Hi, I am trying to understand how I can create a P&L attribution for an option strategy. I know that if I compute the P&L everyday, I can use the greeks to come up with an attribution. In fact I know the delta/gamma/vega/theta of my options and I just use them to see how much of the observed P&L is due to change in underlying, vol or time. But this is ok if I compute this everyday cause greeks are not going to be significantly different from one day to the next. But assume we are approaching expiry or, in general, I want to compute the P&L and see the attribution after many days. If I use the greeks as of the last day I computed the P&L, they can now be very different. An example is below. On May 10 I have an option position with the following greeks: DELTA = 48 GAMMA = 1.9 VEGA = 39 THETA = -1.3 Assume that after 2 days the underlying has moved by 7 and vol has gone up 2%. The following is my P&L attribution: P&L from DELTA = 48*7 = 336 P&L from GAMMA = 0.5*1.9*(7)^2 = 46.5 P&L from VEGA = 39*2 = 78 P&L from THETA = -1.3*2 = -2.6 so a total P&L of about 458. Now let's assume that 15 days have passed and this position expires tomorrow. The greeks now will be much different. Even assuming that underlying and vol did't move at all since I opened the trade, the passage of time has changed my greeks. In particular my VEGA will now be very small, THETA very large and GAMMA probably very large as well if the option is close to ATM. How can I perform P&L attribution in this case? Intuitively, it seems clear that I cannot use the initial greeks I had. Is there a simple way to do this?
Yes. But no. 1) Here's the Yes part: https://www.elitetrader.com/et/thre...-an-x-move-in-underlying.321409/#post-4661199 It references a threesome of other posts, and a pretty good thread from a year+ ago. 2) The No part: the BSM model that you reference is increasingly lumpy/slow/sticky as DTE goes to zero -- precisely the time you wish to estimate. FWIW, this short-time issue was the reason for the creation of the binomial options model(s). (But in checking them out, you lose the ready reference to theta and vol....) 3) The *mechanical* relationship you're shooting at is mostly linear -- the BSM model from which you're borrowing is famously Gaussian. "Uh-ohhhhh." 4) "I want to compute the P&L" -- were it worded, "I want to work the BSM partial differential equation for a change in portfolio-wide values" would get you to the place (I think) you want to go, but would be much more productive in search parameters: Portfolio Greeks, man! Let us know how you do!
Lol There’s options calculators out there to help you figure this stuff out. I think most mainstream brokers offer some of the sort. As far as your delta after a 7 point move delta should increase or decrease a lot more than you mentioned unless you’re trading AMZN or something. Theta decay accelerates at expiration with one day left theta decay will be 100% of what remains but the majority of theta value will already have come off premium due to time. Gamma is how much delta increases for a 1 point move in the underlying so it’s basically the equation that says you’ll get higher delta with a bigger ITM move or less delta with a OTM move. Vega I really don’t track that much, but all these equations are non linear so doing it by hand is difficult. Again I suggest people that want to know all the details use a specified options calculator.
Ooop! Remember that these are all first derivatives that, by definition, are linear. We can all agree that the underlying model is oh-so-Normal Distributional... but constructively, Shoot. We can work with that... And hell, we have the second derivative of movement, Gamma, to help us with the larger excursions. So, what the hell........
You could be right to an extent. I agree that the options models are normal distributions/deviations based on the underlying. Distribution graphs are also parabolic though. But looking at the graphs of each Greek individually results in parabolic and curved graphs, which tells me that it’s not a linear equation, that’s what I mean by not linear the equation aren’t. But again with all the calculators out there. I’d say use and options calculator if you want to be precise. In the end though, I suppose if you know how to trade them and understand the basics of the Greeks what the hell does the behind the scenes stuff matter.
Many years ago I was offered modelling software that produces 3D graphs of Greeks, cannot find it now but you may find that someobedoy is offering such if you really want it. I never trade in isolation so the Greks for me are about relationships and trying to be delta/gamma neutral. However the biggest surprise is always Vega when it's going against me! There are tons of software vendors who could provide this for you, but frankly...... take the profits, take time off to enjoy life. Try this:https://gdcdyn.interactivebrokers.c...softwareTools&selectedClient=tradersInvestors