Delta for Call Option with very long T

how many stocks that last 70 years have died in the last 200 years other than GM and Lehman? not many. if they die, it doesn’t matter whether you own the stock or the option, you lose 100% either way most of the time. so, the downside incremental loss potential is nearly zero. thus if there is no incremental risk of loss, there should be no incremental expectation of return, just a slight incremental sensitivity to the final value of the stock/basket, 70 years from now. just think of the P-C parity. how much would you pay for a put on a stock that matures 70 years from now. the answer is probably not much more than a penny for a diversified basket of assets with a $100 strike price as the EV is $21,800. so if P = 0ish and X(1+i)^t is mostly negligable, the call option will be incredibly expensive. for the call to not reflect the changes in the underlying closely, one would be able to hedge; buy the call and make a risk free return over the 70 years, assuming the expectations in the LT have not changed.

and yes. the greatest risk to this assumption that the company/index/whateveryou’remeasuirng, will last 70 years but not start issuing a dividend is highly improbable. but within this theoretical vacuum, assuming dividends were never expected to be paid, the delta should theoretically be 0.9-1.

IheartMath Wrote: ------------------------------------------------------- > you have to come up with some kind of long term assumption… we obviously dont know what would happen in the future… Given that the US is going to be bankrupt long before 70yrs I’d value any L/T financial instrument at $0. Can we please not go to 10 pages?

purealpha Wrote: ------------------------------------------------------- > Given that the US is going to be bankrupt long > before 70yrs I’d value any L/T financial > instrument at $0. +1

purealpha Wrote: ------------------------------------------------------- > Can we please not go to 10 pages? +1

hahaha yea, good point… you know what i meant though. this is all speculation in a perfect unrealistic world…

I don’t know about everyone else but I for one enjoyed 9 pages of IHeartMath. Too bad KarenC didn’t get in on the action.

I think that there is a good chance that a single stock might not exist 70 years from now. The company may well go bankrupt, be acquired, merge, be chopped up, go private, or the country that it’s chartered in might not exist anymore. Only 80 years ago, it was august 1929. How many companies went under after Sept 1929? Think it can’t happen again? Somehow it seems a lot more likely these days. Indices are more likely to survive long terms, but even so, their risk characteristics can change over time as leverage ratios and sectoral compositions change.

bchadwick Wrote: ------------------------------------------------------- > I think that there is a good chance that a single > stock might not exist 70 years from now. The > company may well go bankrupt, be acquired, merge, > be chopped up, go private, or the country that > it’s chartered in might not exist anymore. > > Only 80 years ago, it was august 1929. How many > companies went under after Sept 1929? Think it > can’t happen again? Somehow it seems a lot more > likely these days. > Agree. It is downright silly to say that Lehman and GM (which by the way still trades) are the only stocks that have gone away in the last 70 years, especially when hundreds of publicly-traded companies go bankrupt in every distressed cycle.

There was a bit in the Level III curriculum this year about the Dow’s changing composition being a good argument for diversification - I believe it said that any given firm is more likely to go bankrupt eventually than to provide an outsized return (depending on the definition of the latter obviously). Also, coincidentally I was flipping through “The Intelligent Asset Allocator” by Bernstein and he made a similar point - go to the library and look at a table of stock prices in a newspaper from the Civil War, you won’t recognize many of the names.

“reconize” I mean.

Does it make more sense if underlying is index, which will very likely exist for more than 70 years, right? Does Index typically paying dividend?

wow. you guys really missed my point with the 70 years thing. if a company is going to go bankrupt and you hold a 70 year option, the option is going to be worthless. it is IDENTICAL to holding the stock itself as they are both worth nothing. thus the INCREMENTAL downside is zero. name ONE stock that, in the last 200 years, was at one point a public company for 70 years and traded at a smaller market price per share 70 years from its inception as a public company, but didn’t go bankrupt. not many 70 year companies will make it 70 years, but have a smaller market cap than they do today, without going bankrupt. it just doesn’t happen. so because the INCREMENTAL downside risk of holding an option over holding the stock is nil, the upside can’t be that much higher than just holding the underlying. because there is no additional risk taken, why should the option holder receive additional return?

i agree with mattlikesanalysis… the risk of holding the stock, buying an option on the stock, the world ending, is priced in the value of the stock. you wouldnt adjust the option price (or delta) for this risk, since its already theoretically priced to reflect that fact. theoretically, a 70 year option is no different than a 1 year option. all the same things could happen to whatever company it is. however, practically a 70 year option is unrealistic and impossible to price (or determine delta).