Guess what, try this on a Single Stock Future on Lehman or MFGlobal ! For sure, 100% in the money !
Option Question about Delta
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Guess what, try this on a Single Stock Future on Lehman or MFGlobal ! For sure, 100% in the money !
yup, 100% in the money - your worst case is a zero payoff. what would you say a zero strike put on Lehman was worth?
if you start talking about value of the firm, it's (a) not BS and (b) not 100% delta at zero equity strikei am trying to understand - are you denying that in a pure B/S world , delta is ito/carry-adjusted probability or trying to say that in a general case it is a hedge ratio?
Quote from sle:
yup, 100% in the money - your worst case is a zero payoff. what would you say a zero strike put on Lehman was worth?
i am trying to understand - are you denying that in a pure B/S world , delta is ito/carry-adjusted probability or trying to say that in a general case it is a hedge ratio?
Both !
As far as + and â are quite different signs, and in a pure BS :
Delta is N(d1) with d1=[log(S/K)+ (r-d + 0.5.vol.vol)(T-t)] / (vol.sqr(T-t))]
Risk neutral prob is N(d2) with d2=[log(S/K)+ (r-d - 0.5.vol.vol)(T-t)] / (vol.sqr(T-t))]
There is a sign difference between the both.
Thus, even in a pure BS world, delta is not 'ito/carry-adjusted probability' at all .
this is a meaningless statement since it's clear that one would ignore the sign when applied to probabilities. in any case, as any experienced exotics book runner (e.g. myself) would tell you (assuming that your rates and volatilities are relatively low and maturity is reasonably close), price of a digital can be approximated by the delta and the delta of a digital can be approximated by gamma.
ps. in a normal case, such as interest rates prior to 2008, the delta=probability is perfectly true, obviously
As an experienced exotics book runner would you claim that the delta of a down and out call that could be much higher than 100% remains a probability (risk neutral or real one) ? You got to be kidding !
But there is nothing wrong with that as far as +0.5.vol.vol and -0.5.vol.vol are the same thing to you.
all i said was (and will be happy to say it again) is that you would be perfectly ok to use asb(delta) of a vanilla as an approximate price for a digital which is, in fact, markets view on ITM probability. this is, as previously noted, because in beign cases dP/dS is very close to dP/dK.
while it is very entertaining to talk about the limiting cases (oh, but if you are taking a quadratic or a discountinuious payoff delta could reach infinity blah blah), the real world approximations such as delta = probability, 0.8 * vol * sqrt(t) of time is approximately atm straddle or 1 day move * 20 is approximately the annual vol are very useful and good for most trades you would do. you disagree?
Please could you elaborate, it's starting to be funny.
Do you thing that delta is a probability (because that's OP's question, remember ) ?
Keep editing you're missing the point. An answer maybe ?