When P-C parity does not hold

[jamesbp]

You’re looking for absolutes, I am not going to give you that.

Robert

... not to be pedantic ... but it was you who, in fact, were suggesting that put-call parity was "absolute" and could be calculated for options with dividends that could be exercised before expiry

I suggested exactly the opposite ... that there was no "absolute" when it came to put-call parity for options with dividends that could be exercised before expiry ... as p-c parity does not necessarily hold as it does with options that cannot be be exercised before expiry

So which side of the fence have you ended up on
... p-c parity absolutely holds ( as you originally claimed ) / may not hold ( as I suggested ) for options with dividends that could be exercised before expiry

Cheers
James

 

[Robert Morse]

Robert

... not to be pedantic ... but it was you who, in fact, were suggesting that put-call parity was "absolute" and could be calculated for options with dividends that could be exercised before expiry

I suggested exactly the opposite ... that there was no "absolute" when it came to put-call parity for options with dividends that could be exercised before expiry ... as p-c parity does not necessarily hold as it does with options that cannot be be exercised before expiry

So which side of the fence have you ended up on
... p-c parity absolutely holds ( as you originally claimed ) / may not hold ( as I suggested ) for options with dividends that could be exercised before expiry

Cheers
James

I had to look up the word "pedantic". I've made my opinion clear. I just won't use your wording. The MMs that post two-sided markets have put-call parity to their model and their expected interest costs and dividend flows. It is that simple. Your cost will be different. The IVOL expressed by your software uses a set of assumptions that do not match the MMs if the Put IVOL calculation is much higher than the call IVOL calculation. They set Interest rates and dividend flows for each stock and index, your software likely uses a default one.

 

[jamesbp]

I had to look up the word "pedantic". I've made my opinion clear. I just won't use your wording. The MMs that post two-sided markets have put-call parity to their model and their expected interest costs and dividend flows. It is that simple. Your cost will be different. The IVOL expressed by your software uses a set of assumptions that do not match the MMs if the Put IVOL calculation is much higher than the call IVOL calculation. They set Interest rates and dividend flows for each stock and index, your software likely uses a default one.

Great answer
... just not to the question being asked

Does put-call parity hold for options that can be exercised early where there is a dividend before expiry
... a simple Yes / No answer will do

 

[guru]

Thanks for all the analysis ... that's the point I have been trying to make
... that p-c parity does not hold for dividend paying stocks that can be exercised before expiry

Don't you really understand such basics? Put-call parity always holds, regardless of dividends. Dividends are included in the put-call parity formula.

https://www.investopedia.com/articles/optioninvestor/05/011905.asp
" the concept also applies to American-style options, adjusting for dividends and interest rates. If the dividend increases, the puts expiring after the ex-dividend date will rise in value, while the calls will decrease by a similar amount. Changes in interest rates have the opposite effects. Rising interest rates increase call values and decrease put values."

 

[guru]

Great answer
... just not to the question being asked

Does put-call parity hold for options that can be exercised early where there is a dividend before expiry
... a simple Yes / No answer will do

Since you're both blind and dumb, let me just quote Robert:
"yes, but Put/Call party includes dividends and cost of carry"
"There is still put-call parity"

This means that put-call parity always holds.
Is this clear now? Oh, you're blind so it may still not be clear. Too bad.

 

[jamesbp]

Don't you really understand such basics? Put-call parity always holds, regardless of dividends. Dividends are included in the put-call parity formula.
View attachment 207089

How does your put-call parity formula apply to this example ?

 

[jamesbp]

Don't you really understand such basics? Put-call parity always holds, regardless of dividends. Dividends are included in the put-call parity formula.
View attachment 207089

We are discussing whether put-call parity holds for American Style ( early exercise ) options where the underlying pays a dividend before expiry.

You presented the following formula ... in an effort to prove that put-call parity holds for American Style ( early exercise ) options where the underlying pays a dividend before expiry.

However, this is actually the formula that shows that put-call parity holds for European Style ( NO early exercise ) options where the underlying pays a dividend before expiry.

A simple mistake to make if you have no idea why put-call parity does not necessarily hold for American Style ( early exercise ) options where the underlying pays a dividend before expiry.

Rather than trying to explain why this is the case to you, I have attached a better explanation from others that might help you get a better grasp on this subject before you embarrass yourself any further.

The highlights are as follows

Hopefully, you will now accept that put-call parity does not necessarily hold for American Style ( early exercise ) options where the underlying pays a dividend before expiry, but is a chain of inequalities

 

[TommyR]

Note, however, that the representation of a given group element as a product of exponentials is very far from unique, so it is very far from clear that Π is actually well defined.

 

[jamesbp]

Since you're both blind and dumb, let me just quote Robert:
"yes, but Put/Call party includes dividends and cost of carry"
"There is still put-call parity"

This means that put-call parity always holds.
Is this clear now? Oh, you're blind so it may still not be clear. Too bad.

Guru ( and Robert )

I presume you now accept that you were wrong to claim that put-call parity holds for American Style options that can be exercised / pay dividends before expiry.

In order to illustrate with a simple worked example, I have used the CBOE IVolatility Option Calculator to generate option prices for both European and American style options and calculate the put-call parity for both.

It should be clear that

#1 Put-Call parity does hold for European Style Options
#2 Put-Call parity does not hold for American Style Options, and the inequality in this case is 9.9643

If you disagree with this, feel free to provide alternative calculations / explanations that support the proposition that you wrongly argued for previously.

Regards
James

 

[Robert Morse]

I presume you now accept that you were wrong to claim that put-call parity holds for American Style options that can be exercised / pay dividends before expiry.

No, I do not. Your definition is different than mine and I'm not interested in this debate anymore. If you can't easily make money from it, the prices are correct.