# Implied Volatility Calculator

The volatility of stock price returns can be calculated from historical data if you have a sequence of consecutive share prices from which to calculate the daily returns and how they fluctuate. However, if you only know the current share price and the specifics of a call or put option, you can calculate the implied volatility of the stock. This is the volatility that is implied under the assumption of a given option pricing model, for example, the Black-Scholes model.

The calculator on the left computes implied annualized volatility under the Black-Scholes model. Just input the current share price, strike price, call/put price, days until expiration, and the interest rate as a decimal. The calculator will then output the corresponding annualized volatility.

Keep in mind that volatility does not tell you about the direction in which a stock's prices move, only how much the returns vary from day to day. Two stocks can the same level of volatility, but one may be generally on the rise while the other may be generally on the decline.

### Example

A stock's current price is $65.28 per share. The price of a European call option is $3.12 with a strike price of $63.50. There are 35 days until expiration and the risk-free interest rate is 2.9% = 0.029. Assuming the value of an option follows from the Black-Scholes pricing model, the implied volatility of this stock is 0.251.To check that this figure is correct, you can plug S = 65.28, K = 63.50, T-t = 35, r = 0.029, and σ = 0.251 into the Black-Scholes model to computed the corresponding price of a call option. Doing so gives you the correct value of $3.12, as expected.

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