How to Calculate Implied Volatility with Black-Scholes

Implied volatility is a measurement of how much the market expects a stock's price to change in the future, and is mostly used by options traders to help them evaluate a fair price for an option. Because options are contracts that haven't reached their expiration date, it can be difficult to evaluate a fair price for an option. According to Scottrade, the Black-Scholes model is one of the most widely used mathematical formulas to help investors find a fair price to bid for an option. Online brokerage services provide investors with both implied volatility percentages and the Black-Scholes price estimate of an option contract. Investors can also calculate both estimates with a spreadsheet or an online calculator using financial data that can be found on financial news websites.

Look for online tools, such as "options valuation" or "theoretical pricing" calculators, or other information that your online brokerage or financial news website provides on a stock's volatility measurements. Online brokerage services, especially those that specialize in trading options, will provide a variety of data on implied volatility, which is expressed as a percentage and can be tracked and charted over different time periods. Calculators give investors a "theoretical" price for the stock using the Black-Scholes model. However, not all free financial news websites provide all of this information, so investors should research what tools are available to find data on the implied volatility of a stock option.

Find up-to-date data on the company and use an online calculator to find both the Black-Scholes price and implied volatility. Investors need the stock's current share price, the option's strike price, the time to expiration, the risk-free interest rate, and the historical volatility, which is expressed as a percentage. U.S. government treasury bills are usually used for the interest rate. Also, free Black-Scholes and implied volatility spreadsheet templates are available online to help investors compute and track this data.

Enter the goal Black-Scholes price into an implied volatility calculator or spreadsheet template. To find the implied volatility percentage, you enter all the data into the calculator except the historical volatility percentage. Instead of using the calculator to find the Black-Scholes price, you enter a goal price, and the calculator or spreadsheet automatically computes the implied volatility.

Tip

• Consider the limitations of the Black-Scholes model, which assumes that the stock doesn't offer a dividend, it can only be a "European" style option that can't be cashed out early, no commissions are charged and interest rates don't change. Some of these could prove false, and the Black-Scholes model is intended to be used only as an indicator. In addition to a Black-Scholes price, your online broker may offer options price calculators based on other models, such as the bionomial or barrier option pricing models.

About the Author

Terry Lane has been a journalist and writer since 1997. He has both covered, and worked for, members of Congress and has helped legislators and executives publish op-eds in the “Wall Street Journal,” “National Journal” and “Politico." He earned a Bachelor of Science in journalism from the University of Florida.

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