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

[davethetrade]

I´m trying to create a spreadsheet and need some help and insight.

Sometimes in the optionchain there´s no strikeprice with the delta 25, so i need a formula really badly to be able to make calculations that dosen´t differ from time to time.

Please if someone could help me it would be really nice

what formula can i use to calculate what implied volatilty (IV) would be for a delta 25 option (both put and call)?

Can i somehow do this by using the greeks? That would be awesome.
Thank you guys so much in advance, and happy trading

 

[Robert Morse]

Since many do not have a 25 delta options, it will require you to make many assumptions that will not be accurate from one stock to another where they each have their unique skew. You are looking for one formula and I expect that will not work. What value do you get from it if you are looking to create a strategy that requires a 25 D options and there are known?

Is this for a research project or to develop a trading strategy?

Bob

 

[spindr0]

Maybe I'm missing something more complicated in the question but it seems to me that there are two simple possibilities.

Average the B/A of each adjacent strike and calculate the IV for each of the two options.

If the two IV's are the same, the missing 25 delta option is between them with the same IV (no IV skew).

If the two IVs are different (skew), extrapolate the IV of the 25 delta option based on the distance the 25 delta is from either of the adjacent strike's delta.

 

[Kevin Schmit]

what formula can i use to calculate what implied volatilty (IV) would be for a delta 25 option

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).

A 2,2 Pade approximant is a rational function with the 0th coefficient in the denominator set to 1. The "formula" you are looing for will have the form:

y = (a0 + a1*x + a2*x^2) / (1 + b1*x + b2*x^2)

rearranging terms give you:

y = a0*1 + a1*x + a2*x^2 - b1*y*x - b2*y*x^2

which is what you want to solve with linest.

 

[tommcginnis]

...I need a formula really badly to be able to make calculations that doesn't differ from time to time.

I don't know what "doesn't differ from time to time" means, but if you're trying to work something as close as practicable to the options chains that come along, you're going to have to work with the strikes that are printed/available. (Your choice -- as per spindr0 and KSchmit above, is to interpolate between existing strikes and your 'ideal' 25δ-strike -- an extra step.)

Unless your need is curiosity-for-curiosity's-sake, you'll need actual strikes.

What I do personally is utilize the mechanics of the spreadsheet as given: an Index function (or some other thing) runs down a specified range looking for a condition to be met/exheeded. When that happens, the function reads the data nearby, and prints to the cell from which you started. Your job here is to arrange the data such that the 'read-down-the-columns' maneuver fits with your desired task.

So, again, for me: if I'm targeting a |0.15| delta strike, I might miss a 0.1495 delta and hit a 0.1811 as the next available (or worse, as DTE shrinks down, right!?!), but I still have to live with the strikes available, not the strikes I might wish for.

And now, having written all this, and having re-read your OP, I realize you're looking to target the IV that would be linked to a specified delta ??? There is no such value or formula, without specifying DTE, too. Maybe that is your issue?

 

[davethetrade]

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).

A 2,2 Pade approximant is a rational function with the 0th coefficient in the denominator set to 1. The "formula" you are looing for will have the form:

y = (a0 + a1*x + a2*x^2) / (1 + b1*x + b2*x^2)

rearranging terms give you:

y = a0*1 + a1*x + a2*x^2 - b1*y*x - b2*y*x^2

which is what you want to solve with linest.

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)

What do you mean with this?:
Pade approximation of the vol by delta curve over your entire chain.

So in the formula, Y is IV?
What is a0, a1, x, a2, b1 stand for?

What inputs do i need to know to use this fomula?

Maybe a newbie question sorry, i know what i want to achive but i´m just new to these terms.
Thanks for the help.
Dave.

 

[davethetrade]

A broker can´t offer all strikes like 128.583 and weird ones like that, it would be to many strikes so they focus on round numbers. But if they could calculate say IV for a strike with delta 27 it should be possible using same formula to calculate what IV would be theoretically if delta was 25. I think it´s very doable I think focusing on delta rather then strike is good idéa, because if stock price change it would mess my calculations up if i instead had a fixed strike i was looking for...if you get what i´m trying to say.

So anyone.

what formula can i use to calculate what implied volatilty (IV) would be for a delta 25 option

I appriciate that you´re trying to help me, thanks
Dave.

 

[davethetrade]

I don't know what "doesn't differ from time to time" means, but if you're trying to work something as close as practicable to the options chains that come along, you're going to have to work with the strikes that are printed/available. (Your choice -- as per spindr0 and KSchmit above, is to interpolate between existing strikes and your 'ideal' 25δ-strike -- an extra step.)

Unless your need is curiosity-for-curiosity's-sake, you'll need actual strikes.

What I do personally is utilize the mechanics of the spreadsheet as given: an Index function (or some other thing) runs down a specified range looking for a condition to be met/exheeded. When that happens, the function reads the data nearby, and prints to the cell from which you started. Your job here is to arrange the data such that the 'read-down-the-columns' maneuver fits with your desired task.

So, again, for me: if I'm targeting a |0.15| delta strike, I might miss a 0.1495 delta and hit a 0.1811 as the next available (or worse, as DTE shrinks down, right!?!), but I still have to live with the strikes available, not the strikes I might wish for.

And now, having written all this, and having re-read your OP, I realize you're looking to target the IV that would be linked to a specified delta ??? There is no such value or formula, without specifying DTE, too. Maybe that is your issue?

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

delta(call) = exp(-rf*Time) * pnorm(d1v)
delta(put) = exp(-rf*Time) * pnorm(d1v) - 1
d1 = (log(spot/strike)+(rf+(sigma^2)/2)*Time)/(sigma*sqrt(Time))
so, solve for d1 first:
d1(call) = qnorm(delta/exp(-rf*Time))
d1(put) = qnorm(delta/exp(-rf*Time) + 1)
and then solve for the strike:
strike = exp( d1 - (rf+(sigma^2)/2)*Time)/(sigma*sqrt(Time) )

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

 

[tommcginnis]

If you're nervous of the math, stop fiddling with "delta=" and find yourself some expositions on IV or volatility or even sigma, and then plug in your 25-delta as a given. MUCH easier.

 

[Kevin Schmit]

What do you mean with this?:
Pade approximation of the vol by delta curve over your entire chain.

I meant find a formula for vol in terms of delta, which is what you asked for. I suggested finding that formual via a rational function approximation using the Pade trick so that it can found via the OLS (ordinary least squares) LINEST function in excel.

So in the formula, Y is IV?
What is a0, a1, x, a2, b1 stand for?

Yes, Y is vol, that is what you are solving for. x is delta. a0 is the intercept returned by linest. a1, a2, b1, and b2 are the coefficients returned by linest. Once you have those coefficients plug them into the formula:

y = (a0 + a1*x + a2*x^2) / (1 + b1*x + b2*x^2)

If this isn't obvious, let me explain that you need (in excel) to create a column of your vols (IV's). That is your dependent variable column for linest. Then create another 4 columns: a column of your deltas, a column of your deltas squared, a column of vol times delta, and a column of vol times delta squared. These four columns are your independent variables for linest. If you use linear algebra instead of linest you'll need an additional column of ones, usually as the first of the now five columns.

Linest will return an intercept and four coefficients (one for each column of the independent variables). The intercept term is a0, the four coefficients are a1.a2,b1, and b2. Plug those coefficients and the numbers 25 and 75 for x into the forumal above and it will return the vols you are after. You will have to use 25 and 75 for your target deltas (or -25 and 25) rather than 25 and 25 or you won't have a function. Or you could fit the two halves of the curve separately.