MattLikesAnalysis Wrote: ------------------------------------------------------- > geez, i shouldn’t have to say this on this forum, > but when I say delta = 1, obviously I mean its > approx. 1 as in 1 less 0.01 to 3. 1 would mean > that the strike = 0. I don’t think anyone’s arguing this point. Most of us are arguing the delta is going to be near 0.5, not some rounding error from 1.
ConvertArb Wrote: ------------------------------------------------------- > IheartMath Wrote: > -------------------------------------------------- > ----- > > Posted by: ConvertArb (IP Logged) > > Date: August 4, 2009 01:56PM > > > > > >gamma for a 70 year call option is approx 0. > > > > > > > > > um, only if its 100% in our out of the money > (i.e > > when delta = 0 or 1)… otherwise > it > > is somewhere between 0 and 1. the graph of > gamma > > looks like an upside down parabola (like the > CDF > > of the normal distribution) > > > > we all know what a gamma graph looks like. > > do you think theta is signifcant for this option? sorry i didnt think you did since your original vague comment about gamma being 0 was wrong. and yes, since theta is a measure of time to option maturity and we’re talking about 70 years.
i’d like to close this discussion by stating that the delta of a non-dividend-paying at-the-money european call with a relatively high volatility (>50%) and long term to expiration (T>20 years) can be much higher than 0.5 in the black-scholes framework, and can very well be close to 1 if volatility is high enough and term is long enough. that’s black-scholes for ya, period. also the use of black-scholes in such situations is total gibberish - constant volatility over 30 years my a*s. so whoever is saying the delta should be around 0.5 based on practical experience or “things that make sense”, they may be right. we have two sides of the story here
BTW, I agree with MAtt on this, normal market conditions, Delta would be approx 1.
Mobius Striptease Wrote: ------------------------------------------------------- > i’d like to close this discussion by stating that > the delta of a non-dividend-paying at-the-money > european call with a relatively high volatility > (>50%) and long term to expiration (T>20 years) > can be much higher than 0.5 in the black-scholes > framework, and can very well be close to 1 if > volatility is high enough and term is long enough. > that’s black-scholes for ya, period. agreed that it would be close to 1 (even with volatility lower than 50%) and a long time to expiration on a NON dividend paying ATM european call option.
Delta ~1 Gamma ~0 Theta ~0 DONE. CLOSE THIS FORUM DOWN.
ConvertArb Wrote: ------------------------------------------------------- > Delta ~1 > Gamma ~0 > Theta ~0 > > DONE. > CLOSE THIS FORUM DOWN. haha wrong.
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ConvertArb Wrote: ------------------------------------------------------- > Delta ~1 > Gamma ~0 > Theta ~0 > > DONE. > CLOSE THIS FORUM DOWN. FAIL
Am I gonna have to quote my friend Warren again? “The ridiculous premium that Black-Scholes dictates in my extreme example is caused by the inclusion of volatility in the formula and by the fact that volatility is determined by how much stocks have moved around in some past period of days, months or years. This metric is simply irrelevant in estimating the probabilityweighted range of values of American business 100 years from now.” How can you POSSIBLY judge the value of an option 70 years from now based on market volatility. The price of such an option would remain unchanged until an abnormally large price movement occurs. Hence delta on a normal day’s movement will be close to 0.
JohnThainsLimoDriver Wrote: ------------------------------------------------------- > ConvertArb Wrote: > -------------------------------------------------- > ----- > > Delta ~1 > > Gamma ~0 > > Theta ~0 > > > > DONE. > > CLOSE THIS FORUM DOWN. > > > FAIL X100 billion
I really wish you guys could make a market for me in SPY $100 options 2079 with all these option experts. Please hypothetically do.
its funny. my argument is based on black-scholes, assuming vol. is constant, and my argument fully backs black-scholes. my call option price takes uses black-scholes, after Iheartmath’s div. adjustment of around $80. the opposing argument is based on black-scholes in that they need a price created from some formula to calculate the price of a call option b/c other wise, the option could be sold for whatever price justifies their conclusion of “approx. 0.5”. for example, for the delta to equal 0.5, it is possible that the option price is higher than the stock itself. and the opposite is true that if someone was selling this option for 10% of the stock price, the delta may be 10 to begin with. the bottom line is that my argument of its possible it could be much higher than 0.5 is more justified as I put full faith in the Black-Scholes, whereas the opposing argument takes some of the model as valid but rejects other parts of it.
