What is 'Local Volatility'

Local volatility is a volatility measure used in quantitative analysis that helps to provide a more comprehensive view of volatility by factoring in both strike prices and expirations from the Black Scholes Model to identify a type of actual volatility.

BREAKING DOWN 'Local Volatility'

Local volatility is similar to implied volatility. Both can provide insight on the market’s actual perceived volatility of an option. Both local volatility and implied volatility are often studied together and compared to historical volatility. Local and implied volatility are generated from current option price levels using the Black Scholes Model while historical volatility can be an input that is used to generate a Black Scholes Model price.

Black Scholes

The Black Scholes Option Pricing Model was created by Fischer Black, Myron Scholes and Robert Merton. The model for pricing options was introduced in the Journal of Political Economy in 1973, in a paper titled "The Pricing of Options and Corporate Liabilities.” In 1997 its creators were awarded a Nobel Prize for the methodology. Since its introduction the Black Scholes Option Pricing Model has become an industry standard for option pricing. Iterations of the model have been introduced to provide for some of its static assumptions such as European option valuation and constant volatility but overall it continues to be used broadly across the industry. (See also: Options Pricing: Black-Scholes Model)

Investors and traders use the Black Scholes Model in a number of ways by manipulating or solving for many of its different variables. Volatility is one variable which can be studied in multiple ways to support the analysis of option pricing.

Overall variables involved in the Black Scholes Model include:

• current underlying price

• option strike price

• time until expiration, expressed as a percent of a year

• volatility

• risk-free interest rates

Historical Volatility

Historical volatility is commonly used to help analyze and arrive at the price of a standard option. Historical volatility is calculated as the standard deviation of a security’s price over a specified time frame. While historical volatility is commonly used to help determine the price of an option it has several caveats. Primarily, the time series used in calculating historical volatility does not always correspond with the market’s view of the option’s actual volatility.

Implied Volatility

Implied volatility provides another way to view the volatility of an option. Implied volatility is calculated by backing out the volatility of an option given its option trading price in the market. Implied volatility however can only provide a view of volatility with a single expiration.

Local Volatility

The concept of local volatility was introduced by Emanuel Derman and Iraj Kani. Local volatility attempts to identify the actual volatility of an option across a range of strike prices and expirations. Local volatility seeks to use two factor analysis to provide a more accurate actual volatility reading than implied volatility.

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