kumar 2014).

In practice, it can be difficult to determine whether institutional investors are intentionally manipulating implied volatility or whether their trading activity is simply responding to market conditions (Fan and Feng 2022). Regulators and market participants may use a variety of tools, such as market surveillance and analysis of trading patterns, to identify potential cases of volatility manipulation (Mixon 2002).

The manipulation of volatility by institutional investors is generally considered to be unethical and illegal in India (Chadha and Kaur 2017). Any attempt to artificially inflate or deflate volatility is considered market manipulation and could lead to significant legal and reputational consequences for the investors involved (De and Chakrabarty 2016). Securities laws prohibit the manipulation of volatility since it could distort market prices and confuse other market participants. The Securities and Exchange Board of India (SEBI), a statutory organization established by the SEBI Act of 1992 and the primary watchdog of the Indian capital market, actively monitors any such activities of institutional investors to detect and prosecute any instances of manipulation (De and Chakrabarty 2016). The Securities and Exchange Board of India (SEBI) enacted new regulations in 2020 that mandate exchanges to keep a watch on and report instances of attempted or apparent manipulation of stock volatility or option prices. In accordance with the regulations, exchanges must also have systems and procedures in place to identify and stop such unlawful market participant behavior (Chadha and Kaur 2017).

For investors, stock mispricing can have serious repercussions because it may result in unforeseen losses or missed possibilities for gain (Pranesh et al. 2017). For instance, if an option buyer overpays for a contract because the implied volatility is overstated, they may incur more losses than anticipated if the option expires out of the money (Fan and Feng 2022). In cases involving options trading and volatility, the Securities and Exchange Board of India (SEBI) has also taken enforcement action against people and organizations suspected of engaging in price manipulation. Several firms were fined in 2021 by the Securities and Exchange Board of India (SEBI) for engaging in manipulative trading activities in stock futures contracts (Tanty and Patjoshi 2016).

Several high-profile examples of alleged stock price manipulation have occurred in recent years (Sridhar and Sanagavarapu 2021). As an example, the Securities and Exchange Board of India (SEBI) charged a trader in 2018 with engaging in a plan to artificially exaggerate the volatility of an exchange-traded fund and manipulate the values of options contracts. The trader is accused of placing false orders for options contracts and engaging in other manipulative trading practices (Sridhar and Sanagavarapu 2021). Another instance was a group of investment banks that were fined by the Securities and Exchange Board of India (SEBI) in 2019 for manipulating the prices of government bond futures contracts, which in turn affected stock volatility. The banks were accused of engaging in collusion to manipulate the market, including using spoofing tactics (De and Chakrabarty 2016). Overall, price volatility tampering is a serious violation of securities laws and can have significant financial and reputational consequences for those involved (Xu et al. 2001). To protect the integrity of financial markets, regulators around the world are aggressively trying to prevent and prosecute such activities (Sridhar and Sanagavarapu 2021).

This study aims to investigate any dynamic associations between options’ implied volatility, FIIs’ net buying pressure, and FIIs’ impact on implied volatility. The findings of this study may be useful to researchers and academicians in understanding how institutional investors influence the implied volatility term structure that leads to option mispricing in the Indian derivatives market.

The remaining structure of this article is as follows: Section 2 deals with reviewing the literature. Section 3 explains the methodology of the study. Section 4 elaborates on the econometric analysis, results, and discussion, and Section 5 and Section 6 deal with the policy implications of this study and the conclusions drawn. Section 7 lists some of this study’s limitations and the scope for further studies.

2. Review of the Literature

This study investigates how institutional investors can impact the implied volatility of options to increase their stock market gains. Previous research has examined the manipulation of stock prices by impacting stock return volatility to make abnormal profits in the stock market (Chadha and Kaur 2017). Chadha and Kaur (2017) developed a mathematical model that shows how traders can abnormally profits from the manipulation of stock prices, and they provide evidence of such manipulation in real-world data. In another study, authors examine several methods for manipulating volatility as well as examples of these strategies in the emerging stock markets (De and Chakrabarty 2016). There is little research on how insider trading and volatility manipulation are related (Lorig et al. 2014). Speculators can influence prices by creating and utilizing information asymmetries as Pranesh et al. (2017) explored in the practices of speculative trading, particularly on stock market price manipulation.

