The study worked out the implied volatility and Theta value of weekly options based on the option data for weighted index number of Taiwan FITX from January 5, 2015 to October 31, 2016.
Apart from employing B-S model for the pricing of options, market investors could also reckon backwards from the market transaction prices to the implied volatility of options. The greater the implied volatility is, the stronger market investors’ mentality and requirements regarding the willingness of risk aversion will be.
The empirical study found that the volatility smile of implied volatility of VIX options generally presents a pattern extending from the lower left to the upper right and the implied volatility increases as the expiration period shorten. On average, the longer the contract is, the lower the implied volatility will be. With the expiration period getting shorter, the slope of the volatility smile increases, which means that the volatility smile will be steeper with the expiration date approaching and the gap of implied volatility between in the-money (ITM) options and out-of-the-money (OTM) options will increase.
Among the VIX options, the expiration date also plays a significantly important role besides the levels of ITM and OTM. Either from the fitness of samples or the evaluation results, errors are greatly improved after adding the factor of expiration date. It is critical to show the expiration date for evaluating of option prices. The maximum accuracy of evaluation will be achieved by taking the ITM and OTM levels and the expiration date as the models for explaining variables. Furthermore, the evaluation errors are fairly stable without any obvious gap among each year.
