ATM straddle vs. delta neutral straddle

C

coolraz

Can someone explain to me the differences between an ATM straddle vs. a delta neutral straddle. What I am trying to compare is this:

Say a stock trades at 55
An ATM straddle would be to buy 1 55 put and buy 1 55 call. Now, theoretically, the price of both the put and the call should be the same, but this is not the case. In reality, sometimes the 55 put will be cheaper. Thus, this straddle would not be delta neutral. So, looking at the option chain, you find the deltas that are most close together to be of the 65 call and 55 put.

So it would seem that the 55call/55put straddle is skewed to the upside (has positive delta b/c the delta of the more expensive call is higher), whereas the 65call/55put straddle is truly neutral b/c the deltas almost cancel each other out. would that be correct?

Now, I put on a true delta neutral straddle in real life, it turned out that it was not delta neutral....
The stock went from 55 to 60, so you would expect the 65 call and 55 put to increase/decrease in value equally but that was not the case. Is that because of the effect of GAMMA? but the gamme for the straddle was also essentially zero (i believe it was .17 or something like that). Is that little differnece in gamma sufficient to explain why the 65 call/55 put did not change in value by the same amount or was it market forces not following the theoretical B-S pricing?

Finally, if in the future I want to put on a truly "market" neutral straddle, should I go ATM rather than delta neutral?

Thanks!
 
(1) You might have been looking at stale data. The ATM put and call should be trading with nearly the same price. (2) The stock you were looking at might have had a big dividend payout on the near horizon. That would "depress" the call and "inflate" the put. (3) If the rally from 55 to 60 was "slow", there was probably some "volatility crush" (vega) taking place that pressured both the put and call. Maybe that can explain why the premiums didn't behave as you expected them to.
 
Hey guys, thanks for the responses!

The stock had no dividend payouts and the data is real time from ivolatility.com. the rally was FAST (i.e it happened as a gap up from close to next day open on earnings announcement). There was an IV crush after the earnings, obviously, but the IV decreased equally on put AND call.
After a few days, the parity was restored (i.e the call price was = put price at the same strike price when stock was at that strike price).

Could it be that it was market forces at work?

This was just before earnings annoucnements, so I was thinking could it be b/c there were a lot of buyers for the calls (people expecting a large pop upwards on good earnnigs) which pushed their price up?!
 
did you check the skew at the time?

also, parity does not mean that the ATM puts and calls will trade at the same price.
carry is distributed lognormally
 
Nevermind, I understand what you meant by skew now. That is what I was referring to when I said "market forced" where the call was being bid up higher b/c people were expecting a pop.
Is that the correct interpretation?
 
Quote from coolraz:

Nevermind, I understand what you meant by skew now. That is what I was referring to when I said "market forced" where the call was being bid up higher b/c people were expecting a pop.
Is that the correct interpretation?
More...

A call and a put generally trade at the same implied volatility - put-call parity!

Most likely, what the OP meant by the skew is that as the underlying moved, the strike moved along the volatility skew curve and thus the implied volatility of those options changed affecting the pricing. Also, an ATM straddle has significant Gamma so as the underlying moves up the call is gaining deltas and the put is losing deltas so the gain on the call will be more than the loss on the put. Gamma of 0.17 means that for every $1 change in the underlying your delta changes by 0.17. In other words, if you start with a delta neutral straddle then as the underlying moves your delta moves away from neutrality.

Finally, the only time a call and a put would trade at the same price is if there's no dividends and the interest rates are zero, which means zero cost of carry, otherwise the call is generally has a higher price due to the cost of carry.
 
MTE, thanks for answering.

Thats pretty much what I would have said.

One other point though, I see alot of talk about delta neutral, whats the gamma?, etc..

Do you intend to trade this straddle?
Scalp your gammas to recude theta risk?

It seems alot of people are getting really tied up in the greeks without a real need for it.
 
Thanks, that definetely makes sense.

Now if I wanted a market neutral straddle (where the P/L would be the same if the undelrying moved -5 or +5, for example), should I try to put on a DELTA NEUTRAL straddle or should I just go with at ATM straddle? Because in the ivolatility.com P/L analysis, the ATM is skewed towards the call (i.e it would be more profitable at underlying +5 rather than -5), and only if i match put/call deltas for delta neutral does the P/L graph look to have equal P/L at +5/-5

I am currently paper trading the two to see the difference between the two for myself, but any theoretical reasoning would be apreciated!
 
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