Shaikh and Padhi (2014) presented empirical evidence of stock price manipulation in real-world data. They studied the effect of market manipulation on option prices using multivariate vector autoregression models that show how institutional investors can create artificial demand for options to earn abnormal profits. Tanty and Patjoshi (2016) examined the effects of buying pressure from the large options trades on realized volatility, implied volatility stylized pattern, and volatility smile. Vardhan and Sinha (2016) examined the relationship between option market volume liquidity and stock price volatility, including the impact of volatility, which provides empirical evidence on the stock market activities that can affect stock price volatility behavior, and they discuss the implications for market efficiency and regulation.

Votano et al. (2004) in their study found that the inflows and outflows of foreign institutional investors in the Indian equity market are significantly influenced by the domestic equity market returns and the currency exchange rate has no effect on FII inflows, but the outflows are influenced by its change. Despite global recessionary conditions, both purchases and sales of FIIs have steadily increased (Bollen and Whaley 2004). It was also found that even though the flows are highly correlated with the equity returns, they are more likely an influence rather than a cause of the returns (Venkatesh et al. 2021). The key findings of Bachmann and Bolliger (2001) were changes in stock return volatility that were directly related to net buying pressure from public order flow, and that simulated delta-neutral option-writing trading strategies generate abnormal returns that match the deviations of the implied volatility above realized historical return volatilities (Wu et al. 2022). They explored that any changes in the implied volatility of the S&P 500 Options Index are most strongly affected by the buying pressure for index puts, while changes in implied volatility of stock options are dominated by the demand for call options. These results support the limits of the arbitrage hypothesis on the assumed hypothesis. Three major findings of (Vardhan and Sinha 2016) are as follows, FII flows are driven by implied volatility in the Indian market, the exchange rate of USD/INR is an important factor that impacts FII flows into the country, and the returns in the Indian stock market are also a contributing factor affecting FII investment, and the exchange rate of USD/INR also affects the expected volatility. These findings suggest that FII investments affect countries’ economies through their influence on factors such as exchange rates and foreign exchange reserves. According to research by Dennis and Strickland (2002), factors like institutional investments do not significantly affect the VIX (volatility index), a proxy for implied volatility. The study also confirms that the implied volatility changes prior to the release of macroeconomic news and falls or adjusts after the announcement. Furthermore, the study found that the implied volatility in the U.S. market causes volatility in the Finnish market, but the implied volatility in the Finnish market does not have any impact on the U.S. market. The direction-learning behavior refers to the tendency of investors to learn from the direction of past price changes and adjust their trading strategies accordingly. Ryu et al. (2022) found that foreign institutional investors are the most directionally informed market participants in the KOSPI200 options market. This indicates that they are more inclined to shift their net demand for options in accordance with the direction of prior price changes, which in turn has an impact on the dynamics of implied volatility. The empirical investigations demonstrate volatility behavior and emphasize its significance in understanding the dynamics of the options market. The study provides several key empirical findings: First, the intraday relationship between expected volatility and net buying pressure is best explained by the direction-learning hypothesis. Second, FIIs strongly support the direction-learning hypothesis. Third, domestic investors trade with mixed purposes in the KOSPI200 options market. Finally, foreign investors’ net demand had significant effects both before and after the market reform in 2012 (Venkatesh et al. 2021), whereas domestic individuals’ net demand partially explains implied volatility dynamics only after the reform (Ryu et al. 2022). Ali et al. (2023), in their study, examined investors’ overall trading behavior during the COVID-19 period and supported the well-known persistence of investor trading, while findings also supported positive-feedback trading by foreign institutional investors and negative-feedback trading by individual retail investors. To demonstrate how the COVID-19 situation affects stock market return volatility in different countries, the article provides evidence that institutional investors profited from the negative bubble from March to April 2020, whereas foreign institutional investors liquidated at negative bubble levels (Ali et al. 2023).

