Academic journal article Business: Theory and Practice

The Behavior of Option's Implied Volatility Index: A Case of India VIX

Academic journal article Business: Theory and Practice

The Behavior of Option's Implied Volatility Index: A Case of India VIX

Article excerpt

Introduction

Implied volatility is the inversion of the Black-Scholes option pricing model, and it is the function of options' traded price; time-to-expiration; risk-free-rate-of-interest and dividend yield; strike price and spot price of underlying. Under the rational expectation and market efficiency, implied volatility is the expectation of the future stock market volatility. The market participant trade into options to hedge the market holdings and risk management, hence the expectation of the investors gauged into the price of options (call/put) and the same traded price used to calculate the implied volatility. Therefore, implied volatility is the best estimate of future realized return volatility (Christensen, Prabhala 1998; Hansen 2001; Shaikh, Padhi 2013, 2014a, 2014b) for 30 days horizon (one month option).

The information content of implied volatility as the market's expected volatility has motivated to construct the volatility index, which is often referred as the "Investor's-fear-gauge-index" (Whaley 2000). The Chicago Board of Options Exchange (CBOE) has started calculating implied volatility index since 1993 known as VIX. The VIX is the premier barometer of the investor's sentiment and the market volatility. The CBOE has calculated more than 19 volatility indices apart from VIX, which means the 30-day implied volatility of different securities. The volatility indices are the key measures of market expectation in near-term calculated based on the listed option prices. From 2003, CBOE has started calculating VIX based on S&P 500 stock index, and also calculate volatility of volatility index (i.e. VVIX) based on the options written on VIX index.

The National Stock Exchange (NSE) of India limited has started trading in options from 2001 based on the S&P CNX Nifty equity index. India's first volatility index has been started and calculated since November 2007, and this volatility index is available to the public on real time basis. India VIX signifies the investors sentiment in near-term for the next 30 calendar days. India VIX (2007) uses the same methodology as developed by CBOE for VIX (2003) methodology. The market participant, analyst and academician have been intrigued by the volatility index; the reason is that stock indices and implied volatility indices are negatively correlated. The high level of implied volatility index signifies towards oversold market condition. The correlation between stock index and volatility index hovers in the rage of-0.70 to -0.90.

Unlike the previous studies on the seasonal anomalies in term of stock returns, exchange rate and fixed income securities, the aim of our study is to analyze the behavior of implied volatility in the emerging market like India. The seasonality of India VIX (herein after IVIX) has been assessed like day-of-the-week, month-of-the-year and options expiration effects.

There are quite good number of attempts (e.g. Dzikevicius, Stabuzyte 2012; Martinkute-Kauliene 2013; Shaikh, Padhi 2013; Padhi, Shaikh 2014) that deals with the market efficiency, sensitivity of options and forecasting, investor sentiment and information content of option prices. However, we do not find any study that deals with the option volatility and stylized nature of implied volatility on Indian derivatives market; hence, this is an attempt in this direction to fill-up the gap. Moreover, recent studies (e.g. Zilinskij, Rutkauskas 2012; Lukasevicius et al. 2013; EvrimMandaci et al. 2013; Stadnik 2013; Vilkancas 2014; Shaikh, Padhi 2014a, 2014b, 2014c) deal on the firm's performance and potential return on investment; dynamics of stock price cycle; determinants of stock market dynamics in advanced and emerging economics; random walk and stock prices; portfolio optimization with respect to omega function; volatility index and forecasting performance of emerging market's volatility index. The studies are in association with the various issues on the stock market development and portfolio optimization, our study identifies the gap on the emerging market volatility index in terms of behavior of volatility index as the expected volatility of the future stock market realized volatility. …

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