Gaussian/ non-Gaussian

Well, I have read a lot of interesting stuff here by 3 or 4 members (they'll know who) and while not being an expert on the topic myself ( not even an option trader) I am hoping to get valuable input on a topic I consider interesting.

First: I've read Mandelbrot and I'm in the middle of Natenberg.

Second: Everybody knows Black-Scholes is based on a lognormal distribution of Gaussian origin. Everybody knows this is effectively incorrect.

Third: If you read well certain interviews, you come to perceive that virtually every successful major options firm has a proprietary model that is basically Black-Scholes scaled to include a higher probability of outliers.

Fourth: Most of the non-proprietary software including that used by many pros and the implied vol numbers of virtually every data feed seem to me non-scaled / Gaussian.

So question 1: When there is ongoing arbitrage of some firms between the Gaussian and the non-Gaussian model implications will that suffice to keep the market efficient?

Question 2: If it does not suffice, is there a strategy at all someone could profit from a possible mispricing outliers vs. moderate ITM/OTM?

 

Feel free to correct me here if I'm wrong, but I think you can use Black Scholes with non- lognormal 2cd and 3rd moments. I've only read the cheesedick version of Mandelbrot (The Misbehavior of Markets), so his real paper might have more meat to it. I don't see why many of the examples he sites in his book can't just be attributed to a non- normal kurtosis and skew. I haven't read Natenburg. What did he write?

The Garch models seem to do alot to account for the volatility clusters that Mandelbrot makes note of. I've heard of traders who are impressed with them, but I've never tried them myself.

 

I have often thought that it would be a good strategy to buy options with strikes just outside of 2 standard deviations sell the next closest strike within 2 standard deviation. Everyone seems to think that this is the magic barrier of likelihood when really it is just a made up number based on piles of academic garbage.

 

Don’t see how that can be called “arbitrage”, it’s merely a disagreement between two parties as to how the underlying is distributed, and I don’t know of anyway to “lock” a profit on that basis.

If you disagreed with the skew / smile then sell the expensive strikes and buy the cheap ?

 

The further from the money, the more the theoretical values are lost in the slippage.

I'm with the crowd that thinks the market sets the prices and it is right, while the models just try to model its behavior. It depends of your reference point, but we all know that the dog wags its tail, and not vice versa.

To take advantage of the equity option IV smile the most favorable strategies are bear vertical spreads, call backspreads and put ratio spreads. You can pick the one that matches your price / IV outlook and time frame.

 

I also think the market is generally efficient. With all the human brains and computer power analysing and monitoring each option market, it's difficult to imagine otherwise.

Where the long strike is lower than ATM. Or Bull verticals, where the Long strike is higher than ATM.

Where the ratio isn’t 1:1 look at the volume weighted IV.

Lot’s of combinations possible. Not sure this answers our friends question(s) though.

 

Don't bother any longer with your Gaussian stuff if you are still dreaming of squeezing money out of the market. You need to be pretty smart to find the right things though. Further, Mandlebrot is nice to look at while killing some time in between trades. Keep on posting about it though, many people take this as very clever stuff.

BTW, as to your " Everybody knows Black-Scholes is ...", this is why they gave them the Nobel prize. Can't make money in markets with these prizes.

 

Well, how I said, I'm not an options trader and wouldn't dare step into that pool in the moment.

My main interest is how beliefs influence markets. There are several unbased religious beliefs over economics and finance and the normal distribution thing has been believed to an enormous extent.

But I actually made my conclusions.

My very personal feeling, according to my very personal evolutionary theories is:

-belief in normal distibution is a potential trap for market makers in options

-I'm not a market maker in options and I don't know how many traps there are, but it should be zillions. Since this topic is pretty old, the existing survivors will know how to deal with it.

-If there were zillions of aspiring newbies waiting to become market makers you could catch some of their money. But aspiring newbies simply don't make markets, they create some fancy Gann cycles.

-So the only effect seems to be some blur in the pricing of outliers (high spread and slippage) because of public insecurity how to price them. Well yeah, that's not news, I know.

My apologies for wasting your time and , yes, the word arbitrage doesn't apply, sorry.