Delta Bleed

segga · June 10th, 2002, 9:12 am

Does anyone have the formula for dDelta/dtime?

goshawk · June 10th, 2002, 9:25 am

Depends on what type of contract you have in mind.

Paul · June 10th, 2002, 9:56 am

Oh, come off it, segga...in the time it took you to post that message you could have worked it out...when did they stop teaching differentiation? P

segga · June 10th, 2002, 12:26 pm

Sorry... i'm lazy and I make way too many mistakes in Calculus to start differentiating things! Please help the calculus stupid.

Chukchi · June 10th, 2002, 2:57 pm

<< Does anyone have the formula for dDelta/dtime? >>Segga,The Delta Bleed formula would be the same for European Call and Put.Call_Delta = N(d1)Put_Delta = N(d1) - 1Here d1(S,K) = (Log[S/K] + (r+Vol^2/2)*t)/(Vol*Sqrt[t])(Delta)' = n(d1)*(d1)'n(d1) = Exp[-(d1^2)/2]/Sqrt[2*Pi](d1)' = d1(K,S)/(2*t)Note, that d1(K,S) is different from d1(S,K) by only the interchanged S & K ( S<-->K ).d1(K,S) = (Log[K/S] + (r+Vol^2/2)*t)/(Vol*Sqrt[t]) = (- Log[S/K] + (r+Vol^2/2)*t)/(Vol*Sqrt[t]).Below is a graph of DeltaBleed(S) for K=100, r=0.05, Vol=0.50, t=0.01

segga · June 11th, 2002, 10:46 am

Thank you very very much Chuckci!Just what I was looking for.

Chukchi · June 13th, 2002, 6:28 pm

<< Thank you very very much Chuckci!Just what I was looking for. >>Segga, you are very very welcome!We like to deal with all these bloody deltas, gammas -- colours, speeds and charms.

rambo900 · December 27th, 2007, 1:39 am

Hi guys,i have a followup question, actually i posted it somewhere else before i saw this message (my bad), i am copying my question below... below is from "dynamic hedging" directly page 195:vol shifts can operate like a time acceleration, with an effect that is linked to the length of the option (more exactly the square of the vol shift is proportional to the length of the option)...a longer dated option, say a one-year call with 20 deltas, would lose, at 16% vol, .04 delta (the delta would go from 20 to 19.96). a change in vol from 16% to 15% would move the delta from 20 to 18.2could you guys please explain that to me? especially where he got this number 18.2.thanks a lot!!!

daveangel · December 27th, 2007, 8:25 am

I wasnt sure what Taleb meant by this but I played around with an option and I think he is trying to explain the equivalence between vol change and time shift on delta. For example, 1-year 20 delta call at 16% vol (spot = 100, strike = 115.85) has a delta of 20.05% and at 15% vol has a delta of 18.3% whereas a 364 day option at 16% vol has a delta of 20.01%, which is 0.04% less. So the 1 pt vol change is equivalent to a 47day change in time.

rambo900 · December 27th, 2007, 11:11 pm

thanks daveangel

Randomness · January 1st, 2010, 11:39 am

QuoteOriginally posted by: daveangelI wasnt sure what Taleb meant by this but I played around with an option and I think he is trying to explain the equivalence between vol change and time shift on delta. For example, 1-year 20 delta call at 16% vol (spot = 100, strike = 115.85) has a delta of 20.05% and at 15% vol has a delta of 18.3% whereas a 364 day option at 16% vol has a delta of 20.01%, which is 0.04% less. So the 1 pt vol change is equivalent to a 47day change in time.apologies for bringing up this old thread. Please could someone take me through the calcs of the 47 day change in time as mentioned above. Not sue I follow it right and Im sure Im missing something

MCarreira · January 2nd, 2010, 2:44 am

It seems ok to me, please see attached.

Randomness · January 3rd, 2010, 1:13 pm

cheers MCarreira