Unusual kurtosis

MasterAtWork · Mar 16, 2010

Hi nitro,

Quote from nitro:

If the risk neutral distribution has a much higher kurtosis than the real
distribution, one possible trade is to sell OTM options (call and put) and buy ATM or near-the-money (NTM) options. So a long butterfly centered around the ATM would be a kurtosis trade if you believe this thesis, or short a butterfly if you don't (if you believe the curve will flatten), or no kurtosis trade at all if the real and risk neutral coincide.

Why are you comparing risk neutral distribution with real one ?
Risk neutral distribution is just a tool to price derivatives. In no way it has to do with real distribution. In fact the real distribution can't be known. The only thing that is known is past prices hence a distribution based on past prices, if one does exist.

Masteratwork

Swan Noir · Mar 16, 2010

Do you actually believe that Lefty said that? Some ghost writer might have put that in a book or someone might add it to a screenplay but no one as sophisticated as he was could ever utter such an absurd statement.

Quote from panzerman:

"Never bet on a long shot."

- Frank "Lefty" Rosenthal

stock777 · Mar 16, 2010

what lefty really said was "Never bet on a longshot unless the fix is in"

GS uses that motto often

Swan Noir · Mar 16, 2010

A nice rhetorical flourish but I think it is safe to assume that Lefty has seen long shots that he believed were drastically under priced.

Quote from stock777:

what lefty really said was "Never bet on a longshot unless the fix is in"

GS uses that motto often

erol · Mar 16, 2010

Quote from nitro:

If the risk neutral distribution has a much higher kurtosis than the real
distribution

what is a risk neutral distribution?

what do you define as the "real" distribution?

I'm genuinely curious since I want to understand what you've posted.

thanks!

MasterAtWork · Mar 17, 2010

Risk neutral distribution is the probability distribution that makes the expected future price be (today) forward price.
Because the trend of an underlying doesn't make sense as one prices a derivative (because pricing models are based on a delta hedge strategy), that way, the expected future price is the forward price.

Given that, if the expected future price is forward price, there's no risk at all (all the risk is erased by a delta hedging strategy).

Of course, that risk neutral distribution has nothing to do with the real one. Real distribution doesn't expected that future price at maturity be today's forward one. That way, it would be better to invest all the money in a cash account.

Masteratwork

erol · Mar 17, 2010

Quote from MasterAtWork:

Risk neutral distribution is the probability distribution that makes the expected future price be (today) forward price.
Because the trend of an underlying doesn't make sense as one prices a derivative (because pricing models are based on a delta hedge strategy), that way, the expected future price is the forward price.

Given that, if the expected future price is forward price, there's no risk at all (all the risk is erased by a delta hedging strategy).

Of course, that risk neutral distribution has nothing to do with the real one. Real distribution doesn't expected that future price at maturity be today's forward one. That way, it would be better to invest all the money in a cash account.

Masteratwork

thank you Masteratwork, this is very helpful!

nitro · Mar 20, 2010

Quote from shortie:

this unusual kurtosis, do you see it only in march options? what about april?

No, at least it is not visible to me in this time frame. But in this thread I hint as to why it might or might not be there.

http://www.elitetrader.com/vb/showthread.php?threadid=194276

If you don't use a telescope, you cannot see the rings of Saturn. If you don't use a microscope, you cannot see microscopic life. It may be that my tools are too blunt to see high kurtosis out in April.