Delta Hedging

Quote from cdcaveman:

yes i am being a little philosophical.. thats an equation from a linear world .. one in which we don't live in.. do you have any experience with delta hedging successfully? i don't but a "implementation shortfall" variable in the equation to me means.. how well can you game the market with your scalps.. which in this case could have a wide range of results.. and dS is implying you know the future distribution of price changes... which of course you do not! i'm not trying to be obnoxious.. i'm just saying
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No I don't have any experience at all. I was only pointing that at least for me this simple equation helped me to understand better the concept than pages of text. Maybe it's just me.

But if you want to be closer to reality you need to consider more advanced models than Black-Scholes (where volatility is flat) with more advanced maths and new sources of risk.

The other very helpful thing with this equation is that you can replace (dS)^2 with (sigma*S)^2 times dt (thanks to Ito) and suddenly your gamma profit is not "random" anymore as it is not a function of dS ie the stock movement. Of course in the Black-Scoles world where volatility is determenistic.

So without using any complex maths (I don't know either) you can gain some better insight with this simple equation.

OK where is the volatility porn now?
(I was going to google it but somehow it sounds extremely kinky - how do you explain that to your wife?)
 
Hey thanks for the feedback guys. I used to work for a regional index options market maker, and Greek hedging management is a pretty important part of "keeping the money".

Just to clear up a couple of points from cdcaveman,

1) The gamma portion of the PnL estimate clearly isn't linear, since it's squared (think variance).

2) dS is the future price deviation, and it doesn't take much complexity to work out the AVERAGE expected future price deviation. This information is necessary for a trader to estimate his trade's EV, along with risk management plans.

Here's an example of doing it crudely in excel,
http://matdays.blogspot.com/2012/11/excel-data-analysis-33-volatility.html

Hope that helped!
 
I dont think layering more math and complexity is the answer... im thinking of taking calculus this coming semester. But i think you can drown yourself in math... Thinking that that next level of math and complexity consumation will give you more edge. its suppose to give you more dimension on reality where sometimes i think it just skews your perception of it.. A weak hand is a weak hand no matter what equations your holding... hypefocusing on optimizing backtesting etc is no reality... Its like walking backwards in history will help you walk forward in the future.. it wont! rules of thumb are often undervalued for lengthy mathmatical arguments... i wanna see the cartoons to!

Most great minds have stated many times that sophistication is in simplicity...
But i got your point i was just saying.... That model makes it seem like there is a linear path to profit via dynamic hedging
 
Quote from cdcaveman:

That model makes it seem like there is a linear path to profit via dynamic hedging
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But delta hedging does exactly that, it takes out of the equation this "linear path to profit" you described.

As I said before I am trying to learn, same as you. I guess it's not easy to dicuss about these topics in a forum especially without adult supervision. University could be a good place for that so by any means take that course if you are interested.
 
Quote from kapw7:

But delta hedging does exactly that, it takes out of the equation this "linear path to profit" you described.

As I said before I am trying to learn, same as you. I guess it's not easy to dicuss about these topics in a forum especially without adult supervision. University could be a good place for that so by any means take that course if you are interested.
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hard knocks seems to be the only school i learn anything at ha :-)
Im not sure what you mean... I think you misunderstood me.. I was just saying plugging in numbers into that equation makes it seem as if what you make from delta hedging is tractable in a linear fashion
 
Quote from tayte:

exactly.
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What exactly would you find "useful", may I ask? The basics are as simple as they get, you rebalance your delta and lock in the gamma gains or losses, while bleeding/collecting theta. The really meaty stuff starts once you get into details:
(a) which vol to use for hedging (generating the delta number) - implied volatility, some predicted volatility or some sort of over-hedge number?
(b) include or not include dVol/dSpot in delta calculation - e.g. use sticky strike vol, sticky delta vol or some sort of a back-bone/volcor model (e.g. SABR)?
(c) should one use or not use some sort of forward prediction/overhedge - e.g. use some sort of statistical arbitrage model to capture that variance yet a touch better?
(d) what frequency should one hedge to find the best balance of transaction costs to best variance capture in case of long gamma or to smooth pnl sufficiently in case of short gamma?
I don't think any of these questions have universal answers and even if you think you have answered them for your own purposes, you frequently would find that you have to make exceptions.
 
Quote from sle:

What exactly would you find "useful", may I ask? The basics are as simple as they get, you rebalance your delta and lock in the gamma gains or losses, while bleeding/collecting theta. The really meaty stuff starts once you get into details:
(a) which vol to use for hedging (generating the delta number) - implied volatility, some predicted volatility or some sort of over-hedge number?
(b) include or not include dVol/dSpot in delta calculation - e.g. use sticky strike vol, sticky delta vol or some sort of a back-bone/volcor model (e.g. SABR)?
(c) should one use or not use some sort of forward prediction/overhedge - e.g. use some sort of statistical arbitrage model to capture that variance yet a touch better?
(d) what frequency should one hedge to find the best balance of transaction costs to best variance capture in case of long gamma or to smooth pnl sufficiently in case of short gamma?
I don't think any of these questions have universal answers and even if you think you have answered them for your own purposes, you frequently would find that you have to make exceptions.
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(e) Can you capture the cash spread when you're hedging long gamma?
(f) Is the width of that spread priced into the the vol?
(g) Have you been distracted by the volatility porn aesthetics (again)?
 
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