With relevance to this study, the scholar has calculated the Nifty Call (CE) and Put (PE) options prices and Greeks daily from 1-Nov -2018 to 25-Nov-2018. For analysis purposes, the research scholar has selected Nifty call and put option prices and Greeks on 1- Nov-2018, 09-Nov-2018, 15-Nov-2018, and 29-Nov-2018, the time to expiry or days left is set at 28 days, 20 days, 14 days, and 7 days respectively [27]. The data can be seen in Tables 1-4 for each selected strike price 10900, 11100, 11300, and 10100. Finally, Greeks are computed for each Nifty option poisons and results are discussed below, under each table (Table 2).
Table 2. Nifty CE and PE option price, and Greeks for strike price-10900.
Above Table 2 exhibits the Nifty CE option price, PE option price, and option Greeks for strike price 10900. According to the observations and analysis, on 1-Nov-2018 delta value and option price of a Nifty CE option are higher, 0.73910 and Rs. 353.5 respectively since the Nifty spot price value is higher at 11008.3 when compared to strike price 10900 i.e., the call option contract is ITM (in the money). Later days when the Nifty CE option contract leans toward the expiry date, the delta value decreases to 0.00569 and Nifty call option prices decrease to Rs. 0.4. This is because the Nifty spot value moves down to 10224.75 which leads the contract to OTM (Out of the money) [28]. In the case of Nifty PE option changes in delta and option price values against the same nifty spot value 11008.3 are exactly reversed in nature, i.e., delta value of Nifty PE option and option prices are lower, -0.29059 and Rs. 100.25 respectively because the put option contract is OTM. In the next few days, while Nifty PE option contracts approach the expiry date, the delta value increases to -0.97023, and the put option price increases to Rs. 576.65 as the contract leans towards ITM since the Nifty spot value decreases to 10224.75. The gamma value of both the Nifty CE option and Nifty PE option decreases as the option approaches close to the expiry date 29-Nov-2018 i.e., time left 7 days to expiry. The gamma value is zero for the Nifty CE option which is the OTM option and the Nifty PE option's gamma value is 0.00023 which is the ITM option. Theta value is high for the Nifty CE option on 1-Nov-2018, -5.22075 and this value decreases as the contract approach closer to expiry, and on 22-Nov-2018 value is -1.80049. While analyzing the case of the Nifty PE option theta value is -2.92252 and it increases as the contract approaches expiry on 22-Nov-2018 the value is -7.05144 since implied volatility is more than 54.84%. Rho value for Nifty CE option on 1-Nov-2018 is higher 5.1176 since the contract is ITM and days left to expiration is more i.e., 28 days. In the latter days, the contract tends to OTM, and the days left to expiration are 7 days. Hence Rho value decreases to 0.00149. Rho values for the Nifty PE option on 1-Nov-2018 are -2.16916 and on 22-Nov-2018 are -0.28746 (Table 3).
Table 3. Nifty CE and PE option price, and greeks for strike price-11100.
The above Table 3 shows the analysis for strike price 11100, detailing the Nifty CE option price, PE option price, and option Greeks. According to the above observation and analysis of the Nifty CE option on 1-Nov-2018, the delta value is 0.58375, and the option price is Rs. 212, therefore the contract is ATM (at the money) since the Nifty spot value is 11008.3 almost touching the strike price 11100 [29]. A few more days later, both delta values and option prices get decreased. In 22-Nov-2018 the delta value is 0.00357 and the option price is Rs. 0.25 as the contract becomes OTM towards the expiry date, since the Nifty spot value is 10224.75. The gamma value is more than 0.00093 on 1-Nov-2018 since the contract is ATM which implies that acceleration of change in delta value is more for every point change in the Nifty spot value. A few days later, the contract tends to OTM as it approaches the expiry date of 22-Nov-2018, and therefore gamma value decreases to zero. Thus the option price will not have a significant change in the movement of the Nifty spot value due to high implied volatility i.e., 51.46%. Further, it is observed that Theta and Vega's values are higher on 1-Nov-2018 i.e., -5.11232 and 11.01249 respectively since the contract is ATM. In later days both the values decrease and on 22-Nov-2018 Theta value is -1.48543 and the Vega value is 0.05732 as the contracts tend towards expiry and become OTM. Rho value is higher, i.e., 4.08707 on 1-Nov-2018, because 28 days are left to expiry. As the contract moves to the expiry date of 22-Nov-2018, the Rho value decreases to 0.00097 so it does not affect the option's price [30]. On observing the Nifty PE option on 1-Nov-2018, the contracts are ATM since the Nifty spot value is 11008.3 which are almost equal to the strike price of 11100. Delta value is 0.452527 and has a higher gamma value, i.e., 0.00082. Later days as contracts tend towards expiry and become ITM. Therefore, on 22-Nov-2018 delta value increases and becomes -1 but the gamma value decreases to zero, which indicates that the option price moves up by Rs.1 which proves that for every one point there exists an upward movement in the Nifty spot value. It is also observed that the Nifty PE option price also increases from Rs. 156.2 to Rs. 772.9. On 1-Nov-2018 Theta value is -2.63457 and the Vega value was 11.06321. During the later days observed on 09-Nov-2018 and 15-Nov-2018 steadily the value decreases [31]. But on 29- Nov-2018 Theta value increases to -3.01289 since Vega and implied volatility is zero. It is also observed that higher value Theta does not affect the option price for the Nifty PE option contract is ITM which has more fundamental value and less time value. The analysis also observed that the Rho value is higher at -3.18038 on 1-Nov-2018 and lesser value at -0.30127 on 22-Nov-2018 (Table 4) [32].
