Comparison of models

[Ravani, Michele]

hi

does anybody know where I can find a comparison of models?
For instance, if I price an American option on a stock with different models keeping all the parameters constant, what is the difference in the theoretical price of the option?
I know that I could do that easily with QL (and I will do it) but I don't have the time right now and I am really curious.
So I am hoping that somebody has already done it :o)
My basic question essentially is: if we take simple vanilla derivatives, does it pay to invest in models which are more advanced that BS or Binomial?

Thanks

Michele

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[Rama Cont]

Of course the model makes a difference in the price.
However the comparison does not make sense for a single option since you
can always choose model parameters in different models to get the same
price for a single option.
However if you use many options, say all vanilla options traded on
a given underlying, you need a model with time-dependence/ price dependent
features to fit the cross section of option prices.
Typical examples are: local volatility models, stochastic volatility
models, jump-diffusion models and combinations of these.
There is a large literature in quantitative finance journals comparing
various models.


--------------------------------------------
 
Rama CONT
 
Centre de Mathematiques Appliquees
CNRS - Ecole Polytechnique
F-91128 Palaiseau, France.
WWW: http://www.cmap.polytechnique.fr/~rama/
--------------------------------------------  
On Thu, 17 Oct 2002, Ravani, Michele wrote:

> does anybody know where I can find a comparison of models?
> For instance, if I price an American option on a stock with different models keeping all the parameters constant, what is the difference in the theoretical price of the option?
> I know that I could do that easily with QL (and I will do it) but I don't have the time right now and I am really curious.
> So I am hoping that somebody has already done it :o)
> My basic question essentially is: if we take simple vanilla derivatives, does it pay to invest in models which are more advanced that BS or Binomial?
>
> Thanks
>
> Michele
>
> "MMS <csfb.com>" made the following
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[Ravani, Michele]

Hi

> Of course the model makes a difference in the price.
> However the comparison does not make sense for a single option since you
> can always choose model parameters in different models to get the same
> price for a single option.

I was looking for an indication. Obviously, one should compare using a wide range of products and parameters, but for a 'quick' feeling I would have been happy to see a cross section of models compared keeping all parameters fixed.

> There is a large literature in quantitative finance journals comparing
> various models.

Do you have any pointers handy?

Thanks
 Michele


"MMS <csfb.com>" made the following
 annotations on 10/18/02 08:21:10
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This message is for the named person's use only.  It may contain confidential, proprietary or legally privileged information.  No confidentiality or privilege is waived or lost by any mistransmission.
If you receive this message in error, please immediately delete it and all copies of it from your system, destroy any hard copies of it and notify the sender.  You must not, directly or indirectly, use, disclose, distribute, print, or copy any part of this message if you are not the intended recipient. CREDIT SUISSE GROUP and each of its subsidiaries each reserve the right to monitor all e-mail communications through its networks.  Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorised to state them to be the views of any such entity.
Unless otherwise stated, any pricing information given in this message is indicative only, is subject to change and does not constitute an offer to deal at any price quoted.
Any reference to the terms of executed transactions should be treated as preliminary only and subject to our formal written confirmation.


==============================================================================

[Perissin Francesco]

Hi I'd like to add a word, too....

>My basic question essentially is: if we take simple vanilla derivatives,
does it pay to invest in models which are
>more advanced that BS or Binomial?


As already written by Rama CONT, the point is building a model that fits the
prices of vanilla derivatives. The prices of vanillas are "always" correct
since, they are given by the market. The model essentially is used for
pricing and hedging exotic instruments, and the hedge is done using
vanillas.
So the answer could be "no", theoretically all models should give the same
prices (and very similar greeks) for vanillas. But rember: if you trade
vanillas, are they still vanilla the day after? On equities this could be
true most of the times, but on interest rates they are a bit less vanilla,
since the expiration dates of vanillas have changed .... THey are still
vanillas, but on day 2 you are not able to close your risks by trading other
vanillas!!!

This is not complete yet, since one could argue that the model is also used
for finding inconsistencies between vanilla prices, and arbitraging them. In
practices, due to transaction costs and bid-ask spreads, this practice is
rather difficult to implement...

Hope this helped somehow...

Francesco
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