# What Implied Volatility Tells Us

Today I recorded a video with Angela Miles for CBOE-TV where we discussed implied volatility.  Implied volatility is a measure that is determine from the market price of an option.  A statistical equivalent is a single standard deviation price change.  A viewer had asked if implied volatility was a price projection for an underlying market.  The answer is yes, but on an annual basis.   Implied volatility is an annualized number, but it may be converted to show anticipated volatility for different time periods.  The formula to convert implied volatility appears below –

Price x Implied Volatility x Square Root (Days / 365)

or

Price x Implied Volatility x Square Root (Days / 252)

Choose 365 or 252 days usually is a decision made based on how many days there are to expiration.  When looking at an option that has just a few days until expiration 252 is appropriate, for longer dated options 365 is appropriate.  We were discussing implied volatility and short dated options today so I’m going to go with 252 in my example.

Consider the following scenario for a Weekly option that has five days left to expiration –

XYZ 5-Day Day 50 Call is trading at 0.45

XYZ 5-Day 50 Call Implied Volatility is 20%

Our formula inputs are price = 50.00, implied volatility = 20%, and 5 days.

50.00 x .20 x Square Root (5/252) ≈ 1.40

So taking the implied volatility of 20%, which is an annualized number, we can see that the market is pricing in with one standard deviation of confidence that XYZ will close between 48.60 and 51.40 at expiration.   So yes, implied volatility is a price projection, but a little math is involved in determining just that projection.