if there’s a dividend, wont the call will just be cheaper and this will in turn absorb any effect the dividend payments will have on delta?
I just used my “black scholes spreadsheet with dividend” formula. Price 1000 Strike 1000 Interest 3% Dividend 2% Volatility 25 Time 70 years. answer Delta = .1120
ok ready… lets say this is an ATM call option with your specs above: sigma = 20% RFR = 5% div = 3% T = 70 d1 = (ln(S/K)+(RFR - div + .5*sigma^2)*T) / (sigma * T^(1/2)) = (ln(1) + (.05 - .03 + .5*.2^2)*70) / (.2 * 70^ 1/2) = 1.67332 N(d1) ~ .9525 call option delta = e^(-T*div) * N(d1) = .9525 * e^(-70 * .03) = .11664
I have to say I’m actually impressed with IHeartMath’s finance skillz after this discussion. Here I thought it was just all looks and sarcasm before.
mark@dirtbags Wrote: ------------------------------------------------------- > I just used my “black scholes spreadsheet with > dividend” formula. > > Price 1000 > Strike 1000 > Interest 3% > Dividend 2% > Volatility 25 > Time 70 years. > > answer > > Delta = .1120 whats the price of the call option?
mark@dirtbags Wrote: ------------------------------------------------------- > I just used my “black scholes spreadsheet with > dividend” formula. i got the same answer with just my skillz.
MattLikesAnalysis Wrote: ------------------------------------------------------- > mark@dirtbags Wrote: > -------------------------------------------------- > ----- > > I just used my “black scholes spreadsheet with > > dividend” formula. > > > > Price 1000 > > Strike 1000 > > Interest 3% > > Dividend 2% > > Volatility 25 > > Time 70 years. > > > > answer > > > > Delta = .1120 > > > whats the price of the call option? $196.56 Eat that I heart math!
mark@dirtbags Wrote: ------------------------------------------------------- > Eat that I heart math! durrty
MattLikesAnalysis Wrote: > whats the price of the call option? Call price = Stock Price * e^(-T*div) * N(d1) - Strike Price * e^(-r *T) * N(d2) where d2 = d1 - sigma * T^(1/2) ill let someone else do this out
JohnThainsLimoDriver Wrote: ------------------------------------------------------- > I have to say I’m actually impressed with > IHeartMath’s finance skillz after this discussion. > Here I thought it was just all looks and sarcasm > before. im so flattered you dont think im a complete moron!
IheartMath Wrote: ------------------------------------------------------- > im so flattered you dont think im a complete > moron! No problem. So…what are you wearing?
so is the conclusion that its either vastly greater than 0.5 with a non-dividend payer and vastly less than 0.5 for a dividend payer?
MattLikesAnalysis Wrote: ------------------------------------------------------- > so is the conclusion that its either vastly > greater than 0.5 with a non-dividend payer and > vastly less than 0.5 for a dividend payer? No, 0.5 and <0.5.
bchadwick Wrote: ------------------------------------------------------- > > I have heard that one can interpret delta as a > *rough* approximation of the likelihood that the > option will expire in the money. If we think > about it that way, and accept that the average > stock (or stock index) tends to grow over the very > long term, it could be conceivable that delta > might be > 0.5, perhaps even substantially closer > to 1. > bchadwick, I don’t agree with this interpreation of delta although I’ve seen it thrown around. stricitly speaking the probability that a call will expire in the money is the N(d2) factor in the B-S formula. this should be interpreted with a lot of care though, because it is a risk-neutral probability. one possible way to get to the “real-world” probability is to read off the N(d2) factor from the B-S formula after substituting the risk-free rate with the expected return of the stock. this adjustment can have significant effect on the probabilities you get out of the model. it may tell you that the risk-neutral probability of finishing in the money is close to zero, whereas the real-world probability is actually over 50%.
IheartMath Wrote: ------------------------------------------------------- > ok ready… lets say this is an ATM call option > with your specs above: > > sigma = 20% > RFR = 5% > div = 3% > T = 70 > > d1 = (ln(S/K)+(RFR - div + .5*sigma^2)*T) / (sigma > * T^(1/2)) > = (ln(1) + (.05 - .03 + .5*.2^2)*70) / (.2 * > 70^ 1/2) > = 1.67332 > > N(d1) ~ .9525 > > call option delta = e^(-T*div) * N(d1) = .9525 * > e^(-70 * .03) = .11664 I haven’t played with B-S since I took L2 a few years back, but IIRC Option DELTA = N(d1) ~ 0.9525 Option PRICE = N(d1) - PV(divs) = 0.11664 (I’m assuming the calculator work was correct)
MattLikesAnalysis Wrote: ------------------------------------------------------- > so is the conclusion that its either vastly > greater than 0.5 with a non-dividend payer and > vastly less than 0.5 for a dividend payer? Price 1000 Strike 1000 Interest 3% Dividend 000000000000% Volatility 25 Time 70 years. answer Delta = .1198
MattLikesAnalysis Wrote: ------------------------------------------------------- > so is the conclusion that its either vastly > greater than 0.5 with a non-dividend payer and > vastly less than 0.5 for a dividend payer? yes
Mobius Striptease Wrote: ------------------------------------------------------- > bchadwick, I don’t agree with this interpreation > of delta although I’ve seen it thrown around. > stricitly speaking the probability that a call > will expire in the money is the N(d2) factor in > the B-S formula. > > this should be interpreted with a lot of care > though, because it is a risk-neutral probability. > one possible way to get to the “real-world” > probability is to read off the N(d2) factor from > the B-S formula after substituting the risk-free > rate with the expected return of the stock. > > this adjustment can have significant effect on the > probabilities you get out of the model. it may > tell you that the risk-neutral probability of > finishing in the money is close to zero, whereas > the real-world probability is actually over 50%. agree
bchadwick Wrote: ------------------------------------------------------- > > Option DELTA = N(d1) ~ 0.9525 > no, Option DELTA = N(d1)*exp(-q*T) where q is dividend yield. If non-dividend paying stock, then q=0, so the expression reduces to Option DELTA = N(d1), something often seen around in textbooks
i said this like 20 min ago, but i bet theyll listen to you.