Looking for a math term

Can one reformulate the question like this? :

If the underlying moves >= 3% intraday, then
- what is the probability that a Call will go ITM?
- what is the probability that a Put will go ITM?

I think one of the Greeks out there can already give you the answer to this question :) Just ask all the Greeks out there... :)
 
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You're missing the point here.

Your question has nothing to do with options. You're looking for the shape of the return distribution of the underlying which - for stocks - is left tailed (goes down faster than it goes up)
 
Skew would impact p/c pair identically. It's not skew. The two identical strikes cannot move at materially different rates. Or there would be a riskless arb. unless there was something like an HTB
 
SoCalOptionsWriter said:
(It's not, I think, one of the Greeks or minor Greeks, but I posted here thinking this group might be more mathematically minded.) Anyway, is there a term for the phenomena by which a call going into the money (or a stock or future rising) will do so slower than a put going ITM (or stock or futures falling), when the move is large and sharp -- meaning, say, over 3 percent in less than one day? I'm looking for like speed or velocity or something. (Maybe it has something to do with the put-call ratio, but I don't think so, as that is volume, but hey, who knows?)
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This may be a stupid question, but have you ever observed this phenomenon?
The reason I ask is, if you have, depending on when you looked, and when you made the comparison, could it be there's an ex-dividend date that's incorporated into the pricing of the put/call? On the surface at least, if one did not know that, what you describe above would in fact appear to happen. Especially if you happen to look on a day the market was selling off but it also had a few erratic up-spikes.

I'll paste Investopedia because they write better than I do lol:

Both call and put options are impacted by the ex-dividend date. Put options become more expensive since the price will drop by the amount of the dividend (all else being equal). Call options become cheaper due to the anticipated drop in the price of the stock, although for options this could start to be priced in weeks leading up to the ex-dividend.

Just a thought. You might have already known that though.
 
vanzandt said:
This may be a stupid question, but have you ever observed this phenomenon?
The reason I ask is, if you have, depending on when you looked, and when you made the comparison, could it be there's an ex-dividend date that's incorporated into the pricing of the put/call? On the surface at least, if one did not know that, what you describe above would in fact appear to happen. Especially if you happen to look on a day the market was selling off but it also had a few erratic up-spikes.

I'll paste Investopedia because they write better than I do lol:

Both call and put options are impacted by the ex-dividend date. Put options become more expensive since the price will drop by the amount of the dividend (all else being equal). Call options become cheaper due to the anticipated drop in the price of the stock, although for options this could start to be priced in weeks leading up to the ex-dividend.

Just a thought. You might have already known that though.
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But this is also something that could apply in non-stock options like futures as the OP stated so it might not be related to ex-dividend.
 
TheDawn said:
But this is also something that could apply in non-stock options like futures as the OP stated so it might not be related to ex-dividend.
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Yeah, the question really wasn't worded quite well enough, for me at least, without some kind of example to look at. Was it hypothetical or did he see this on one (or across multiple instruments) over time? I'm pretty sure it doesn't happen in reality because there would be some kind of split second arbitration play if it did... so if it was something he observed on numerous occasions, that's the only explanation I could come up with. And even that would be obvious to a somewhat seasoned options trader. The first thing I'd look for would be an ex-dividend date encompassing that particular strike/expiration.
 
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vanzandt said:
Yeah, the question really wasn't worded quite well enough, for me at least, without some kind of example to look at. Was it hypothetical or did he see this on one (or across multiple instruments) over time? I'm pretty sure it doesn't happen in reality because there would be some kind of split second arbitration play if it did... so if it was something he observed on numerous occasions, that's the only explanation I could come up with. And even that would be obvious to a somewhat seasoned options trader. The first thing I'd look for would be an ex-dividend date encompassing that particular strike/expiration.
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Yeah but the thing is the phenomenon that the OP is describing wouldn't give rise to any arb opportunities because the same condition is only affecting one type of option and not another. How can one arb it I wonder. What the OP is describing looks like some kind of difference in gamma which directly affects the delta between puts and calls given the same magnitude of price movement in the underlying. Is that difference simply due to put-call parity or is there something else in addition? If there is, if there is a mathematical term to describe it. I think this is what OP is asking.

I dunno if there are any studies out there that have studied this phenomenon in real time.
 
$50 stock
Zero interest rate and zero dividends
The p/c pair are each the same price and each 50 delta - calls are positive delta and puts are negative.
As has been mentioned a positive interest rate makes the call more expensive and the put cheaper.
Dividends make the carry cheaper - calls are less valuable and the puts more valuable.
If options are exactly ATM - the net carry is the difference between p/c prices. There are spreads so the moves can be a little more/less then their calculated value.
HTB and this is fun can be thought of as a negative dividend. Bumps the put value because that needs short stock to hedge - does impact the call as long as the stock can be freely bought.
Most retail models look at varying price and volatility. So the bumped up put looks like it's trading a higher volatility - which it is not. The put and call are trading with different carry calculations. There are other factors at play, but no pricing model is immune to short term supply and demand. In fact most retail vendors don't calculate the delta for the put and call - they calculate the call and default to the put.
So price action in the underlying - should have a longer explanation - runs the call to a 55 delta. The put would go to -45 delta. Still an absolute value of 100(can be thought of as 100 shares) and they would move at different rates, p/c parity would still hold.
What if an uncorrelated move could occur.
The stock rallies and the call goes to 60 delta and the put goes to -20 delta. I would do a conversion S+P-C=T-bill except the mis-valued p/c would make this a much higher yielding bill.
Thoughts: Not exactly a risk-less T-bill if these are American options, but no sensible investor would exercise the overpriced call early. Doesn't mean it can't happen, but it would be an unexpected act of kindness. Can supply/demand create a short-term disruption. Of course. Old floor expression - "even Ray Charles would see that mispricing." How many MMs and desks would see this? "The lights would flicker in a handful of trading centers. BTW this is why put buying is not a haven for HTB - it's priced in as are dividends.
B/A makes this more valuable for MMs.
Can prices stay out of whack for long? Depends on how readily tradable and liquid the pieces are.
The conversion/reversal business paid a lot of bills for a lot of years for the MM community
 
TheDawn said:
Yeah but the thing is the phenomenon that the OP is describing wouldn't give rise to any arb opportunities because the same condition is only affecting one type of option and not another. How can one arb it I wonder. What the OP is describing looks like some kind of difference in gamma which directly affects the delta between puts and calls given the same magnitude of price movement in the underlying. Is that difference simply due to put-call parity or is there something else in addition? If there is, if there is a mathematical term to describe it. I think this is what OP is asking.

I dunno if there are any studies out there that have studied this phenomenon in real time.
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Yeah well... that's why I said it wasn't perhaps worded as well as it could have been.
Way too many unknowns.
 
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