On the implied volatility from a "purified" option price process

Abstract

The option price, the implied volatility and the volatility index are often used as indicators of market sentiment about the future volatility. We proposed an alternative price process so-called the "purified" option price and its implied volatility for this purpose. Our aim is to reduce the impact of stock price movements on the implied volatility, provided that there are sufficient sets of price data and the underlying option contracts are European-style options. Since option prices are only available for finite sets of strike prices and expiration times, we suggested to use quadratic interpolation on the available contracts to approximate the missing prices. For this paper, we demonstrated the implied volatility of the proposed process on S\&P 500 Index Options.