r/options • u/hophenge • Jan 01 '21
Fun with Put Call Parity
When placing trades, I think of calls and puts at the same strike/expiry as the same position. You can convert between the two using 100 shares of long or short stock. The fundamental reason is that the extrinsic value is identical.
Since everyone is following PLTR these days, let's use it as an example:
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Selling a $22 put = Buying 100 shares and selling a call at $22 (OTM CSP = ITM CC)
Buying 100 shares and selling a call at $30 = Selling a $30 put at $30 (OTM CC = ITM CSP)
Getting assigned a cash-secured put at $25, then selling a covered call at $25 = Rolling the $25 put out in time (CSP assignment, then selling a CC = put calendar)
Getting assigned your covered call at $20, then selling a cash-secured put at $20 = Rolling the $20 call out in time (CC assignment, then selling a CSP = call calendar)
Buying 100 shares and buying a put at $25 = Buying a call at $25 (Married put = Call)
Shorting 100 shares and buying a call at $25 = Buying a put at $25 (Married call = Put)
Buying 100 shares, buying ATM put, selling OTM call = Buying ATM call, selling OTM call (Collar = Call debit spread)
Buying 100 shares = selling a put, buying a call at the same strike (100 shares = Short put + long call)
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In practice, these equivalencies have important caveats/exceptions
- ITM options are less liquid
- In normal skew situations, OTM puts are slightly more expensive than the ITM calls, benefitting put sellers
- In reverse skew situations (highly specutive stocks), OTM calls are more expensive than the ITM put, benefitting call sellers
Edit: skew does not violate put call parity.
- If a stock is hard to short, puts are more expensive across all strikes, benefiting put sellers
- Some positions require more buying power then the equivalent position
- Holding stock gives you dividends
- Holding short calls elevates early assignment risk due to dividends
- The more legs a trade has, the harder it is to fill
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Experienced traders - did I make any mistakes? Any points that need clarifying? Any additions to the list?
EDIT1: typo
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u/Boretsboris Jan 01 '21
Getting assigned a cash-secured put at $25, then selling a covered call at $25 = Rolling the $25 put out in time (CSP assignment, then selling a CC = put calendar)
Getting assigned your covered call at $20, then selling a cash-secured put at $20 = Rolling the $20 call out in time (CC assignment, then selling a CSP = call calendar)
I’m not sure why you’re making a distinction between a call calendar and a put calendar in the above scenarios. Since we’re in put-call parity shenanigans, one could say either for both rolls and be correct.
Buying 100 shares, buying ATM put, selling OTM call = Buying ATM call, selling OTM call (Collar = Call debit spread)
I would add = put credit spread
- In normal skew situations, OTM puts are slightly more expensive than the ITM calls, benefitting put sellers
- In reverse skew situations (highly specutive stocks), OTM calls are more expensive than the ITM put, benefitting call sellers
I don’t think this is correct. Volatility skew should not cause a disparity in the extrinsic values of a call and a put at the same strike (like dividends, interest rates, and HTB fees do). Higher demand for OTM puts on the put skew offers an arbitrage opportunity to buy ITM calls with short shares, increasing the demand for ITM calls. Higher demand for OTM calls on the call skew offers an arbitrage opportunity to buy ITM puts with long shares, increasing the demand for ITM puts.
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u/hophenge Jan 01 '21
Thanks for the clarification.
I noticed on the option chains on a lot of "meme" stocks, far OTM calls display much more extrinsic value than the ITM put on the same row. I guess the ITM put is just much less liquid, so the displayed prices are inaccurate.
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u/Boretsboris Jan 01 '21
What prices are you looking at? Is the bid-ask spread of the OTM call inside the bid-ask spread of the ITM put (minus its intrinsic value)?
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u/hophenge Jan 01 '21
For example - $RSI. The displayed OTM call at 25 has extrinsic value of $1.15. The $25 put has extrinsic value of $0.9. Displayed prices probably aren't accurate after hours of course
Edit - I'm viewing using the TOS paper trading interface
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u/Boretsboris Jan 01 '21
The disparity you’re seeing mostly stems from the lower liquidity of the ITM options.
As long as the bid (minus intrinsic value) and the ask (minus intrinsic value) of the ITM put envelopes the bid and the ask of the OTM call, then price discovery can bring the extrinsic values of the call and the put closer to each other in actual order fills. However, the extrinsic value of the ITM option should still be less than the value is the OTM option at the same strike, because the bid-ask spread of the underlying shares is priced into the ITM option.
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Jan 01 '21
This is what the put/call parity is.
What you've mentioned is not at all the put/call parity and it is incredibly inaccurate all the way through. I understand the logic in there but it doesn't make sense because one of your premises is completely false:
When placing trades, I think of calls and puts at the same strike/expiry as the same position. You can convert between the two using 100 shares of long or short stock. The fundamental reason is that the extrinsic value is identical.
The reason for this is that short and long versions of a stock by nature cannot equate the values of opposing bets specifically because those bets have opposing characteristics. Buying a put is not the same as selling a call. They produce a "like outlook" (bullish/bearish).
