I read Mandlebrot's book, "The (Mis)Behaviour of the markets." In my honest opinion, the book had no new information, no interesting perspective to communicate, and obviously had absolutely no useful tools or ideas for risk management. All he did was list a bunch of tired, 25 year old criticism of bell curve modeling. He combined this with a bunch of pretty pictures and sophisticated math words. For the life of me, I can't figure out why anyone listens to this guy when it comes to finance. Taleb referred to this book as "The deepest and most realistic finance book ever published.â I can't tell if Taleb and Mandlebrot are involved in some sort of academic circle-jerk, but it is obvious that they are in love. I supposed that their ideas build off of one another. Between the two of them though, they haven't produced a shred of value to the risk management world using their chaos/black swan theories. Taleb's "Dynamic Hedging" is a wonderful book. Funny thing is that the entire"Dynamic Hedging" book is about how to tweak the BS model to manage risk in real life--exactly what actual traders do, and exactly what Taleb and Mandlebrot soap-box against.
Please show me where he has said anything brilliant. He's been pushing his Mandlebrotian market ideas for ever, His entire premise is based debunking Gaussian distributions--which presents in his book as some sort of revelation. In reality, the financial world has been aware of the limitations of the BS model, of CAPM, of Monte Carlo simulations, etc for at least 20 years. Even though they are flawed, we use these tools because they allow us to quantify risk. A good risk manager knows that the numbers are only part of the story, and every stress test imaginable needs to be run on any portfolio of risk. The big problems I have with Mandlebrot and Taleb are that they 1) present an extreme strawman version of the BS risk management methods, 2)act as if their critiques of Gaussian distribution market modeling is somehow their fresh idea, and mostly 3)THEY FAIL TO OFFER A BETTER WAY TO MANAGE RISK. I can promise you that Taleb would look at and use his greeks if he had an options portfolio to manage. There simply is no other way.
I don't mean that he's said anything brilliant in the field of finance. His contribution to mathematics as a whole is quite substantial, though... For the record, I am in agreement with you regarding Taleb/Mandelbrot.
well delta is measured (quoted by memory...), say...N(j), whereas j= (log(s/x) + (r+0.5*q^2)*t)/(q*sqrt(t)) I believe the variables are selfevident to name them... There are at least a few things wrong here: 1. Assumption that volatility is normal and stock gravitates around a mean = there is no evidence for such thing, using the levy distribution can leave better results and hence better price. 2. Assumption that the risk free rate is known in advance...and there is no such thing as a risk free rate. 3. Volatility...what volatility? a) it's not constant b) Is it historical, is it stochastic, is it implied or is it historical mean over implied volatility, that is "historically implied" volatility? 4. The CDF of the normal distribution is really hard to estimate so calculating a closed form solution without the erf function will never the give the exact result - but just approximation. So...the delta can and it will always have some margin of error compared to realtime market trading - you can still use it as a good indicator though, plus no real trader uses delta... only geeks who lose money.
Thank you so much for getting all these option folks all riled up. I imagine a lot of them have hit the liquor over this. What you showed us is that real option prices don't follow the theoretical model very well unless you have a physicist in your basement with a super computer, and a well stocked liquor cabinet. Don't lose sleep over all the nasty comments. I've never seen any evidence that the real market gives a fig for the "efficient markets hypothesis" either. Of course we should/shouldn't conclude that knowledge of the greeks is useless to an option trader. Knowledge of them is quite useless/usefull actually. I couldn't come up with a very intelligent comment, so I'll just observe that at least the "real" delta and the "theoretical one" occasionally intersect. And thanks again for getting these option guys all confused, or whatever.
Perhaps try the following extremely fast options-trading computer/system (already on the market since Sept2009) at home: http://www.elitetrader.com/vb/showthread.php?s=&postid=2551270&highlight=computer#post2551270 "In testing, the system was found to be capable of handling data at 21 times the speed of Options Price Reporting Authority (OPRA), the world's single largest market data feed, while maintaining ultra low end-to-end latencies."
I found this: So gamma scalping is just a standard delta neutral long vol play for which you pay your theta decay? Here is a more general method that enables you to scalp volga as well as gamma. Dynamically hedge your net position such that: 1. You are delta-neutral. 2. You are vega-neutral. 3. You have positive gamma. 4. You have positive volga. 5. You have gamma*volga > (vanna)^2. This may be difficult to maintain, but if you can, then you will be at the bottom of a "profit well". It's a standard theorem in analysis that whatever directions spot and volatility move, together or independently, the value of your position will always increase. However it is not a risk-less profit because theta will lower the bottom of your well over time. On average it will keep you hedged against theta. If spot and volatility are changing rapidly, however, then you'll make a profit. If they are frozen, you'll make a loss. If you can build this position with mis-priced contracts, then you may be able to cut out most or even all of your theta and guarantee a profit!! (All this ignores trading costs, of course. It also depends on how you calculate your position vega, volga and vanna, since, strictly speaking, you need to do this with respect to a unique common indicator of volatility, not IVs.) ------------------------- volga = dvega / dvol vanna = dvega / dspot = ddelta / dvol -------------- Gamma > 0 gives you a 1-dimensional well along the spot axis. Volga > 0 likewise along the volatility axis. The extra condition you ask about prevents leakage from the well in any other direction in the 2-d spot/volatility plane. (It guarantees a 2-d minimum.) I dug out my old Analysis text-book from when I was an undergraduate. The book is "A Course Of Analysis" by E.G.Phillips, CUP 1962. The reference is section 10.5, pp256-259. See also "Partial Derivatives" by P.J.Hilton, Routledge & Kegan Paul, 1963, Chapter 4. Younger members of the forum may be able to point to more recent texts still in Print