To be fair, especially judging by their current economy, it has also confused those Greeks themselves ...
Googling "delta gamma approximation" will bring up a number of great resources, but I just found this one: https://www.cognizant.com/whitepapers/VaR-Approximation-Methods.pdf which contains a delta-gamma-theta approximation, too. For myself, I run an "overnight portfolio risk" set-up throughout the day, for a range of ±0.25%, ±0.50%, ±0.75%, and ±1.00%, of the SPX. {Rem: I am 99% exclusively SPX, so going beyond ±1% is not useful -- I already have an "@Risk" total, which would be hit pretty quickly.} Applying that range to delta and gamma, I then incorporate theta*0.25 (the "overnight" [or, ≈ 1.0 trading day], and then, vol ("vega") at the arithmetic inverse of the delta -- for a 0.25% delta rise, I use a -0.25% vega fall. Scarily accurate. So roughly, Port = delta + 0.5gamma^2 + 0.25theta + [arith.inverse]vega Swee-eeet.
I am trying to wrap my head around your premise here. Are you saying that if the delta rises by a certain percentage (say from 0.50 to 0.60 it would be a 20%, which for a call implies the underlying moving higher) then the Vega would fall by the same percentage (for example from 0.10 to 0.08)? Do you account for not only the decrease in Vega but also the decrease in actual IV that usually comes with the underlying moving higher? I find this approximation could be really useful but I want to understand its foundation better...
Yeah: not well-written on my part: "and then, vol ("vega") at the arithmetic inverse of the delta -- for a 0.25% delta rise, I use a -0.25% vega fall." "delta" is so-called portfolio delta, such that, given a $1 move in underlying (SPX), portfolio value changes by [$1*Pdelta]. "vega" is similarly portfolio vega, such that, given a ±1pt move in underlying vol, portfolio value changes by that [Pvega±1] amount. With a quarter-point move in the SPX, this set-up would infer [0.25*SPX]*Pdelta dollars of Distance-to-Market capitalization, being tempered by [arith.inverse]0.25ptsPvega Volatility-Expansion/Contraction dollars. Further, 1% Pdelta<==> [arith.inverse]1pt.Pvega etc etc. Right now, for example, the SPX is 0.07% (13:53 ET), while the VXST is down by -0.08pts. Not perfect, but Handy! (And much, much better than nothin'...)
Thank you all for the response. The strike 249 would be closer to atm and its iv would be higher. Undestood. I would like to ask a question. I know, after few months of real trading in options, that Implied volatility is the key. Some people say implied volatility is an input and some others say it is the supply and demand that establishes the options prices. I suppose it depends on the moment, but when you want to buy or sell an option you only can take the price the market is quoting. Obviously I know greeks are used to see what will happen to the option's value due to changes in time, implied volatily and move of the underlying. And I know the behavior of the greeks when there are changes in one or more of these 3 forces. e.g. what happens to theta with a change of iv. But I know all this in a general way, I mean I have not entered in the details of the models that put it all toguether, I have not studied the specific formulas. Do you think it is necessary for a retail trader to study the difeferents models and all the specific details to be able to succed in options trading? or also try to generate a personal model to auto evaluate the option prices? Will these give the key to find something that only the professionals know? It is a handicapp to only understand the models in a intuitive way? Untill now I had more issues and doubts with things relationated with the broker than with the strategies itself. And that's another ineresting question, maybe you can know all about options but a Retail account doesn't allows you to implement strategies effectively.
Humble advice from a relatively new comer, a mom and pop retail option trader with lots of battle scars: 1. Keep things simple. You need to understand and try simple option strategies like long call/put and short call/put before you get into complex combinations. 2. You have to remember that the market is generally very efficient, meaning neither buyer nor seller has any real advantage, i.e., it is generally a zero sum game. The difference is seller of options tends to have a higher probability of profit most of the time but once in a while big losses. Buyer, mostly loses but occasionally big win. If you do it enough time blindly (mechanically) neither buyer nor seller make money. Your broker on the other hand loves you. 3. To be profitable, think out of the box. For every trade ask why your counter party is willing to trade, what does he know that you don't? Why is he willingly hand you profit? I am still trading options full time after 4 years. Best of luck to you.
I think for a retail trader it is useful to know all this especially the relationships and interactions of the different greeks and actually to simply be aware that the greeks interact with each other and that there are some higher order greeks etc. I do however agree with you that an intuitive understanding of this is far more important and relevant to potential profits. In my case I do look at portfolio-weighted delta, gamma, theta and vega and I use certain knowledge of their interaction (vega is higher with longer time to expiration, theta/gamma explode as expiration approaches, when there is a down move in the underlying, IV tends to go higher so I should have negative delta to cushion this if I am short Vega etc) but unless you are managing hundreds of millions of dollars in positions, most of the other effects are probably negated by commission costs/bid-ask spread etc so knowing this is good but on a conceptual level not so much on a mathematical/formula level.
Opening salvo: i: Historic norm of 15-20 vol has been squeezed down to ≤10 over the past two years, making selling options "tough" (to be polite). ii: I have yet to meet someone in the flesh who pays the mortgage by buying options. 1) Yes. Trained monkeys can trade options (and play piano, and ride motorcycles in artful circles). But to make a living at it, you must be, always and without fail, at the top of your game, and your game must top (nearly) everyone else. The majority of "knowledge" out there is dead wrong (in tiny, subtle, but incipient ways), and horribly, sadly, there seems (to my eye) no single, direct fount from which to drink Options Trading Wisdom. It is all SO much simpler than presented -- if driving an automobile in traffic was like trading, we'd all have been *dead* long, long ago. 2) The key is practice, and time, and conserving your capital while you learn where the myths lay and were reality bites. 3) Yes, and a huge and dangerous one, as while your intuition steers you (maybe 3/4s well) around the pitfalls, you won't even *see* the disaster that eats you, until you're well in it. RULE #1, ALWAYS: Keep your capital.
Tom is right .. preserve your capital,trade small and learn... then size up accordingly. In your earlier example, the delta of .34 is the delta at that time, at that price.. as SPY moves up, the delta increases due to gamma at it gets closer to strike , your .34 will be get higher ..but dampened by the skew as price rides up the IV curve.
@raf_bcn you don't need to know the models... if by models you mean the way the options price/IV is calculated based on the general inputs of underlying, strike, maturity, dividend, interest rate. But, you do need to know how your risk parameters work, which are delta, gamma, vega and to lesser extend rho etc. Your risk params give you a genereal idea of current position and where the risk is. The problem is that these change over time and when underlying moves.. So you should also know what those parameters are at say 1%,2%,5%,10% moves up/down. Especially when you trade multiple strikes in spreads etc. And finally you should have an understanding how the implied volatility curve works and how IV moves or how you would expect it to move. So IMO: - models are not that interesting - risk parameters (greeks) very important - understanding the dynamics very important Options are not very straightforward, which makes it more interesting but also more unpredictable, especially if you're not taking those things in.