Quick question on Gamma and impact on P&L
Just a quick question on Gamma and its impact on P&L.
If you're long 100 gamma and spot moves by 1%, what's your P&L (assume to be 0 before the spot move)?
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lol, it depends. For example:
If you buy a Call Option on a stock/currency, you are long gamma and long delta, so if spot moves 1% UP, then your PnL will go up. Conversely, a 1% drop in spot will decrease your PnL.
Naturally it's the opposite for a put option.
I'm being facetious here, but make your question a little more specific and we'll come back with a clearer answer.
(I'm anticipating your next response and have already prepared the answer, but nevertheless, rephrase it lol)
Let's assume you're long gamma on a call. How do you arrive at a specific P&L with that though?
I know the P&L will go up. What I am interested in knowing is whether you can determine the P&L without knowing the delta?
Would appreciate some clarifications on that. Cheers.
No you cannot. Remember that delta is what determines the (change in position value with each move in spot)
So for example: On a call option, if it has a delta of 0.5 and a gamma of 0.1 and spot is at 100.
At that instant, we understand that if spot goes to 101 (an increase of $1), your position increases by $0.50. But we note that on the way from 100 to 101, gamma was moving the delta from 0.5 to 0.6. So your PnL is actually somewhere between $0.50 and $0.60 depending on how fast your gamma is moving (volgamma/vomma).
However if the call option had a delta of 0.2 and the same gamma of 0.1 and spot at 100, your PnL increase for a move from 100 to 101 would actually be somewhere between $0.2 and $0.3.
So as you can see, the gamma was the same in both the 50 delta and 20 delta call option, but the PnL was completely different.
Conclusion: gamma doesn't determine your exact PnL, it just determines how fast your PnL (in concrete terms) will change. You will need that delta figure.
Hope that helps.
Thanks. Check your PM...
"What I am interested in knowing is whether you can determine the P&L without knowing the delta?"
no, it's like saying "i'm in a car accelerating 10 miles per hour, how fast am I going."
But honestly, getting a proper handle on your gamma, and how it buckets out is not the easiest thing in the world. I used to use the old "how much is my pnl mispredicted by" method. works like a charm.
Thanks guys.
As a matter of fact, I perfectly understand what FXTrader is trying to illustrate. The problem isn't so much about the mathematical theory, but rather the lingo being used and understanding it in its relevant context. Maybe I wasn't being concise at the start.
Coming from where I come from (non-FX), I have never actually heard anyone use the term "long X gamma" on my desk. Hence, I am trying to clarify what that really translates to.
It's just a risk management measure, so on this FX desk, when Trader A says to Trader B, "I need to move some inventory off this book, what's ur gamma?" Trader B responds, "heavy! I'm long X gamma!" More often than not, all Trader A is trying to determine is how trader B is positioned, so he can determine how much risk he can offset with him.
Remember, for the most part these guys want to maintain low gamma, low delta, low vega (unless its a prop trade). So they refer to these measures to give each other an idea of which direction they should move their inventory in order to stay flat.
So in the example above with Trader A and Trader B, Trader A is clearly not going to sell options to Trader B, because Trader B would be buying them and getting LONGER gamma.
That conversation will probably end with Trader A saying: "Ok fuck it, thanks"
Fair enough?
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