I think this statement/claim is incorrect but I need confirmations

[sleepybird]

I'm reading a report that contains the following statement/claim: "Option pricing theory tells us that a put and a call on an asset will have the same value if the strike price and exercise dates are the same, and volatility of the asset itself is the same."

My FRM/CFA knowledges tell me that this is totally incorrect per the put call parity formula: S+P=C-Xe^rT.
Are you guys with me on this one?
I would appreciate your confirmation on this one.

I agree the volatility will be the same per the volatility smile chapter.

Thanks.

 

[Hend Abuenein]

Hi,
1- Why did you deduct here : "C-Xe^rT."
off my memory the parity goes : C+Ke^rt=S+P

2- The statement doesn't specify whether options are of the same kind (European Vs American or otherwise). Are they?

 

[sleepybird]

Hi Hend,
Happy holidays.
You're right. Typo. European option as inferred by the context.
All I'm trying to say is that this statement is wrong. Do you agree?
Thanks.

 

[Hend Abuenein]

Hi Sleepybird,

Thanks, and happy holidays to you too.
You're right about the inference. Sorry.

About the statement, I think I have to disagree with you for the same reason: the put-call parity.

Unless the 2 options were offered/priced in 2 different markets/countries (i.e. risk-free rate is not the same) then there remains no reason for the 2 options to be differently priced. This of course is per theory of option pricing, meaning that some pricing mistake, or underlying information, could cause deviation from theory.

I'd like to know your thoughts about why statement is wrong.

 

[sleepybird]

Hi Hend
Thanks for taking the time to respond during holidays.

The statement seems to mean P=C. Shouldn't it be P=C+Xe^rT-S? (Just rearranging the put call parity formula).
No?

 

[Hend Abuenein]

Ohhhh I get it now.

I guess you're right then. There should be a difference in their values equal to X^rt+S

 

[Jas]

Not assuming heteroskedasticity and irrespective of volatility as per BS, this statement will be true (out-of-money call equals the in-the-money put) when the stock price becomes equal to the present value of the strike price.
In other conditions, P and C will vary (as per BS model). In practice, however, they may have a broader stock price band where these may be equal.

 

[vt2012]

I'm reading a report that contains the following statement/claim: "Option pricing theory tells us that a put and a call on an asset will have the same value if the strike price and exercise dates are the same, and volatility of the asset itself is the same."

My FRM/CFA knowledges tell me that this is totally incorrect per the put call parity formula: S+P=C-Xe^rT.
Are you guys with me on this one?
I would appreciate your confirmation on this one.

I agree the volatility will be the same per the volatility smile chapter.

Thanks.

Of course this is bullshit in general. Sometimes/for some kind of options it happens.
Are you really CFA Charterholder? -

 

[sleepybird]

Of course this is bullshit in general. Sometimes/for some kind of options it happens.
Are you really CFA Charterholder? -

That was my reaction too. That sentence just stands out to be odd to me.
It may be true under certain circumstances as many of you pointed out, but I don't think this is the case here - it's just a report on option in general.
Thanks.

 

[Robert]

Hi sleepybird,

You are absolutely correct: the value of the call and put can and will be different unless the underlying spot price is at-the-money (i.e. F=K and call/put delta = +50/-50). If the underlying spot price is not ATM then the absolute value of the deltas of the call and put will be different (e.g. call delta = +70, put delta = -30). Since, by definition, delta is an option's probability of being in-the-money, one would not willing to pay the same price for a call and a put if they had an asymmetric probability of being in-the-money.

Thanks,
Robert