backtesting a deltahedged option portfolio

Quote from TskTsk:

Thanks for the reply, yes it will be used for multiple options. Could you explain what you mean with path-dependant nature of p&l? if one assumes frictionless deltahedging, shouldnt final pnl derived from iv-rv be the same as the continously deltahedged (frictionless) final pnl? again it wont be used for any trading but more of a way for me to study options...
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We live in a world of discreet time, not continuous time, with friction..

a range of different price distributions. Both make the terminal point of the distribution the same, but vary heavily in how the prices got there..

if a stock stays in a range of fifty cents and goes between the bounds of that range alot, your pnl will look quite different then one that mostly trends.. yet they can't end up at the same point, causing a totally different PNL of delta hedging.. hence "path dependent"


I would suggest using R programming.. bigger community of help..
 
Yes, but RV is determined by the terminal point? In other words, if your IV is 13 and final RV is 14, your final PnL will be the exact same regardless of which "end" of the distribution it occured at, as long as RV is 14. But PnL in the process of getting there, will vary widely. If I understand. This is what you mean by path dependant, or? From this I understand that the terminal P&L of a continously deltahedged, frictionless option, in which IV is 13 and RV is 14, will always be the same, but the way it gets there is path-dependant, ie. varies widely..
 
Quote from TskTsk:
if one assumes frictionless deltahedging, shouldnt final pnl derived from iv-rv be the same as the continously deltahedged (frictionless) final pnl?
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I am far too drunk to get into this now, let me just say that above would only be true for two specific cases - either a case where implied volatility use to calculate your delta along the path is equal to the terminal realized volatility or a case where you are hedging a log contract.

Think of it this way - if you have an option, your P&L for any given time period can approximated as

pnl = delta * dS + 0.5 * gamma * dS^2 +vega * dIV - theta * dT

To start, assume that you have hedged delta prior to this period so delta P&L is zero. For a vanilla option, gamma is non-constant depending on a few parameters - (a) the time to expiration, (b) log(S/K) and (c) level of implied volatility. Now you can see that a combination of moves in the stock that would produce the same realized volatility number could produce wildly different P&L - e.g. a large shock move in the beginning of the options life would not be as consequential as a large move right before expiration or the same shock move would be totally inconsequential if the stock has drifted away from the strike and there is no gamma left.

Quote from TskTsk:
by the way how do you back out pnl from looking at difference in implied and realized? i.e. is there a formula for it?
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in the first approximation, it is going to be vega * (rv - iv).

PS. ok, off to walk the dogs and to bed.
 
Thanks sle, its starting to make sense. Basically variance in gamma means it will be path-dependant. So what if we take a hypothetical scenario where your gamma for the same underlyer, is kept constant until expiration? Would your final PnL in this scenario be more predictable?

From 0.5 * gamma * dS^2 I then understand that a short portfolio with more theta for each gamma (gamma and theta kept constant), would have higher profit than one with less theta for each gamma (gamma and theta kept constant). Is this right?
 
Quote from TskTsk:
Thanks sle, its starting to make sense. Basically variance in gamma means it will be path-dependant. So what if we take a hypothetical scenario where your gamma for the same underlyer, is kept constant until expiration? Would your final PnL in this scenario be more predictable?
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Yes. It goes beyond theoretical - a delta-hedging P&L of a log contract (which is constant gamma by construction) is perfectly predictable difference between RV^2 and square-root weighted IV^2. It's a variance swap, that's why it is so "easy" to replicate.

Quote from TskTsk:
From 0.5 * gamma * dS^2 I then understand that a short portfolio with more theta for each gamma (gamma and theta kept constant), would have higher profit than one with less theta for each gamma (gamma and theta kept constant). Is this right?
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Yes. For example, if you sell a lot of far OTM options with high implied volatility and buy some ATM strikes against it, you can produce that kind of profile (collect theta for fairly little short gamma or even with a long gamma). Of course, my usual conjecture about free lunches is still true - you will get progressively short gamma if you move toward the lower strike.
 
Nice, just what I wanted to hear actually. Alright, that's enough theory for this year. Again thanks for the help and happy holidays!
 
sorry TskTsk, digging up some old threads to ask you something

http://www.elitetrader.com/vb/showthread.php?threadid=237843
http://www.elitetrader.com/vb/showthread.php?t=280693

did u manage to fix the pnl attribution?

When i use the Black'76 and the pde, i can only explain about 60% of the pnl. And 40% is still quite large and unexplained. Did you manage to solve it?

i am using pde pnl = previous delta * change in forward + previous vega * change in vol + 0.5 * previous gamma * change in forward^2 + previous theta * num of days passed

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sorry i posted too fast

is it because 1D is a big time step and hence pde is not accurate? would it be fixed if we do it continuously throughout the day?

is it also because the change are large enough that the assumption that changes are small is invalid?

had this problem for quite some time and has been sweeping it under the carpet ahha
 
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bad example. let me regen and repost. not sure how i can remove post. sorry :D

first day pnl is bid ask spread.
 
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