[R-SIG-Finance] Option valuation for arbitrary distribution using monte carlo simulation

[Patrick Burns]

I think it *is* clear what the volatility
of a stable distribution (other than
Gaussian) is: infinite.

That implies, I believe, that the price
of most options would also be infinite.
I'm not so convinced that doing a Monte
Carlo for options pricing with a stable
distribution is a good idea.

Caveat: I'm basically ignorant about options
pricing.

Pat

On 24/11/2011 15:36, Matthew Clegg wrote:
> The stable distribution is among the earliest distributions that have been
> proposed for describing the returns of financial assets.  It was first
> suggested by Benoit Mandelbrot [1], the same person after whom the
> Mandelbrot set is named.  It's probably fair to say that Mandelbrot's work
> launched the study of asset price distributions.  Since then, there have
> been dozens of distributions proposed that have been argued to have better
> properties.  From a modeling perspective, one of the disadvantages of the
> stable distribution is that the variance is undefined (infinite) if alpha<
> 2, so it is not clear what it would mean to talk about the volatility of a
> stable-distributed process.
>
> [1] Mandelbrot, Benoit, "The Variation of Certain Speculative Prices," The
> Journal of Business, Vol. 36, No. 4 (Oct. 1963), pp. 394-419.
>
>
> On Thu, Nov 24, 2011 at 8:04 AM, msalese<massimo.salese at gmail.com>  wrote:
>
>> Hi guys, I think that you can use what distribution you want.
>> Stable is one of that better fits the log returns (it's my opinion!)
>> But you can have more info giving a look at
>> http://www.mathestate.com/tools/Financial/map/Overview.html).
>> If you prefer you can price with GARCH to better reproduce the smile
>> effect.
>> I'm a buyer side trader (risk taker), I price options only to create future
>> scenarios and on that scenarios I plan the reaction.
>>
>>
>> --
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>> Sent from the Rmetrics mailing list archive at Nabble.com.
>>
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>
>
>

-- 
Patrick Burns
patrick at burns-stat.com
http://www.burns-stat.com
http://www.portfolioprobe.com/blog
twitter: @portfolioprobe