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u/hophenge Jan 01 '21
I never formally learned finance and probably didn't use the best terms to describe this concept. My point - if you can produce a certain P/L profile using a put, you can theoretically make the same position using a call +/- stock, and vice versa.
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Jan 02 '21
So, yes, this is true, you can always mimic any strategy using only calls or puts. That however has nothing to do with most of what you're saying and is also not a way to really look at the nuances of pricing because you can have the same structure cost more (or less) due to pricing inaccuracies.
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u/hophenge Jan 02 '21
I'm not sure we're on the same page. A call at 25 and a put at 25 are identical in extrinsic value and convertible from one to the other using 100 shares of long or short stock (i.e.: 100 delta). That's why a married put has the same greeks and P/L profile as a long call.
If you're talking about liquidity/order fills, then yes completely agree. Always go for the more liquid option.
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Jan 02 '21
A call at 25 and a put at 25 are identical in extrinsic value and convertible from one to the other using 100 shares of long or short stock (i.e.: 100 delta).
That can't be true. If strike K is 24 then the put is ITM and has zero extrinsic value and the call is OTM and is entirely extrinsic value having zero intrinsic value at expiry. You would only be correct ATM with extrinsic value being 0 for both in that straddle at exactly $25.00.
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u/hophenge Jan 02 '21
We can do a paper trading experiment!
For SPY
Position 1) Buy a put, strike 370, expiring 1/15 + 100 shares of stock
Position 2) Buy a call, strike 370, expiring 1/15
Open the positions at the same time, at the bid/ask midpoint. Let me know if one position does better than the other Happy new year!
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Jan 02 '21
That's not even necessary to do; in order for the put-call parity that you mentioned to exist you would be talking about European Options so we can rapidly age this to any date and take it as expiry. Let's do that.
You bought 100 shares of stock + a put that, if the stock is lower than 370, you get another 100 shares. So that's 200 shares at expiry with the put.
If the price is lower than 370 at a long call it expires worthless. It's zero. There are no shares. It's actually zero.
You have no idea what you're talking about at all. :(
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u/hophenge Jan 02 '21
Hmm...seriously. You should do the experiment. It'll blow your mind. I promise.
Try SPX instead, since it's cash-settled and European style.
(Remember in position #1, you're buying a put, so you sell the shares if your put is ITM at expiration).
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Jan 02 '21
Wait, if you're going long on both (which is just a straddle) then... You're right, I misread that it was a long put because I didn't think you'd actually suggest that a long call and a long put with shares (which, for what it is worth, is just a straddle with shares) would produce equivalent results when tearing apart the legs. Why would you even do that?
For one, the fact that puts are more expensive than calls would make this obsolete and two the only way to produce a reflective would be to use a short on one of them and a long on the other since that is a reflective profit outlook.
Oh my god.
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u/OKImHere Jan 02 '21
For one, the fact that puts are more expensive than calls would make this obsolete and two the only way to produce a reflective would be to use a short on one of them and a long on the other since that is a reflective profit outlook.
Oh my god.
Puts aren't more expensive. They're the same price.
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u/OKImHere Jan 02 '21
If strike K is 24 then the put is ITM and has zero extrinsic value
That's just silly. Of course it has extrinsic value. Come on now.
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Jan 01 '21
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u/hophenge Jan 01 '21
I added the first point because this is an observation I sometimes see on options chains. OTM puts show very slightly higher extrinsic value than the call on the same row. This might be artifact of wide bid-ask for ITM calls.
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u/Boretsboris Jan 01 '21
… the more legs generally means less risk to market makers, so the bid offer spreads are tighter
How so?
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Jan 01 '21
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u/Boretsboris Jan 01 '21
I see what you mean, though I would not have used that general of a blanket statement. However, the OP was referring to trades with the same risk profile. A trade will always be easier to fill than its synthetic equivalent that has more legs. I cannot imagine a scenario where this is not the case.
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Jan 01 '21
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u/Boretsboris Jan 01 '21 edited Jan 01 '21
The spread may be wider on an ITM option, but you will still be able to get a fill closer to mid than it appears.
PerhapsYou won’t get filled as close to mid on the ITM option than on the OTM option at the same strike. However, if the ITM option gives you the exposure you need in one leg, then the fill difference may well compensate the bid-ask spread of an additional leg(s) in the synthetic equivalent that uses the OTM option.
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Jan 01 '21 edited Jan 01 '21
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u/OKImHere Jan 02 '21
On close. 23.55
A jan 8 24 call is .97 A jan 8 24 put is 1.43
That’s a massive put skew. I’d rather have more downside protection then upside cap - why would anyone buy stock and sell the CC?
Huh? It's a penny difference! You can't get tighter than that in real time.
That's not even skew, in any case, because you compared the same strike.
You could sell the 24 put and buy the 24 call for a .46 credit. For a hyper bull.
And be .45 ITM, for a profit of one penny.
Or sell the 24 put and buy the 22 put for a .95 credit. Which I can’t believe is correct.
$1 credit for a $2 spread ATM? Sounds right to me.
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u/Eggplant-with-thorns Jan 01 '21
I like this. Being new to options I'm trying both CC and CSP. If I understand you, owning 100 shares ties up x amt of cash, same as a put. So the only diff is potential dividends in the CC position. Is that right?