What am I missing about put-call parity and American style options?

markuzick

markuzick

I read that it only works for European style options.
Can anyone give me an example of how early execution/assignment would add risk to arbitraging IV differences between ATM puts and calls?
Let's say the underlying is 100 and the ATM calls and puts are 6 and 9: if I shorted the stock; bought a call; and shorted the put, what would be so bad if the stock dropped and was assigned to me early - wouldn't I just be ahead by 3 plus any residual value of the call sooner than expected?
 
That scenario would only exist if there was a dividend or borrow costs equaling 3 dollars. It's sub optimal to exercise a put BEFORE the dividend so if it played out like you said, you would make three dollars but in all likelihood you would owe three dollars in borrow or paid in Leiu dividends.
 
OK, so if there is no dividend; and borrowing costs are small, then put-call parity will hold for American style options?
BTW: when you're short stock, in the case where puts are more expensive than calls, dividends and borrow costs are just as much a factor for European style options as American style options; and when calls are more expensive than puts, you would be long stock so, in that case, these are not costs for either style options.

How does the possibility of early execution/assignment make a difference? What am I overlooking?
 
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Early exercise really only matters on the call side. On the putside the difference between American and Eurpopean option is a financing trade (if you are long a put and the stock goes to zero, it's worth exercising so you can reinvest the strike price in the risk free rate).

It's not whether the calls or the puts are more expensive. It has to do with the market value of the forward vs your ability to fund / carry that forward. If you had a scheme where you didn't have to pay borrow costs you would make a fortune even if the calls are more expensive than the puts.
 
And I'll just add, from a retail account size perspective there's almost never arbitrage opportunities like you're outlining here. Things like dividends, roll yields, and all the other things that affect the expected outcome of an underlying are all taken into account in the prices of options. I guess what I'm saying is, unless you have some kind of edge in reducing the carry costs and transaction fees (which would likely only exist for institutional traders) there are likely not going to be any arbitrage opportunities like the one you're trying to find.

Occasionally you'll see something that stands out, or effective use of a market screener will flag something odd and you can take advantage of a very small sliver of an opportunity, but for the most part all mathematical edge is eaten away by carry costs and transaction fees, and in the end you'd really only be speculating on future price movements.
 
I understand that dividends and borrow costs can affect put-call parity. My issue, though, is about why put-call parity is said only to apply to European style options.

My other issue is that put-call IV for ATM options on non-dividend paying stocks will sometimes diverge by a large margin due to bullish/bearish sentiment. Are you saying that this phenomenon is too fleeting to capture?
 
Put call parity holds for American options but it's an inequality. You can look up the American put call parity inequality.

The impled vol for a ATM option will never differ by much (excepting bid offer in illiquid instruments). If they do it's because of borrow or dividends. Put call parity means (and this holds for American options) that you can synthetically create one option with the other option and stock. The only difference would be the borrow and dividends which don't affect implied volatility.
 
My other issue is that put-call IV for ATM options on non-dividend paying stocks will sometimes diverge by a large margin due to bullish/bearish sentiment. Are you saying that this phenomenon is too fleeting to capture?
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Yeah pretty much. I'm sure there are those occasional times like I said where you might be able grab a sliver of profit from some weird price action, but as far as trying to build a strategy around it, it's pretty futile.

If you were to consistently be grabbing profit out of these kinds of trades, it would not be because of inefficient divergences in the volatility. It would simply be because you've created a price bias and have been correct more often than not.

The only mathematical edge that would exist is only available to those who have access to better prices and reduced carry costs. Not for us little guys I'm afraid...
 
You used to be able to trade these for special dividends when the occ was inconsistent with their treatment of those divs. That opportunity is over.
 
markuzick said:
I understand that dividends and borrow costs can affect put-call parity. My issue, though, is about why put-call parity is said only to apply to European style options.

My other issue is that put-call IV for ATM options on non-dividend paying stocks will sometimes diverge by a large margin due to bullish/bearish sentiment. Are you saying that this phenomenon is too fleeting to capture?
More...

Good observation!
 
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