Thus, the research that has been conducted on volatility and institutional investor behavior has produced inconsistent outcomes. The empirical results of certain studies indicate that volatility has an impact on institutional investors’ behavior, whereas the empirical findings of other studies indicate the opposite. Institutional investors, including FIIs, are large investors in the Indian equity derivatives market in terms of volume, trade, and capital flows (Sridhar and Sanagavarapu 2021). Indian domestic investors are highly dependent on the investment behavior of FIIs in both the cash and derivatives segments of the NSE (Mall et al. 2014). Thus, an empirical investigation is needed to understand the investment practices of FIIs and the effects of these practices on the implied volatility of options. Some of the literature already shows evidence of the impact of the investment behavior of FIIs on stock price volatility; however, any solid empirical study on the Indian derivatives market is missing to explain the investment behavior of FIIs and the underlying volatility of options in the world largest equity derivatives exchange, i.e., the National Stock Exchange of India (NSE). Thus, the objective of this study is to fill the gap in the literature on the impact of FII’s net buying pressure on implied volatility changes, which leads to the mispricing of options.

3. Methodology

This study was conducted to investigate the impact of foreign institutional investors (FIIs) on the Indian capital market, which continuously affects the price of options by affecting market volatility. This empirical study applies the financial econometrics model to examine the FIIs’ open interest and implied volatility dynamics using ten years of weekly data from the year 2012 to 2021. The data collected for the study are secondary in nature. The FIIs’ open interest, Nifty 50 index spot price, and exchange rates (Indian Rupees to U.S. Dollar) were extracted from the CNBC Bloomberg database and the implied volatility of the Nifty Index (India VIX) was obtained from the NSE real-time online data feed on special request from the NSE databank service. This study explores the long and short-run causality between the implied volatility and FIIs’ behavior in the Indian equity derivatives market.

3.1. Variables Used in This Study

• FIIs’ Open Interest (FIIs_OI): This is the total number of outstanding options contracts held by foreign institutional investors as market participants each day or week. It is a measure of FIIs’ flows of money into options and futures markets. To maximize their returns and reduce risk, FIIs frequently change their positions in the Indian capital market, which causes the options to get mispriced (over or undervalued).
• Implied Volatility (Implied Vol): Implied volatility is a forecast of future expected volatility in the options market over the next 30 calendar days. In option pricing, it is one of the important components in any asset pricing model such as the Black–Scholes option pricing model. Here, in this study, ten years of weekly data on implied volatility were collected to examine the possible FII flows in the Indian derivative market.
• Return on Nifty (Niftret): From the previous literature, it is clear that there is a strong relationship between the Nifty return and the FII investment flows in India. The Nifty return was measured using the weekly lognormal return on the Nifty 50 spot price.
• U.S. Dollar-Rupee (USD-INR) Exchange Rate: A change in exchange rates affects the flow of funds from foreign institutional investors in India and can affect equity returns and the net demand for options. The INR-USD exchange rate on a weekly basis was collected from the CMIE Prowess database. The Indian rupee and the U.S. dollar were used as a proxy for exchange rates as the U.S. dollar is a universally acceptable currency and is easily convertible into other currencies.

3.2. Testing of Stationarity of All-Time Series Data

Stationarity refers to a property of a time series in which its statistical properties, such as mean, variance, and autocorrelation, remain constant over time. In other words, a series without a seasonal component is said to be stationary in a time series. Stationarity is a prerequisite for performing various statistical tests and for hypothesis testing on time series data. If a time series is non-stationary, it may require transformations to achieve stationarity. Common transformations include differencing, logarithmic transformations, or seasonal adjustments. Tests such as the Augmented Dickey-Fuller (ADF) test or the Phillips-Perron (PP) test are commonly used to test for stationarity (Org and Politis 2013). These tests help in determining the presence of unit roots, which indicate non-stationarity. The ADF and PP tests have been applied to all variable series to test their stationarity using the standard equation:

$$Y_t=\mathsf{\alpha }+{\beta }_t+\mathsf{\varphi }·Y_{t-1}+{ϵ}_t$$

where $Y_t$ is time series data on which we can perform a linear regression against t and $Y_{t-1}$, and test whether ϕ is different from zero. If ϕ = 0, then it is a random walk process; otherwise, it is a stationary process (Harris 1992). The ADF test is an extension of the Dickey–Fuller test and considers the possibility of multiple unit roots in the series.

