Not my favourite source to quote but this may help.
http://www.investopedia.com/article...anding-how-dividends-affect-option-prices.asp
http://www.investopedia.com/article...anding-how-dividends-affect-option-prices.asp
ex-dividend and options
- Thread starter misterkel
- Start date
It seems you are confused about the definition of premium for an option.
option_premium = option_price - option_intrinsic
option_price <= $2.35 (the visible asking price)
option_intrinsic = $1.83 ($71.83 stock price - $70 call strike)
option_premium <= $2.35 - $1.83
option_premium <= $0.52
Granted, this calculation ignores the ~$0.01 - $0.03 bid-ask spread that appears to be typical of HCN today outside of the times near the open, but that wouldn't put the premium anywhere near $1.15.
If you think I'm wrong about this, it would help if you would indicate exactly which of the above lines you think is in error.
Beerntrading, it does not make a difference to my preceding post, but just to clarify some things that might be distracting you, the prices I quoted from today were after the stock went ex-dividend, and the reason I used the ask price rather than the midpoint was to point out how there would have been a huge "free money" opportunity if what I believe atrp2biz's claim was were correct.
Oops, you're right. I thought it was still the 3rd today when I posted that.
I don't see anything inconsistent in this explanation with my approximate model of the price using a combination of three options.
I have to run now, but, very quickly, skimming this paper, I think the following paper makes mention of what I'm talking about (that early exercise just before ex-dividend is usually rational for calls in the money by more than their premiums):
Draft that I downloaded: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=931777&download=yes
Actual paper behind a firewall, which I haven't looked at: https://www.researchgate.net/publication/46513263_Ex-dividend_Arbitrage_in_Option_Markets
Umm...where exactly is the arb in this example?
Yes--that's what I said in the second post of this thread. The premium remaining in the calls can be approximated by the put value.
What I'm objecting to is your notion that calls would reduce by the dividend amount following x-div.
Thanks for asking a question intended to help get to the bottom of this.
The arbitrage is in what you could have done the day before (that is, pre-dividend) if the stock price had been the same (yesterday's price = today's price + dividend) and if the call price did not experience a similar change due to the dividend (my interpretation of your phrase, "The options already reflect the value of the dividend").
In reality, the price of HCN did move, but let's pretend that HCN had same dividend-adjusted price yesterday and when I made my post today.
Prices when I made that post (after the $0.87 dividend):
HCN stock: $71.83
HCN $70 call expiring August 18th, asking price: $2.35
Imaginary prices yesterday (before the $0.87 dividend), had the value of the assets been the same as today:
HCN stock: $72.70 ($71.83 + $0.87 that had not yet gone ex-dividend)
HCN $70 call expring August 18th, asking price: ~$2.40 ($.05 to back out premium decay, otherwise following my understanding of what I think is an incorrect theory on your part. I contend that this call would only have been available for about $0.87 more, about $3.27).
So, the arbitrage opportunity in that imaginary yesterday would have been the following.
Short 100 HCN @ $71.83
Buy 1 HCN $70 call at $2.40
[The above two lines could be expressed a single combination order to avoid risks of price slippage.]
Finally, exercise the call.
Let's compute the profit from that imaginary yesterday, ignoring commissions, etc.:
$7270 raised from shorting 100 shares of HCN
-$240 spent buying the $70 call
-$7,000 spent exercising the $70 call
---------------
$30 profit (per contract)
The difference between my understanding of your claim, described above, and my belief, is that I think that the call in that imaginary yesterday would not cost about $3.27, changing that $30 profit to a $57 loss.
That is the arbitrage I was trying to describe. If you can identify which part(s) you think are my mistake or my misinterpretation of your position, that would help. Mostly I wonder if you really think that that call would have been available to buy for $2.40 in that imaginary yesterday.
I'll try to respond more generally to your other post, which addresses this sort of scenario in general rather than particular prices for HCN and one its call options.
At the outset of this huge post, let me disclaim that I am just winging it here, and that there must be books and other publications that more correctly explain this.
I'm not sure what you mean exactly by "the premium remaining in the calls." I would agree that just before the stock goes ex-dividend, the puts should have higher premiums than the calls by an amount such that reducing the stock price by the dividend amount would make put and call premiums at each strike equal.
Let's start with a ridiculously simple, mostly qualitative example: imagine a call with a strike price of zero.
A call with a strike price of zero that can be exercised immediately on demand should be worth whatever the stock is worth at that moment (ignoring transaction costs, carrying costs, etc.). If stock XYZ is selling for $10 today, will go ex-dividend of $1 tomorrow, and therefore will trade at $9 tomorrow if the market's opinion of its value does not change, the price of a $0 XYZ call will also have those same prices at those times. So, I hope you would agree that a call with a $0 strike will experience a drop by the amount of the dividend in the absence of any change in the market's opinion.
At this point, you might be tempted to consider whether a $0 strike can be dismissed as just a special case. If so, imagine a call with an almost as ridiculous $0.01 strike. It would have been worth infinitesimally more than $9.99 yesterday and infinitesimally more than $8.99 today, where these "infinitesimally more" values are the value of protection from the underlying stock share price dropping below $.01 before the option expires. Those "infinitesimally more" values are the premiums yesterday and today, where today's premium might be higher due to the lower $8.99 price making it more likely that the stock will drop below $0.01 or lower due to less time remaining under the option's expiration. So, I hope you would agree that a call with a very low non-zero strike price can experience a drop by the amount of the dividend in the absence of any change in the market's opinion.
