Generalization of the Implied Volatility of Options Applied to Shares

Abstract

Background: The historical volatility of assets has been widely studied and used in financial markets. In addition, the implied volatilities of options are increasingly being used as possible predictors of future volatility. Although the market works by pricing future expectations, there is no formal definition in the literature of what we call the implied volatility of a stock.

Objective: To generalize the concept of an option’s implied volatility and derive a new volatility to be assigned to the underlying stock, now named “asset implied volatility”.

Methods: The implied volatilities of options were calculated within the Black-Scholes model using historical stock and option prices, as well as characteristics such as expiration date, strike price, and others. The theoretical option price was calculated using variables extracted from the market, except for implied volatility, which was calculated by numerically inverting the price equation. Option’s greeks were also calculated and used to calculate the weighted average of the implied volatilities. Historical volatility was calculated using the Yang-Zhang method and was used for comparison.

Results: The “implied volatility of the asset” showed no correlation with the asset’s historical volatility. This new implied volatility, assigned to the asset, suggests that this metric may contain additional information since it does not incorporate information already measured in another way.

Relevance: The results have a potential contribution to economic agents as they can be used as an additional tool in financial resource allocation strategies for investment or asset trading.