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I understand how to calculate volatility and how to calculate call or put price. However I don't understand something about input parameters.

For an example.

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At the moment I am writing this post, implied volatility for Appl with 190 Strike Call is 22,69%. My question is, based on what TERM? (Time). Because if you want to calculate real implied volatility you must need to know what period of time to include. Time to excerise doesn't tell you much, if you don't know what period you must watch. One month, half a year, one year, 2 years etc.. I assume this 22,69 implied volatility is based on days_to_expire_parameters/some_period. I am trying to figure what is this some_period. I

Dindi
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The implied volatility is defined as the volatility parameter that gives you the option price currently trading on the market. That is, you will observe market quotes for option prices or implied volatilities and you use the Black-Scholes formula to convert from one to the other. The implied volatility is not therefore something you computed based on stock price data, it's really a price determined by the market.

There are as many implied volatilities as there are options traded. In fact, options are frequently quoted in implied vols. You have one implied volatility for every strike price and for every maturity. This defines the "Volatility surface". Instead of the strike price you frequently see on one of the axes the "moneyness", that is the ratio of current price to the strike price.

Take a look at this graph. https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/23316/versions/2/screenshot.jpg

That means, for example, that the 3-month 1-moneyness implied vol is the volatility parameter that you need to input in the BS formula to obtain the observed market price of the 3-month 1-moneyness call option.

bbecon
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  • @dindi:What br1 said is fine but, to give a different take, the implied vol computed is of that particular underlying stock price, whatever the expiration, Therefore, In an ideal world, you'd think that, all different options that underlie stock X say, ( whether 1 month expiration, 1 year expiration etc ) should give you quite similar implied vols since they all underly the same stock price. Unfortunately, they don't because the option prices ( of stock X ) reflect the demand for options of different expiration dates. So, you get a volatility smile if you plot them.rather than a constant. – mark leeds Jun 14 '18 at 21:25