Option valuation for arbitrary distribution using monte carlo simulation
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. -- View this message in context: http://r.789695.n4.nabble.com/Option-valuation-for-arbitrary-distribution-using-monte-carlo-simulation-tp4095718p4103714.html Sent from the Rmetrics mailing list archive at Nabble.com.
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