A:

Implied volatility is a parameter part of an option pricing model, such as the Black-Scholes model, which gives the market price of an option. Implied volatility shows how the marketplace views where volatility should be in the future. Since implied volatility is forward-looking, it helps us gauge the sentiment about the volatility of a stock or the market. However, implied volatility does not forecast the direction in which an option is headed.

## Using the Five Other Inputs

Implied volatility is not directly observable, so it needs to be solved using the five other inputs of the model:

• the market price of the option
• the underlying stock price
• the strike price
• the time to expiration
• the risk-free interest rate

Implied volatility is calculated by taking the market price of the option, entering it into the B-S formula, and back-solving for the value of the volatility. But there are various approaches to calculating implied volatility. One simple approach is to use an iterative search, or trial and error, to find the value of an implied volatility.

## The Iterative Search

Suppose that the value of an at-the-money call option Walgreens Boots Alliance, Inc. (WBA) is \$3.23 when the stock price is \$83.11, strike price is \$80, risk-free rate is 0.25%, and the time to expiration is one day. Implied volatility can be calculated using the B-S model, given the parameters above, by entering different values of implied volatility into the option pricing model.

For example, start by trying an implied volatility of 0.3. This gives the value of the call option of \$3.14, which is too low. Since call options are an increasing function, the volatility needs to be higher. Next, try 0.6 for the volatility; that gives a value of \$3.37 for the call option, which is too high. Trying 0.45 for implied volatility yields \$3.20 for the price of the option, and so the implied volatility is between 0.45 and 0.6.

This procedure can be done multiple times to calculate the implied volatility. In this example, the implied volatility is 0.541, or 54.1%.

## Historical Volatility

Historical volatility, unlike implied volatility, refers to realized volatility over a given period and looks back at past movements in price, and one way to use implied volatility is to compare it with historical volatility.

From the example above, if the volatility in WBA is 23.6% on Nov. 30, 2017, we look back over the past 30 days and observe that the historical volatility is calculated to be 23.5%, which is a moderate level of volatility. If a trader compares this to the current implied volatility, the trader should become aware that there may or may not be an event that could affect the stock's price.

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