The null hypothesis is that the series is non-stationary and has a unit root, i.e., ϕ = 1, and the following null hypothesis was investigated using the ADF test (Org and Politis 2013):

H0. 

The time series is non-stationary and has a unit root.

H1. 

The time series is stationary.

A more thorough theory of unit root non-stationarity has been developed by Phillips and Perron. Their tests are comparable to the ADF tests but include an automatic correction to the ADF method to support autocorrelated residuals.

3.3. Granger Causality Test

The Granger causality test is a statistical test used to determine whether one-time series variable can be used to predict another time series variable (Diks and Panchenko 2006). This test indicates Granger causality when one variable is helpful in predicting another variable. It was proposed by Clive Granger in 1969 and since then has become the most acceptable econometric method (Hendry 2017). The Granger causality test’s basic equation entails estimating autoregressive models and determining the significance of the variables’ lagged values (Hendry 2017). The test is based on the concept of temporal precedence, which suggests that a cause must precede its effect in time (Diks and Panchenko 2006). Assume that we have two time series variables, Y and X, and that we want to figure out whether X Granger causes Y. The Granger causality test is based on the following OLS regression model:

$${\mathrm{Y}}_{\mathrm{i}}=\mathsf{\alpha }+{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\mathsf{\alpha }\mathrm{j}·{\mathrm{Y}}_{\mathrm{i}-\mathrm{j}}+{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\mathsf{\beta }\mathrm{j}·{\mathrm{X}}_{\mathrm{i}-\mathrm{j}}+\mathsf{ϵ}$$

(1)

where

• ${\mathrm{Y}}_{\mathrm{i}}=$ dependent variable;
• ${\mathrm{X}}_{\mathrm{i}-\mathrm{j}}$ = independent variables;
• α = constant term;
• $\mathsf{\alpha }\mathrm{j}$ = coefficient of the lagged value of Y;
• $\mathsf{\beta }\mathrm{j}$ = coefficient of the lagged value of X;
• ∈ = error terms for the dependent variable.

Null Hypothesis (${\mathit{H}}_{\mathbf{0}}$).

The lagged values of variable X do not provide any significant information in predicting variable Y.

Alternative Hypothesis (${\mathit{H}}_{\mathit{A}}$).

The lagged values of variable X do provide significant information in predicting variable Y.

The general steps to conduct a Granger causality test are as follows:

The test involves comparing the significance of the coefficient β in the model that includes both Y and X to the model that includes only Y. Statistical tests, such as the F-test or likelihood ratio test, are used to determine whether the addition of the lagged values of X improves the prediction of Y significantly. If the coefficient β is found to be statistically significant, it suggests that X Granger causes Y, indicating a causal relationship between the variables (Hendry 2017).

3.4. Cointegration Test and Vector Autoregression (VAR)

The cointegration test is a statistical property that estimates the long-term equilibrium association between non-stationary time series variables. This is applied to variables that are individually non-stationary and exhibit a stable association when combined (Lütkepohl et al. 2004). The test helps to determine whether a set of variables is cointegrated and has a long-term relationship that persists over time. This estimation is important because it helps to analyze the dynamics of variables that are individually non-stationary but have a stable combination (Naidu et al. 2017). Johansen’s cointegration model, developed by Soren Johansen, is a widely used method for estimating and testing cointegration relationships among multiple time series variables. It is an extension of the Engle-Granger two-step method and allows for the estimation of multiple cointegrating vectors (Hendry 2017).

