Status1, (everybody is rushing to answer your questions about IV. Isn't it nice?

)

what Gary suggested is very (VERY!!!) important. You have to clearly specify your goal. I understand it may not be easy task if you don't play with iv often. I will (also) try to answer your question assuming that:

- you deal with single, liquid underlying

-you just want to see how calculation is done

**without any further goals**.

So, let's look at today's options chain.

We randomly pick 11 Nov 2019 expiration and 3020 strike, Put.

You see that MID is 22.75.

I assume that 'risk free' interest rate is .25% (that is not important for that short dte).

We have all necessary data. Let's do our math.

I use Python, so I did find some BSM formula for Python. You probably use Excel, so you should find BSM formula for Excel.

You may also want to code formula by yourself - all depends what you aim to achieve.

Here is how it looks on my screen:

Mind that this is very simplified approach.

BS is my formula, in green are model inputs, second line calculates iv number.

You see that we get 9.52%. Now compare this to TOS number which is 9.68%. If you wish you can compare this to

ONE, OV, IB and other calculations and you, most likely, will see different numbers.

The differences in iv calculations come from different inputs that were used by each party. I used simple formula which didn't take dividends into account, I didn't use optimized interest rate. I also could use better number for underlying value (forward). I didn't bother putting more exact dte number - just used what TOS displayed. I didn't verify if Put price is in line with neighbor prices. Changing those inputs will produce different outputs.

Now, which of those numbers is correct?

Hmmm,

- none is, as it was discussed in posts above

or...

- all are correct. All numbers are correct in a sense that calculations were done properly from math point of view.

Let's plug my calculated iv to BS model and see what put price will pop out.

Is it close enough? You have to decide.

Now, you have your calculation. What do you want to do with it?