So what happens as the strike price becomes substantial? I believe that my made-up model I described earlier in this thread can explain the part of the call price drop the occurs earlier than the ex-dividend dividend event and the price drop that occurs only when the stock finally goes ex-dividend, although I did make a mistake in describing it, in that the strikes that I listed as k-dividend should have been k+dividend (where k is the original strike price),
II believe that the value of an option with strike price k across an ex-dividend event of d should be approximately the same as this combination of options on the stock if it were instead retaining the dividend (ignoring carrying costs, interest rates, etc.):
1. a long option (call or put) at strike k, expiring just before ex-dividend date.
2. a short option (same type) at strike k + dividend, also expiring just before the ex-dividend date.
3. a long option (same type) at strike k + dividend, expiring at the expiration date of the real option,
...with the imaginary restrictions that if you want to exercise this, both long options get exercised and the short option gets assigned, and that is the only way that the short position in line 2 gets assigned (or at least that the premium saved from getting assigned pays for your recreating the short leg in line 2).
The first two lines of the above position form a spread, which gradually drops to no value if the price just before the ex-dividend event ends up below strike k, in which case there is no gap down in value when the stock goes ex-dividend, assuming if the dividend-adjusted value of the stock remains the same. I think this is the case you had in mind.
But now let's consider what happens if the pre-dividend price ends up being above strike price k, in other words, the spread expiring just before ex-dividend date is at least partly in the money. In that case, although it is possible for the first two lines to produce some decay in value before the ex-dividend event if the pre-dividend price ends up being close to the strike k, the first two lines of the position have value at the ex-dividend event, and a decision must be made either to exercise/assign all three positions together or forfeit the profit from from the first two lines in order to preserve the premium of the third line. Forfeiting the value of the spread from the first two parts of this combination position is what happens if you don't exercise a call going ex-dividend. The value of that spread, which has a maximum value of the full dividend amount, is value by which the call should gap down when the underlying stock starts trading ex-dividend if the underlying price does not do anything other than drop by the dividend amount.
So, I hope you can now better understand why I think that calls can be expected to gap down by amounts approaching the dividend amount at an ex-dividend event.
I'm not sure what you mean exactly by "the premium remaining in the calls." I would agree that just before the stock goes ex-dividend, the puts should have higher premiums than the calls by an amount such that reducing the stock price by the dividend amount would make put and call premiums at each strike equal.
Let's start with a ridiculously simple, mostly qualitative example: imagine a call with a strike price of zero.
A call with a strike price of zero that can be exercised immediately on demand should be worth whatever the stock is worth at that moment (ignoring transaction costs, carrying costs, etc.). If stock XYZ is selling for $10 today, will go ex-dividend of $1 tomorrow, and therefore will trade at $9 tomorrow if the market's opinion of its value does not change, the price of a $0 XYZ call will also have those same prices at those times. So, I hope you would agree that a call with a $0 strike will experience a drop by the amount of the dividend in the absence of any change in the market's opinion.
At this point, you might be tempted to consider whether a $0 strike can be dismissed as just a special case. If so, imagine a call with an almost as ridiculous $0.01 strike. It would have been worth infinitesimally more than $9.99 yesterday and infinitesimally more than $8.99 today, where these "infinitesimally more" values are the value of protection from the underlying stock share price dropping below $.01 before the option expires. Those "infinitesimally more" values are the premiums yesterday and today, where today's premium might be higher due to the lower $8.99 price making it more likely that the stock will drop below $0.01 or lower due to less time remaining under the option's expiration. So, I hope you would agree that a call with a very low non-zero strike price can experience a drop by the amount of the dividend in the absence of any change in the market's opinion.
So what happens as the strike price becomes substantial? I believe that my made-up model I described earlier in this thread can explain the part of the call price drop the occurs earlier than the ex-dividend dividend event and the price drop that occurs only when the stock finally goes ex-dividend, although I did make a mistake in describing it, in that the strikes that I listed as k-dividend should have been k+dividend (where k is the original strike price),
II believe that the value of an option with strike price k across an ex-dividend event of d should be approximately the same as this combination of options on the stock if it were instead retaining the dividend (ignoring carrying costs, interest rates, etc.):
1. a long option (call or put) at strike k, expiring just before ex-dividend date.
2. a short option (same type) at strike k + dividend, also expiring just before the ex-dividend date.
3. a long option (same type) at strike k + dividend, expiring at the expiration date of the real option,
...with the imaginary restrictions that if you want to exercise this, both long options get exercised and the short option gets assigned, and that is the only way that the short position in line 2 gets assigned (or at least that the premium saved from getting assigned pays for your recreating the short leg in line 2).
The first two lines of the above position form a spread, which gradually drops to no value if the price just before the ex-dividend event ends up below strike k, in which case there is no gap down in value when the stock goes ex-dividend, assuming if the dividend-adjusted value of the stock remains the same. I think this is the case you had in mind.
But now let's consider what happens if the pre-dividend price ends up being above strike price k, in other words, the spread expiring just before ex-dividend date is at least partly in the money. In that case, although it is possible for the first two lines to produce some decay in value before the ex-dividend event if the pre-dividend price ends up being close to the strike k, the first two lines of the position have value at the ex-dividend event, and a decision must be made either to exercise/assign all three positions together or forfeit the profit from from the first two lines in order to preserve the premium of the third line. Forfeiting the value of the spread from the first two parts of this combination position is what happens if you don't exercise a call going ex-dividend. The value of that spread, which has a maximum value of the full dividend amount, is value by which the call should gap down when the underlying stock starts trading ex-dividend if the underlying price does not do anything other than drop by the dividend amount.
So, I hope you can now better understand why I think that calls can be expected to gap down by amounts approaching the dividend amount at an ex-dividend event.