The Vector Autoregression (VAR) model is a popular and powerful econometric model used to analyze and forecast multivariate time series data (Bashir and Wei 2018). It extends the autoregressive model to multiple variables, allowing for the simultaneous analysis of their interdependencies and interactions (Bashir and Wei 2018; Nkoro and Uko 2016). In a VAR model, each variable in the system is modeled as a linear combination of its own past values and the past values of all other variables in the system. The general form of a VAR (p) model with p order is as follows (Naidu et al. 2017):

$$\mathrm{Yt}=\mathrm{c}+{\mathsf{\Phi }}_1· \left({\mathrm{Y}}_{\mathrm{t}-1}\right)+{\mathsf{\Phi }}_2 {(\mathrm{Y}}_{\mathrm{t}-2})+\dots +{\mathsf{\Phi }}_{\mathrm{p}}({\mathrm{Y}}_{\mathrm{t}-\mathrm{p}})+{\in }_{\mathrm{t}}$$

(2)

where

• Yt is a vector of time series variables at time t;
• c is a constant term or intercept vector;
• Φ₁, Φ₂, …, Φ_p are coefficient matrices representing the lagged values of the variables up to lag order p;
• ${(\mathrm{Y}}_{\mathrm{t}-1})$, ${(\mathrm{Y}}_{\mathrm{t}-2})$, …, $({\mathrm{Y}}_{\mathrm{t}-\mathrm{p}}$) are lagged values of the variables;
• ε(t) is a vector of error terms at time t.

Each element of the vector Y(t) in a VAR model is regressed based on its own lagged values and the lagged values of the other elements of the system. The number of earlier time periods considered in the model is indicated by the lag order p (Series 2006).

The VAR model captures the dynamic relationships and interdependencies between the variables in the system. By including lagged values of the variables as predictors, it accounts for the feedback effects and short-term dynamics among them. In this study, an effort has been made to study the dynamic causality between the implied volatility and the investment behavior of FIIs in the Indian derivatives market. Thus, dynamic VAR is a suitable method to model the time series variables. VAR models are widely employed in economics, finance, and related fields for forecasting, policy research, and examining the association between time series variables. It provides a flexible framework to analyze the interactions and transmission mechanisms among the variables.

The VAR model allows for the estimation of the coefficients in the system, which provides insights into the dynamic relationships between the variables (Series 2006). This study examines the relationship between FII investment behavior and implied volatility using the following VAR models:

$${\mathrm{F}\mathrm{I}\mathrm{I}\_\mathrm{O}\mathrm{I}}_{\mathrm{t}}={\mathsf{\alpha }}^{\prime }+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\beta }}_{\mathrm{i}}{\left(\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{V}\mathrm{I}\mathrm{X}\right)}_{\mathrm{t}-1}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}\mathsf{\gamma }{\mathrm{i}}^{\prime }·{(\mathrm{F}\mathrm{I}\mathrm{I}\_\mathrm{O}\mathrm{I})}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}\mathsf{\theta }\mathrm{i}{\mathrm{N}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{t}}_{\mathrm{t}-1}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}\mathsf{\pi }\mathrm{i}·{\mathrm{D}\left(\mathrm{U}\mathrm{S}\mathrm{D}\right)}_{\mathrm{t}-1}+{{\mathsf{\epsilon }}^{\prime }}_{\mathrm{t}}$$

(3)

$${\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{V}\mathrm{I}\mathrm{X}}_{\mathrm{t}}={\mathsf{\alpha }}^{\prime }+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\beta }}_{\mathrm{i}}{\left(\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{V}\mathrm{I}\mathrm{X}\right)}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}\mathsf{\gamma }{\mathrm{i}}^{\prime }{·(\mathrm{F}\mathrm{I}\mathrm{I}\_\mathrm{O}\mathrm{I})}_{\mathrm{t}-1}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}\mathsf{\theta }{\mathrm{N}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{t}}_{\mathrm{t}-1}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}\mathsf{\pi }·{\mathrm{D}\left(\mathrm{U}\mathrm{S}\mathrm{D}\right)}_{\mathrm{t}-1}+{{\mathsf{\epsilon }}^{\prime }}_{\mathrm{t}}$$

(4)

4. Results Analysis and Discussion

4.1. Test of Stationarity

The unit root stationarity condition of all data series was tested using the Augmented Dicky-Fuller (ADF) test and the Phillips-Perron (PP) test. The results are as below

Table 1. Test results of stationarity of data.

