HiI have searched this site to find answer to question and as I cant download "Know Your Weapon" I was wondering if someone cld put me out of my miseryMy question is: how come atm delta remains constant with changes in vol (I guess strictly speaking as vol decreases the delta slightly decreases but overall is failry flat around 50). Is it due to the fact that atm options have no EXtrinsic value -and vol affects the time value?Thank you

OTM delta is favored by vol whilst ITM delta is harmed by vol. ATM delta is better off being neutral. vol means bilateral movement which does not change the prob of ending up ITM if its ATM now.

hi thnx very much for reply but i am still none the clearer -when you say bilateral movement - i take it you mean up and down -i cant see how if i change vol -my atm delta is not affected

Delta can be viewed as an agent for the (risk neutral)prob the underlier will end ITM,. When it's currently OTM, vol increases the odds(coz more upside than downside), samely, when it's now ITM, vol decreases it. When its now ATM, vol(which means equally up and down) does not affect the winning prob.

As per KYW Part 1 (buy Collector's book and you'll get the articles !), dDelta/dVol for an ATMF option is 2 Sqrt[t/2 Pi] Exp[ - t vol^2 / 8 ].If you plot this as a function of vol, you'll find that it changes very slowly. Edited to add ATMF qualifier.

thnk you very much - i think i will buy book - could i just ask if my comment re atm options not having time value is a contributor to vol having minimal affect on the delta. ie otm and itm will have varying levels of time value (extrinsic value) in them - atm doesnt ? your help is greatly appreciated

ATMF options are all time value.Plot vanna (dDelta/dVol) as a function of strike and you'll see that it changes sign at the ATMF strike.

oh yes - i got that one a bit wrong - thks - and thks for quick reply

sorry one more if you dont mind - how do i plot vanna as fn of stirke when the equation supplied seemsto not have any K or S input-thk u in advance

function for vanna

ok - thnx - i found that also on net today - without that i wldnt be able to understand what the symbols meant- i will work on what everyone has suggested and i thank you all for the time - i was hoping though for a non mathematical answer as i always respond better to intuition as opposed to a number crunching answer

If your return distribution is roughly simmetrical around the forward, increasing vol will not change the delta of the ATMF - it's balanced.Consider a deep ITM call; with low vol its delta will be close to 1. Increasing vol will increase the chance of this call not being exercised => decrease delta (negative vanna)Consider a deep OTM call; with low vol its delta will be close to 0. Increasing vol will increase the chance of this call being exercised => increase delta (positive vanna)

thank you once again - your time is appreciated - not wanting to annoy anyone by ignorance - re atmf - so delta is stable with a vol chg due to the distribution of returns assumption in BS - I can understand OTM and ITM delta with respect to chgs in vol- so it comes down to the distribution and the forward ie the fwd is not driven by vol but i rates and time and carry assumptions - I hope my next sentence doesnt annoy but the fwd is driven also by Spot -ie this is one of the inputs -wldnt an extremely high vol environment chg spot thereby chg where the fwd is - or is this the piece i am not understanding -ie atmf is atmf and it is distribution that evolves from this that matters - also so this is why the gamma of atmf with respect to chg vol decreases quite resoundly with chg vol ie gamma is representing the speed of chg of our delta and this is not chging much (delta that is) with vol chgs

Think of a really low vol ... the pdf of the fwds will look almost like a DiracDelta function, quite concentrated, so gamma is high (OTM options become worthless quite quickly).Think of a really high vol ... the pdf of the fwds will look almost like an uniform distribution within a broad range, so gamma is lower (if OTM options do not lose value that quickly, they have higher deltas; if the deltas do not change quickly, gamma is lower).Strongly suggest you read KYW.

thnx once again ! unless you are in NYC its late so much appreciated - I will buy article as your advice has been great - thnx for your patience