Question about deltahedging

TskTsk · Mar 2, 2012

Quote from Martinghoul:

I am normally not sure of anything... However, there's one thing that I am relatively sure of: gamma doesn't remain the same after the underlying moves.

I don't really understand the argument you're making. Just do the actual arithmetic and see if you disaagree.

Yes, but even if we accounted for DgammaDspot we would get the same problem, as the formula is exponential, that is PnL builds up in an exponential, not linear fashion....so I will have to go about this another way than using percentages...

Quote from babutime:

Isn't the formula for delta and gamma PnL:

$d*(dS/S) + G*[(S^2)*(ds/S)^2]/2

where d is delta

ds/S is stock return

G is gamma

?

That's what I thought...

Yes, there are several formulas, yours is from the BS formula ( I think ), the one I used is Taylor series expansion.

babutime · Mar 2, 2012

Quote from TskTsk:

Yes, but even if we accounted for DgammaDspot we would get the same problem, as the formula is exponential, that is PnL builds up in an exponential, not linear fashion....so I will have to go about this another way than using percentages...

Yes, there are several formulas, yours is from the BS formula ( I think ), the one I used is Taylor series expansion.

Yeah mine is Black Scholes- a good approx.

You might wanna try this:

http://pnlexplained.com/PEP_PnL_Explained_FAQ.html

TskTsk · Mar 3, 2012

Quote from babutime:

Yeah mine is Black Scholes- a good approx.

You might wanna try this:

http://pnlexplained.com/PEP_PnL_Explained_FAQ.html

Thanks, yeah I looked at this site...

And I kind of figured it out.

Use this formula to figure out your gamma/delta PnL since the last rehedge.
0.5*gamma*(delta/gamma)^2

Once a new trade is made everything will be recalculated, so you have to save the old value each time a new trade happens. I used Excel to make a list of all old values.

Sum up the entire list. You now have your entire realized gamma/delta PnL for all trades ever made.

sle · Mar 3, 2012

Quote from TskTsk:
Sum up the entire list. You now have your entire realized gamma/delta PnL for all trades ever made.

Let me ask you a question fist - are you trying to use this for P&L explanation? In this case, if you are doing the above, you will show a lot of unexplained p&l from a variety of N-th order risks. If you are trying to use this metric as a simple back-testing gimmick, it's quite ok

TskTsk · Mar 3, 2012

Quote from sle:

Let me ask you a question fist - are you trying to use this for P&L explanation? In this case, if you are doing the above, you will show a lot of unexplained p&l from a variety of N-th order risks. If you are trying to use this metric as a simple back-testing gimmick, it's quite ok

Well the point was to use it as a tool for PnL explain for gamma / delta PnL. I'm not sure if the nth order risk will matter with smaller positions, at least thats what I've been told.

sle · Mar 3, 2012

Quote from TskTsk:
Well the point was to use it as a tool for PnL explain for gamma / delta PnL. I'm not sure if the nth order risk will matter with smaller positions, at least thats what I've been told.

Well, depends what risks you are taking. If most of your cares are focused on delta, any other risks gonna appear small. If you are trying to trade vol convexity against gamma (a position of 3 options) you will find that all 'em pesky secondary risks do matter.

Best way is to double-check your risk-factor P&L explanations to modify the market inputs from yesterday to today. Something where you'd would keep all market inputs as of yesterday and only modify one of them at a time.

TskTsk · Mar 6, 2012

Quote from sle:

Well, depends what risks you are taking. If most of your cares are focused on delta, any other risks gonna appear small. If you are trying to trade vol convexity against gamma (a position of 3 options) you will find that all 'em pesky secondary risks do matter.

Best way is to double-check your risk-factor P&L explanations to modify the market inputs from yesterday to today. Something where you'd would keep all market inputs as of yesterday and only modify one of them at a time.

I trade all kinds of positions, so I wouldnt be surprised if second order risks rear their heads. however it hasnt been a problem yet, lets hope it stays that way

BTW the solution i posted previously does not work after all. so its back to the drawing board for me...