	ADF Test		PP Test
	t-Stat	Prob.	t-Stat	Prob.
FII_OI	−19.86627	0.0000	−20.26125	0.0000
Implied_vol	−5.706235	0.0000	−4.826477	0.0001
Niftret	−22.57758	0.0000	−22.86969	0.0000
D(USD_INR)	−12.61767	0.0001	−37.63333	0.0003

** 1% level of significance. * MacKinnon (1996) one-sided p-values.

.

All the data series are stationary at level except the USD_INR exchange rate, which is stationary at first difference (Table 1). The estimated values of foreign institutional investors’ open interest (FIIs_OI), implied volatility (implied vol), and CNX Nifty return (Niftret) as reported by the ADF test at the level are (−19.86627), (−5.706235), and (−22.57758), respectively. The estimate value of the USD_INR exchange rate at the first difference is (−12.61767). The test statistics exceeds the critical value at 1%, and hence, the null hypothesis is rejected for all variables. Therefore, all variables are said to be stationary and ready for the Granger Causality Test.

4.2. VaR lag Length Selection

The selection of optimum lag length is the main challenge in VAR modeling. Many lag selection criteria are used to select the optimal lag length of variables such as the likelihood ratio (LR), final prediction error (FPE), Akaike information criteria (AIC), Schwarz information criteria (SC), and Hannan-Quin information criteria (HQ).

Here is inferred that the lag length l is found to be significant under the Schwarz information criteria (SC) and the Hannan-Quinn information criteria (HQ), whereas lag length 2 is significant under the other criteria (

Table 2. VAR lag length order selection.

Sample:529
Included Observation: 520
Lag	Log L	LR	FPE	AIC	SC	HQ
0	−4400.055	NA	266.9774	16.93867	16.97139	16.95149
1	−2921.932	29.2781	0.964273	11.31512	11.47873	11.37922 *
2	−2898.654	45.7511 *	0.937664 *	11.28713 *	11.58163	11.40251
3	−2890.635	15.6361	0.966921	11.31783	11.74321	11.48447
4	−2877.844	24.7466	0.978978	11.33017	11.88644	11.54808
5	−2854.739	44.3430	0.952668	11.30284	11.99	11.57203
6	−2847.45	13.8771	0.985246	11.33635	12.15439	11.65681
7	−2836.463	20.7496	1.004592	11.35563	12.30456	11.72736
8	−2817.603	35.3251	0.993822	11.34463	12.42445	11.76763

* Indicates lag order selected by the criterion. LR: sequential modified LR test statistics (at 5% level). FPE: Final prediction error. AIC: Akaike information criterion. SC: Schwarz information criterion. HQ: Hannan-Quinn information criterion.

). Therefore, lag length 1 is selected for testing the pairwise causality in terms of all tests for the full sample period. A higher lag length cannot be tested for two reasons, i.e., a higher lag may be too long for the analysis of implied volatility and FII investment flows due to the large probability of change and taking a higher lag length will unnecessarily decrease the degree of freedom.

4.3. Granger Causality Test

The Granger causality test was performed to explore the short-run dynamic causal relationship between the data series. The results (

Table 3. Pairwise Granger causality test.

Null Hypothesis	Obs.	F-statistics	Prob.
Implied Vol does not Granger cause FII_OI	527	3.0163	0.07980
FII_OI does not Granger cause Implied Vol		0.3187	0.07200
NIFTRET does not Granger cause FII_OI	526	0.6188	0.03900
FII_OI does not Granger cause NIFTRET		1.4425	0.23730
D(USD_INR) does not Granger cause FII_OI	526	0.6483	0.52330
FII_OI does not Granger cause D(USD_INR)		0.0587	0.97840
NIFTRET does not Granger cause Implied Vol	526	2.1627	0.11600
Implied Vol does not Granger cause NIFTRET		2.2862	0.00050
D(USD_INR) does not Granger cause Implied Vol	526	1.9170	0.14810
Implied Vol does not Granger cause D(USD_INR)		0.2896	0.74870
D(USD_INR) does not Granger cause NIFTRET	526	0.6885	0.50280
NIFTRET does not Granger cause D(USD_INR)		0.8088	0.44600

) suggest that (p-value < 0.05) there was a unidirectional causality between the FII’s open positions and implied volatility during the study period. This would imply that the FIIs’ positions and buying pressure Granger caused the implied volatility but the change in implied volatility did not Granger cause the FIIs. Furthermore, there was unidirectional causality found between the Nifty Index return and the FII investment behavior. This indicates that the NSE Nifty index return attract FIIs’ investment in the equity derivatives market.