ZeroBonus Wrote: ------------------------------------------------------- > Am I gonna have to quote my friend Warren again? > > “The ridiculous premium that Black-Scholes > dictates in my extreme example is caused by the > inclusion of volatility in the formula and by the > fact that volatility is determined by how much > stocks have moved around in some past period of > days, months or years. This metric is simply > irrelevant in estimating the probabilityweighted > range of values of American business 100 years > from now.” > > How can you POSSIBLY judge the value of an option > 70 years from now based on market volatility. The > price of such an option would remain unchanged > until an abnormally large price movement occurs. > Hence delta on a normal day’s movement will be > close to 0. we were just having a hypothetical discussion, but i agree with you for different reasons. its closer to 0, especially on a dividend paying stock.
MattLikesAnalysis Wrote: ------------------------------------------------------- > its funny. > > my argument is based on black-scholes, assuming > vol. is constant, and my argument fully backs > black-scholes. my call option price takes uses > black-scholes, after Iheartmath’s div. adjustment > of around $80. > > the opposing argument is based on black-scholes in > that they need a price created from some formula > to calculate the price of a call option b/c other > wise, the option could be sold for whatever price > justifies their conclusion of “approx. 0.5”. for > example, for the delta to equal 0.5, it is > possible that the option price is higher than the > stock itself. and the opposite is true that if > someone was selling this option for 10% of the > stock price, the delta may be 10 to begin with. > > the bottom line is that my argument of its > possible it could be much higher than 0.5 is more > justified as I put full faith in the > Black-Scholes, whereas the opposing argument takes > some of the model as valid but rejects other parts > of it. no your argument is mathematically only valid for a non dividend paying stock. my argument throws in another variable that threatens the validity of the model, because of the ridiculous time horizon. ROAR! haha
ZeroBonus Wrote: ------------------------------------------------------- > Am I gonna have to quote my friend Warren again? > > “The ridiculous premium that Black-Scholes > dictates in my extreme example is caused by the > inclusion of volatility in the formula and by the > fact that volatility is determined by how much > stocks have moved around in some past period of > days, months or years. This metric is simply > irrelevant in estimating the probabilityweighted > range of values of American business 100 years > from now.” > > How can you POSSIBLY judge the value of an option > 70 years from now based on market volatility. The > price of such an option would remain unchanged > until an abnormally large price movement occurs. > Hence delta on a normal day’s movement will be > close to 0. go talk to Taleb about this. I bet he has a few books addressing this. oh wait, he does.
IheartMath Wrote: ------------------------------------------------------- > > agreed that it would be close to 1 (even with > volatility lower than 50%) and a long time to > expiration on a NON dividend paying ATM european > call option. great. and if we have a dividend, the exp(-q*T) factor will quickly dominate for long maturities, driving the delta to zero.
yup.
iheartmath is back pedalling. someone proposed valuation SPY on normal market conditions. vol range it from 10-30 IR range 2%-9% DVD % - range 2%-4% 70 year call option will be Delta ~1.
Mobius Striptease Wrote: ------------------------------------------------------- > i’d like to close this discussion by stating that > the delta of a non-dividend-paying at-the-money > european call with a relatively high volatility > (>50%) and long term to expiration (T>20 years) > can be much higher than 0.5 in the black-scholes > framework, and can very well be close to 1 if > volatility is high enough and term is long enough. > that’s black-scholes for ya, period. > > also the use of black-scholes in such situations > is total gibberish - constant volatility over 30 > years my a*s. so whoever is saying the delta > should be around 0.5 based on practical experience > or “things that make sense”, they may be right. we > have two sides of the story here The B-S framework does suggest that there is a reason to expect that an at-the-money option could have delta higher than 0.5. There are reasons to criticize the B-S framework, but the fact that it predicts a rising delta for long-dated options with non-negligible volatility is something worth taking seriously. 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. Normally, options are not priced through a PV(expected-value-at-expiration) mechanism. Instead, they are priced through arbitrage relationships, and these relationships typically assume zero transaction costs. To hedge an option requires either another option or dynamic hedging, which is buying and selling the underlying in proportions dictated by delta (and sometimes gamma). But doing dynamic hedging every trading day for 70 years or whatnot is bound to have enormous cumulative transaction costs. As a result, it may make more sense to price these in terms of PV(expected value), which would definitely imply a much higher than 50% chance of expiring in the money. I don’t know the answer, but I can see an argument why delta would be >0.5, even if delta is pretty much always = 0.5 for ATM short-dated options.