Cornell and French used daily data to investigate the "cost of carry" model in stock index futures pricing and arbitrage opportunities, and discovered that there is mispricing. A lot of research looks into arbitrage trading opportunities and the disparities between theoretical and actual option prices. Arbitrage is predicated on the reality of a frictionless market where traders perform transactions whenever the prices of options and futures contracts stray from their respective fair values. However, there are various barriers to the time-arbitrage process, including operational and regulatory constraints; transaction costs; the risk inherent in the process; margin risk; short-selling restraints; and even more real-time hazards. In his research, Sundaresan discovered that arbitrageurs lose "interest earnings" on the proceeds of short-sale equity when the pricing band goes below the fair price. Lazibat and Bakovic state that price risk is one of the most important and many foreign trade companies face [11]. This can be solved by concentrating on options Greeks, usually considered as foremost factors for speculation, which can successfully be implemented for price risk elimination. Yuh-Dauh and Teng in their research found that risk hedging through option Greeks is less varied from the authentic result, which helps predictions by using various formulas numerically which are unbiased [12]. Xishen and Xiaoke state that the Greek letter measures the sensitivity of an option price, relating to the changes in the value of a given underlying asset's price, value, time, etc. Jelena explores market risk management from the options trader perspective and explains how to describe the risk characteristics of European stock option contracts by applying the Greeks. Kakati experimented with the pricing option contracts for ten Indian stocks using Black-Scholes (BS) model, which is considerably mispriced in many cases. However, it is hard to draw generalized conclusions from research studies since the limitations are restricted to only ten Indian stock option contracts [13]. Saravanan and Pradeep state that the accuracy of the Black-Scholes option pricing model and its relation to market prices also helps in finding whether the stock options are properly priced. Khan et.al found that the credit rate in India is being assessed using the Black-Scholes-Merton model which resulted in an unsolved dispute between liquidity premium and transaction costs of market spreads [14].
Sanjana observed that trading options and option strategies are based on risk factors and can only be predicted using Greeks [15]. Paired sample T-test proves that there is no significant difference between the expected option prices calculated through the Black- Scholes model and the market price of options Panduranga. It is conditional that the model is relevant for cement stocks only. Whereas Nagendra and Venkateswar state that the robustness of the Black-Scholes model in pricing, and stock options in India and that pricing is further improved by incorporating implied volatility in the model [16]. Nilakantan and Shalini in their study observed that the Black-Scholes model is defective notwithstanding its prevalent use in hedging because it predicts continuous hedging and zero transaction cost. The research work of Rajanikanth and Lokanadha explored the price of a European option in the future and its sensitivity through Greek letters and measure the risks using delta, vega, theta, rho, and gamma. Muthusamy and Vivek identified that in most contracts, the option prices calculated are different from the market value of the contract [17]. However, many studies suggest that the BSM model is appropriate for estimating the European option's price, and also it provides an arbitrage opportunity for the financiers in India. Bhardwaj states that the financial market in India is to grow rapidly in the long run, owing to the developments brought in by the Indian government [18]. Even though a derivative contains risk factors, investors have to handle the situation carefully so that they can do wonders. The effectiveness of commonly used Greeks; (Delta, Gamma, Theta, Vega, and Rho) and their significance in managing various types of risks is commonly associated with an option contract was stated by Kumar in his research. Therefore, patrons use the Greeks under the Black-Scholes model framework as a benchmark for appropriately adjusting option positions, enabling them to manage risks [19].
In this empirical paper, the focus is on the Nifty index option and analyzes the impact of each Greek option from the buyer's perspective [20]. This paper also includes the estimated daily Nifty option value (both call and put) and option Greeks, which expired on 25-Nov-18 within the framework of the Black-Scholes option pricing model. For this analysis, four strike prices 10100, 10900, 11100, and 11300 have been selected. Finally, the estimated Greeks value helps in understanding the different dimensions of the risk in a Nifty option position enabling successful management of risks [21].
Objectives of the study
The following objectives are set based on the reviews collected for this paper:
• To estimate the Nifty option price and Greeks is using the Black- Scholes model for each selected strike price. • To examine the different dimensions of risk involved in Nifty option positions, using Greeks.
Research methodology
Determining the strike price is very important for an options investor since it has a very momentous impact on the profitability of an option position [22]. Working on necessary base calculations to select the optimum strike price is a very necessary step to improvise the chances of accomplishing options trading. The sample of the study covers the daily European call and Put Nifty option price for strike prices 10100, 10900, 11100, and 11300 which expired on 25- Nov-2018. This secondary data is collected from 01-November-2018 to 25-November-2018 from the NSE website. The researcher used Nifty option Greeks and estimates within the Black-Scholes model framework for selected strike prices, using an available online calculator for Black-Scholes option pricing model and option Greeks [23].
The researcher has used the online calculator to estimate the daily implied volatility. As per the Black-Scholes, option pricing model assumptions implied volatility and risk free interest rate remains constant [24]. But in this empirical paper, we consider fluctuation and change in the implied volatility for each day from 1-November-2018 to 25-November-2018. Implied volatility is taken as fluctuating input variables (%), underlying Nifty spot value, and days until expiration; the risk free interest rate is 10% as per the NSE website. The dividend yield is zero since the Nifty option is an index option [25].
Formulae or models used
Black-Scholes option-pricing model: (Dividend yield is zero)
S-Spot price
K-Strike price
σ -Volatility
T-Time till the expiry date
r-Risk-free interest rate
N represents a standard normal distribution with a mean of 0 and a standard deviation of 1, and ln represents the natural logarithm of a number. Natural logarithms are based on the constant e (2.71828182845904) [26].
Option Greeks
Delta (Δ): Delta is the most important of all the options for Greeks. It measures the impact of change in the price underlying (that is, the premium of an option) resulting from a change in the underlying security. A positive value for the call option varies from 0 to 1 and a negative value for the put option varies from-1 to 0.
Gamma (γ): It measures the rate of change in delta over time, for the change in the underlying price. Gamma is positive for both call and put options in this paper.
Theta (θ): Theta measures the impact of change in time expiration. Generally, it is shown in a negative value for both call and put options, indicating the option price decreases each day that is approaching the time of expiry.
Vega (ν): Measure the impact of change in volatility of the underlying value. Vega is positive for both call and put options in this paper.
Rho (ρ): Measure the impact of change in the interest rate of the underlying value. Generals, call options to have positive Rho value and put options to have negative Rho value (Table 1).
Table 1. Moneyness of options.