4.4. Johansen’s Unrestricted Cointegration Rank Test

The Johansen’s unrestricted cointegration rank test is used to identify the long-term relationship within non-stationary variables. In time series analysis, Johansen’s unrestricted cointegration suggests that the variables move together in the long run even though they may exhibit short-term deviations from each other.

The Johansen’s cointegration test allows the testing of hypotheses by considering them effectively as restrictions on the cointegrating vector. The first thing to note is that all linear combinations of the cointegrating vectors are also cointegrating vectors. Therefore, if there are many cointegrating vectors in the unrestricted case and if the restrictions are relatively simple, it may be possible to satisfy the restrictions without causing the Eigenvalues of the estimated coefficient matrix to change at all. However, as the restrictions become more complex, “renormalization” will no longer be sufficient to satisfy them, so imposing them will cause the Eigenvalues of the restricted coefficient matrix to be different from those of the unrestricted coefficient matrix. If the restrictions implied by the hypothesis are nearly all already present in the data, then the Eigenvectors will not change significantly when restrictions are imposed. On the other hand, if the restriction on the data is severe, then the Eigenvalues will change significantly compared with the case when no restrictions were imposed. In applying Johansen’s cointegration procedure, the researcher allowed for a linear deterministic trend.

In

Table 4. Johansen’s unrestricted cointegration rank test result.

Hypothesized No. of CEs	Eigenvalue	Trace Statistics	Critical Value (0.05)	Prob.	Max. Eigen Statistics	Critical Value at 0.05	Prob.
None *	0.286300	362.6951	47.85613	0.0000	176.4038	27.58434	0.0000
At most 1 *	0.150565	186.2913	29.79707	0.0000	85.34524	21.13162	0.0000
At most 2 *	0.127151	100.9461	15.49471	0.0000	71.12438	14.26460	0.0000
At most 3 *	0.055425	29.82167	3.841465	0.0000	29.82167	3.841465	0.0000

* Trace test indicates 4 cointegration equations at the 0.05 level. ** Max-Eigenvalue tests indicate 4 cointegration equations at the 0.05 level. *** Denotes rejection of the hypothesis at the 0.05 level.

, the test is significant, and the null hypothesis is rejected at a 5% level of significance. This implies that the series are correlated, and the VAR model can be used for long-run and short-run estimates.

4.5. VAR Analysis

Vector Autoregression (VAR) is commonly used to forecast interrelated time series and to analyze the dynamic impact of random disturbance on the system of variables. The VAR approach is needed for structural modeling by considering every endogenous variable in the system.

From the result of the above VAR analysis (

Table 5. Structural vector-autoregression (VaR) result.

Dependent Variable: FIIs_OI
	Coefficients	SE	t-Statistics
FIIs_OI (-1)	0.129050	0.04369	(2.95370)
FIIs_OI (-2)	0.020835	0.04335	(0.48066)
IMPLIED_VOL (-1)	0.010742	0.00581	(1.85009)
IMPLIED_VOL (-2)	−0.013030	0.00575	(−2.26443)
NIFTRET (-1)	−0.009544	0.01067	(−0.89411)
NIFTRET (-2)	−0.006507	0.01074	(−0.60615)
D (USD_INR (-1))	0.008265	0.01315	(0.62841)
D (USD_INR (-2))	0.013384	0.01272	(1.05197)
$R^2$	0.23489
$\mathrm{Adj}. R^2$	0.119874
Dependent Variable: IMPLIED_VOL
	Coefficients	SE	t-Statistics
FIIs_OI (-1)	0.628272	0.32218	(5.70852) *
FIIs_OI (-2)	0.620193	0.31970	(5.68876) *
IMPLIED_VOL (-1)	1.137908	0.04281	26.5776
IMPLIED_VOL (-2)	−0.236570	0.04243	(−5.57523)
NIFTRET (-1)	0.367754	0.17871	(8.13130) **
NIFTRET (-2)	−0.003233	0.07916	(−0.04084)
D (USD_INR (-1))	−0.095793	0.09699	(−0.98765)
D (USD_INR (-2))	−0.173482	0.09382	(−1.84914)
$R^2$	0.966553
$\mathrm{Adj}. R^2$	0.864488

