You are using an out of date browser. It may not display this or other websites correctly. You should upgrade or use an alternative browser. Discussion in ' P2. Cart My Account Log In Sign up Free! Relationship between American Calls and Put Options no dividends Discussion in ' P2. Hi David, The inequality for american options is I use "X" for the strike price: Is it always a covered call either with an american or european call greater or equal than a protective put constructed with an american put?

Bruno , Aug 28, Sorry my previous question contained an error. I mean fiduciary call and not covered call. Is it always a fiduciary call either with an american or european call greater or equal than a protective put constructed with an american put? On the American side, I get a different result: If we take put-call parity, but replace American with European replace c with C and p with P , then Hull 9.

Understanding Put-Call Parity | The Options & Futures Guide

But technically, I am not sure what to call this. I don't think this is a fiduciary call.

I think technically the fiduciary call is discounted strike, per the put-call parity because per the delta hedge you are borrowing only as much as you need for the exercise in the future. David Harper CFA FRM , Aug 28, Sorry to keep bothering you, but would you please check the following: Therefore, a fiduciary American call should be equal to than a covered European Call because it does not make sense to "exercise" the fiduciary american call early.

That is, the investor can keep the cash equal to K, which would be used to exercise the option early, and invest that cash to earn interest on expiration. Since exercising the american call early means that the investor would have to forgo interest, it is never optimal to exercise an American call on nondividend-paying stock before the expiration date. Bruno , Aug 29, Hi Bruno, Please, it's no bother I can't agree with any of this, sorry. But I surely may be wrong! My best guess is that is a typo David.

David Harper CFA FRM , Aug 29, Bruno, I looked up the CFA texts, and indeed they say this is quite news to me: Right now, I don't have the CFA books with me. I guess you are referring to the one written by Chance. I will take a look at the book next Monday. Do we really agree that it is never optimal optimal to exercise an American call on nondividend-paying stock before the expiration date under the restrictive assumptions?

Therefore, you can choose to immediately "pay" the strike price for the stock. In other words, the lower bound for an American call in-the money must be S-K because you can exercise it right away. Therefore, under the restrictive assumptions both C and c should trade at the same value.

So we are back to the beginning. I don't see the light.

The lower bound for an American call in-the money must be S-K because you can exercise it right away. It may be worth more for the fact that there is a probability that S, t, and volatility will decrease before expiration penalizing c.

But once again, is it true that it's never optimal optimal to exercise an American call on nondividend-paying stock before the expiration date? Bruno , Aug 30, It is easily shown that if the stock increases at the risk free rate, the PV of the future gain is this minimum value long history; FAS allowed it for private company options, calling in the 'minimum value' 2.

This is consistent with: Here is what I have not logically been convinced of: You ask, "Do we really agree that it is never optimal optimal to exercise an American call on nondividend-paying stock before the expiration date" and I think it's important this has a specific meaning.

It isn't true in practice i.

It is a statement about what is rationale behavior under perfect forecasting the stock price will continue to increase, is not temporarily mis-priced and, more importantly, restrictive assumptions namely, the holder does not value the liquidity. So, my question is still: Now instead I will ADD A FEATURE the early exercise option and instead sell you an American call C. David Harper CFA FRM , Aug 30, David, I cannot agree more with you.

An American call option on an asset without dividends should never be exercised early—but perhaps sold. It therefore has the same price as a European call option.

Why does put-call parity not hold, when option is American

Suppose that you are pretty sure that price of the underlying will drop tomorrow. The above argument shows that you should still not exercise the call option, but it might be sensible to sell the option today. If we exercised early, then we would effectively through away the put protection against downside movements inherent in the call option and be left with the underlying asset recall from the European put-call parity that the call option can be thought of as a portfolio of the underlying, a put, and some cash and also pay the strike price now instead of later—neither of which is good and which a potential buyer of the call option would be willing to pay for.

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