Implied volatility is derived from the Black-Scholes formula, and using it could actually provide significant advantages to investors. Implied volatility is an estimate of the long run variability for the asset underlying the choices contract. The Black-Scholes model is used to cost options. The model assumes the value of the underlying asset follows a geometrical Brownian motion with constant drift and volatility.

The inputs for the Black-Scholes equation are volatility, the value of the underlying asset, the strike price of the choice, the time until expiration of the choice, and the risk-free rate of interest. With these variables, it’s theoretically possible for options sellers to set rational prices for the choices that they’re selling.

Calculating Implied Volatility

As with every equation, Black-Scholes will be used to find out any single variable when all the opposite variables are known. The choices market is fairly well developed at this point, so we already know the market prices for a lot of options. Plugging the choice’s price into the Black-Scholes equation, together with the value of the underlying asset, the strike price of the choice, the time until expiration of the choice, and the risk-free rate of interest allow one to unravel for volatility. This solution is the expected volatility implied by the choice price. Subsequently, it is named implied volatility.

Assumptions

The Black-Scholes model makes several assumptions that won’t all the time be correct. The model assumes that volatility is constant. In point of fact, it is usually moving. The Black-Scholes model is restricted to European options, which can only be exercised on the last day. Nevertheless, American options will be exercised at any time before expiration.

Black-Scholes and the Volatility Skew

The Black-Scholes equation assumes a lognormal distribution of price changes for the underlying asset. This distribution can be generally known as a Gaussian distribution. Often, asset prices have significant skewness and kurtosis. Which means high-risk downward moves occur more often available in the market than a Gaussian distribution predicts.

The belief of lognormal underlying asset prices should, due to this fact, show that implied volatilities are similar for every strike price in line with the Black-Scholes model. For the reason that 1987 market crash, implied volatilities for at-the-money options have been lower than those further out of the cash or far in the cash. The rationale for this anomaly is that the market prices in the next likelihood of a pointy downward move.

That has led to the presence of the volatility skew. When the implied volatilities for options with the identical expiration date are mapped out on a graph, a smile or skew shape will be seen. This phenomenon can be generally known as a volatility smile. As a consequence of volatility smiles, an uncorrected Black-Scholes model shouldn’t be all the time sufficient for accurately calculating implied volatility.

Historical vs. Implied Volatility

The shortcomings of the Black-Scholes method have led some to position more importance on historical volatility versus implied volatility. Historical volatility is the realized volatility of the underlying asset over a previous time period. It is decided by measuring the usual deviation of the underlying asset from the mean during that point period.

Standard deviation is a statistical measure of the variability of price changes from the mean price change. This estimate differs from the Black-Scholes method’s implied volatility, because it relies on the actual volatility of the underlying asset. Nevertheless, using historical volatility also has some drawbacks. Volatility shifts as markets undergo different regimes. Thus, historical volatility might not be an accurate measure of future volatility.

Implied Volatility and Upcoming Events

Essentially the most significant good thing about implied volatility for investors is that it could be a more accurate estimate of future volatility in some cases. Implied volatility takes under consideration all of the data utilized by market participants to find out prices in the choices market, as a substitute of just past prices.

The very best example of this will be quarterly earnings reports. Stock prices sometimes jump up dramatically on positive earnings news. Investors know this, in order that they are willing to pay more for options as quarterly earnings announcements approach. Consequently, implied volatility also goes up near those dates. Dividend declarations, quarterly earnings, and other upcoming events cannot directly influence any volatility estimate based entirely on past prices.

Liquidity Issues

Implied volatility will be extremely inaccurate when options markets aren’t sufficiently liquid. Lack of liquidity tends to make market prices less stable and fewer rational. In extreme cases, mistakes by a single amateur trader can result in wildly irrational options prices in an illiquid market. If those prices are used to estimate implied volatility, then those estimates may even be inaccurate. That could be a significant issue because many parts of the choices market suffer from an absence of liquidity.