** Significant at 1% level. * Significant at 5% level.

), it is evident that the first and second lags of the FIIs’ open interest positively related to its own first and second difference and the first and second lags of the implied volatility and the first lag of the Nifty returns. Here, estimates clearly show that FII investment behavior has a high explanatory power in explaining the implied volatility term structure (where the adjusted R square value is 0.96448). The VAR model describing the FIIs’ buying pressure has a significant impact on the implied volatility’s structural changes. On the other hand, the FIIs’ open interest as a dependent variable has a very low explanatory power (where the adjusted R square value is 0.019874), and hence, the implied volatility does not significantly influence the FIIs’ capital flow. In the second finding, the implied volatility and Nifty returns exhibit a significant long-term positive association, and the independent variable (Nifty return) has the ability to explain the dependent variable (implied volatility).

5. Contributions and Implications of This Study

The outcome of this study reveals that FIIs do influence the implied volatility of options in the Indian derivatives market. There is barely any study on the dynamic behavior of implied volatility of options due to a change in the positions of foreign institutional investors in India, which is the uniqueness or novelty of this research study. The results of this study assist options traders, policymakers, and retail investors to understand how FIIs influence asset mispricing and the volatility of the derivatives market. This study has its own importance due to the significant amount of capital flows by FIIs in the Indian equity market that affect market volatility and investors sentiment.

6. Conclusions

This empirical study explores the dynamic relationship between the investment behavior of FIIs and the implied volatility of options in India’s equity derivatives market. The study covers a ten-year period to examine any significant impact of FII open interest, which could lead to mispricing of options. A number of studies conducted on the association between FIIs’ investment and realized volatility in the equity market have argued for both positive and negative associations, but rarely any study has explained the significant relationship between FII investment flows and implied volatility movements in the Indian equity derivatives market.

The findings of this study demonstrate how FIIs’ net open interest affects implied volatility’s term structure and how the performance of the Nifty Index affects FIIs’ net capital flows in the Indian derivatives market. As a result, the unexpected shift in implied volatility due to net buying pressure raises the probability of the options premium being mispriced. In the past, studies on developed countries like the U.S., China, and the UK, among others, have produced contradictory results about the association between implied volatility and institutional investors. The institutional investors, including FIIs are the major source of capital flows in the Indian stock market, which manipulates the assets price by influencing implied volatility in order to maximize their gain and to reduce their risk. This study is important as FII investments are one of the major contributors besides domestic institutional investors in the Indian stock market. This analysis supports the notion that FII participation influences options’ implied volatility and, consequently, market sentiment.

The results of this study may be utilized by options traders, hedgers, speculators, investment bankers, and retail investors to understand the influence of big investors and their impact on market sentiments and asset mispricing. The outcomes of this study may be used by regulators to better understand how institutional investors affect the equity derivatives market, which might help them in developing and enacting regulations to prevent acts that fall under the category of market manipulation. The findings of this study may be used by researchers to further explore other factors that have an impact on option premiums and may contribute to option mispricing in the derivatives market.

7. Limitations and Scope for Further Study

The study is focused on the Indian equity derivatives market, but it is generic in nature, and its findings are transferable to all capital markets worldwide because institutional investors have an impact on stock and index prices not only in the derivatives segment of the capital market but also in the cash segment. Researchers may use the findings of this study to further investigate the mispricing of options caused by institutional investors’ investment decisions.