#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
We can synthesize stock ownership with a synthetic forward plus cash: S(0) = (c-p) + K*exp(-rT). That's put-call parity! My memorization mnemonic is "call plus cash equals protective put:" c + K*exp(-rt) = p + S(0)

David's XLS is here: https://trtl.bz/2IzY0ui

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#### Eustice_Langham

##### Active Member
Hi, for my understanding why is it that put-call parity only holds for European style options and not American style as well. Obviously it is to do with the early exercise that American style options have when compared to European style, but can you be more specific on this please, I would hazard an educated guess to say that with American style options dividends can mean that it is profitable for early exercise and that this means that the equilibrium between put and call is no longer in place?

#### sulemanms202

##### Member
Subscriber
Dear sir David:

Is Put call parity sommehow related to BSM assumptions?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @sulemanms202 Great question! My answer is: No, put-call parity is not directly related to (i.e., a function of) BSM assumptions. Put-call parity is a no-arbitrage condition that does not require any option pricing model, BSM or binomial or otherwise. Put call parity says, for European options with identical maturities and strikes, that the current (P)V price of protective put (i.e., a package of long p + long S) must equal the price of the "package" of a long call plus cash (equal to the discounted strike price): p + S(0) = c + K*exp(-rT). This is true because the future payoff of each of these packages is identical, and if they vary too much, there an an arbitrage opportunity the exploits the gap (and brings the prices into "compliance"). Notice how none of this requires an option pricing model to validate either c or p.

In the video above (at about 8:05) I do use the BSM OPM to price the call and the put. Most of my BSM sheets do include the put-call parity: I do this partly to "verify" the outputs. If put-call parity doesn't work, then the model has a mistake. So, it's an indirect validation step for me! In this way, we do expect the BSM outputs to comply with put-call parity! But that is not to say that put-call parity requires BSM: put-call parity should apply even if traded prices vary from the BSM outputs. (But we would not expect perfect compliance in markets, right? Technical factors, namely supply/demand and liquid, often cause the traded prices to temporarily violate no arbitrage conditions). I hope that's helpful!

#### Warloski

##### New Member
Subscriber
I use the mnemonic: cow boys sing pretty, by mark meldrum

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