Explaining option's P&L by greeks

[vivaskyliska]

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?

That's a precise breakdown.
Have you found the answer?

 

[sle]

That's a precise breakdown.
Have you found the answer?

Unless you're running a complex position, you can wrap the 2nd derivatives into the calculation directly. Then it's as straight forward as it gets:
delta/gamma contribution = average(Delta_sod + Delta_eod) * change_in_underlying
vega/vega^2 contribution = average(Vega_sod + Vega_eod) * change_in_underlying
theta = theta * change_in_time

 

[faust]

FlexTrade (Derivix), FT Options, Imagine, SpiderRock is your answer

 

[Matt_ORATS]

FlexTrade (Derivix), FT Options, Imagine, SpiderRock is your answer

I have used all of those and know they have simulated slides but I do not recall them having P&L attribution.
If I understand the intent, each open position would have a P&L since inception and that would be attributed to the greeks.
The P&L attribution calculation would have to be done daily and greeks netted out.
Daily because theta is not time linear so this wouldn't work right: theta = theta * change_in_time
Daily too because the rest of the greeks (delta, gamma, vega) do not change linearly with time.

We are working on the risk component of our software over the coming months so I am interested to hear what is important to other traders. I have typically used the P&L slides like the above vendors have but not any off the shelf P&L attribution. When I backed market makers, we would time stamp all the trades and review daily the greeks at each trade and try to understand where we were making and losing money.

I think there is an interest in the journaling of trades / P&L attribution to see what strategies are working for traders and understand why they are making money.