How to calculate implied volatility for a delta 25 option? :)

[Kevin Schmit]

i can calculate what the strike would be for a chosen delta no matter if it´s in optionchain or not by this formula.

No, you can't. Not accurately. The best you will do with this method is approximate the linear interpolation. You're arguing in a circle, see below.

strike = exp( d1 - (rf+(sigma^2)/2)*Time)/(sigma*sqrt(Time) )

Here is your circularity. You need sigma to calc strike, but sigma (vol) is what you are looking for in the first place,

Maybe this works? Just dont´t know what to do with it next if it´s correct

Well if it actually worked you could rearrange the equation above to get sigma in terms of d1 and strike.

The code you posted, using pnorm and qnorm instead of the more usual N, Phi, etc.. suggests that you program in R. If so, and you want to see the complexity of a rational function fit without the Pade trick, type the following in R console:

require(pracma)
rationalfit

 

[spindr0]

Hi, i appriciate the answers (from all of you) The reason i need to calculate IV for delta 25 is because i want to see how it change over time. If an optionchain has a strike with delta 26 as closest and next time closest i can get to delta 25 is a strike with delta 23, that would mess everything up when i want to look how IV change over time. I need a fixed delta, and i think 25 is good. (i now that time affects IV to but i´m planning to set this to a fixed number in the formula)

If you want to see how delta changes over time, use a pricing model and advance it one day at a time, keeping all other variables constant.

Time affects IV, delta and price but if you fix delta in the formula, you're monkeying around with the entire premise and then you are calculating how IV and price will change if delta doesn't change.

 

[spindr0]

The linear interpolation described by spindr0 above will almost certainly be suitable for your purposes. It will yield vol estimates very slightly high, but not by enough to matter.

If you need more accuracy, a 2,2 Pade approximation of the vol by delta curve over your entire chain will be pretty accurate and can be trivially fit in excel using LINEST or a little linear algebra (MMULT, MINVERSE, and MTRANSPOSE).

When I read your posts I realize how little I know about options beyond my retail trading. Thanks for your ongoing contributions here.