Table 4. Nifty CE and PE Option price, and greeks for strike price-11300.
Above Table 4 exhibits the strike price of 11300, along with the Nifty CE option price, PE option price, and option Greeks. The observations and analysis of the Nifty CE option on 1-Nov-2018 in the contract are OTM (On the money) since the Nifty spot value is 11008.3. Consequently have a lesser delta value, 0.38786 and it further decreases to 0.00255 as contracts approach the expiry date on 22-Nov-2018 and become deep OTM since the Nifty spot value moves down to 10224.75. The gamma value is also higher, 0.00097 on 1-Nov-2018, and steadily decreases become zero towards 22- Nov-2018. It is also observed that the Nifty CE option price on 1- Nov-2018 is Rs. 103.9 which decreases to Rs. 0.24 on 22-Nov-2018 as contracts become further deep OTM. Theta and Vega value seem higher on 1-Nov-2018 i.e., -4.2457 and 10.81369 respectively. Further, it is observed that both Theta and Vega value decreases as contracts approach the expiry date of 22-Nov-2018, values are -1.31810 and 0.04252 respectively. Rho value seems higher than 2.73932 on 1-Nov-2018 because 28 days remain to expiry. Rho value seems to decrease to 0.00072 on 22-Nov-2018 as only seven days are left to expire [33]. It is also observed that on 1-Nov-2018 Nifty PE option contract is ITM since the Nifty spot value is 11008.3 reflecting the delta value as 0.59806 and higher gamma value, 0.00089. Movement of contract towards to expiry date proves to become further deep ITM as Nifty spot value increases to 10224.75. Therefore on 22-Nov-2018 value of delta increases to -1, the value of gamma decreases to zero, and obviously, option prices increase from Rs. 241.4 to Rs. 969.9 Rs. It is also observed that on 1-Nov-2018 values of Theta are -1.66531 and Vega is 10.91944. Movement of contract at a later stage, nearing the date of expiry, on 22-Nov-2018 Theta impels a higher value of -3.06767, and Vega decreases to zero due to implied volatility. It is observed that on 1-Nov-2018 Rho value is -4.48764 with 28 days left to expiry, gradually Rho decreased to -0.30677 on 22-Nov-2018 because only seven days were left to expiry (Table 5) [34].
Table 5. Nifty CE and PE Option price, and greeks for strike price-10100.
The above table shows the analysis of Nifty CE option price, PE option price, and option Greeks for strike price 10100. Observations and analysis decipher that on 1-Nov-2018 Nifty CE option contract is deep ITM, proving the Nifty spot value is 11008.3 and the Nifty option price is also higher, Rs. 1068.85. Throughout the life span of the contract, delta value is unconditionally 1 and gamma is zero, as implied volatility Vega is also zero. While the contracts approach the date of expiry, it becomes less ITM i.e., proving that the Nifty spot value travels downwards from 11008.3 to 10224.75, resulting in moving the option price towards descending phase, reaching Rs. 224 on 22-Nov-2018. This behavior is because, though a contract has an absolute delta value of 1 the gamma, Vega and implied volatility is zero which will not reflect many options prices with the movement of the Nifty spot value. It is also observed that the Theta value ranges between -2.72176 to -2.73897 till the expiry of the contract. Rho value is 6.53226 on 1-Nov-2108 in 28 days still pending expiry. On 22-Nov-2018, the Rho value decreased to 0.2738 with only seven days left to expire. Further, it is observed that on 1-Nov-2018 Nifty PE option carries a lesser delta value, -0.04832 as the Nifty spot value is 11008.3 i.e., the contract is deep OTM position. While the contracts approaching the expiry phase, on 22-Nov-2018 delta value went up to -0.07068 as the Nifty spot value falls in descending phase, 10224.75 and the contract becomes lesser OTM. On the 1-Nov-2018 Option, the price was Rs. 14.25 on 10-Nov-2018 its value is Rs. 36.4 due to an increase in Delta value -0.14224 and higher Gamma, 0.00045. Theta value is less on 1-Nov-2018 i.e., -1.30005 compared to the Vega value of 2.8339. In 22-Nov-2018 the Theta value gets increased to -10.43448 due to higher implied volatility of 29.38% and the Vega value falls to 0.72387. On 1-Nov-2018 Rho value is -0.3591 because of the lavish 28 days remaining for expiry, and on 22- Nov-2018 Rho value has decreased to -0.01994 with only seven days left to expiry [35,36].