Yep, and don't some seem to get too caught up in "figuring stuff out" - just to "figure stuff out?" Too many get caught up in the "what if's" instead of just taking the simple road, learn the basics, and, well, TRADE. Enough "analysis paralysis" already, LOL. All the best, Atticus. Don
The number, in isolation, is meaningless. You can't be given the number and solve for your $risk. Of course it's a moving target as vol is the major variable to speed. I certainly understand if trading American exotics. I understand conceptually how my twin-turbo functioned, but wouldn't want to work on it. And yeah, next time I am buying normally-aspirated. It's no fun blowing a turbo on the interstate in WY.
Now I CAN help with twin turbos. I installed many Gale Banks turbo's back in my racing boat days. But, yes, normally aspirated is preferred for long term and easy running. In WY too, wow, bummer. Don
Good points. Intriguing that your gamma remained stable by taking alternating long and short positions on alternating strikes. You mention that if you have a lot of time remaining, speed is less of an issue. How far out are we talking? Definitely, achieving gamma for cheap is the top priority, but assuming we've managed that, it seems desirable to neutralize speed so as to keep gamma strong throughout the life of a long gamma position. As I was inquiring in a previous post, are there any other higher order Greeks as significant as speed? Thank you again. I appreciate the ongoing lesson!
This is all really just "options common sense." I'll try to illustrate with a few examples. Let's imagine options on XYZ with 300 days remaining, no dividends and no interest rate, volatility of 30%. XYZ stock is at 100. The 100s (puts and calls) have a gamma of .015. The 110s have a gamma of .014. From a common-sense POV, the 100s and the 110s have almost the same gamma because with so much time remaining, the probability that XYZ will be at 100 at expiration isn't THAT different from the probability it will be at 110 at expiration. If you buy 1000 of the 100s (puts or calls of course) and sell 1000 of the 110s, you are long 1000 x .015=15 gammas at the 100 strike and short 1000 x .014=14 gammas at the 110 strike. So your overall position gamma is 15-14=1. Imagine XYZ goes up to 110. Now your long 100s each have a gamma of .012 and your short 110s have a gamma of .013. You are long 12 gammas at the 100 strike and short 13 gammas at the 110 strike, so your total position gamma is -1. Not a huge change. Fast forward to 100 days remaining. XYZ is back at 100. Now each option at the 100 strike has a gamma of .025. Each option at the 110 strike has a gamma of .022. So your overall position gamma is 3. If XYZ goes up to 110, your long 100s will have a gamma of .018 each, and your short 110s will have a gamma of .023 each. So your overall position gamma will now be -5. That's a lot bigger swing in total position gamma than when there were 300 days remaining. It reflects the fact that with 100 days remaining, there is relatively much more probability that XYZ will settle at the current price at expiration rather than ten points away. Fast forward once again to 7 days remaining. XYZ is back at 100. Now the 100s have a gamma of .095 each and the 110s have a gamma of .007. See how the relationship between the two strikes has broken down completely? That reflects the fact that it is FAR more probable at this point that XYZ will settle at 100 at expiration than at 110. Your total position gamma now is 95-7= 88 gammas. But if XYZ suddenly goes up to 110 now, your gammas reverse wildly. Your long 100s would have a gamma of .006, while your short 110s would have a gamma of .087. Overall position gamma would now be 6-87= -81. Even assuming you were delta neutral to start with, you would lose a fortune in such a move with so little time remaining. With 300 days remaining, assuming delta neutrality, such a move would have been virtually meaningless. Are there any other higher-order greeks as important as speed? No. And as Atticus and Don pointed out, speed itself as a standalone number is unimportant too. What's important is to understand how your overall position gamma will change over a range of underlying prices. That's particularly important when you have strikes where you are long options and strikes where you are short options, because you can go from long gammas to short gammas pretty quickly, especially as expiration approaches.
What dmo refers to above is "gamma decay", or "Color". See picture: Other than that, I agree you won't really need any formulas unless you're in an investment bank (or just really love math).
Pretty much any book containing barriers or volatility derivatives is as much fun to manage as having a rectal exam. However, in general, exotics traders do not use analytical approaches for secondary risks, you usually just use scenario approaches. So I'd say there is no reason to (a) know what is the way to calculate it and (b) actually know the sexy names for the secondary Greeks - saying that "I have a 100k of dVega/dSpot per percent of SPX" is more informative and clearer then saying "my Vanna is 100k". The only one I remember is charm which is delta decay per day (yeah, that one is important).