I'm new to this and would like to try it out on the above question. A more detailed description is shown below:
My professor has asked me to come up with a formula that will highlight, say the 100 highest, vega and gamma trades for any currency pair. In my data I have been using GBPUSD however it should work for any currency as long as you normalise the vega and gamma formulas by excluding the spot price in the formulas. If you want the formulas for gamma and vega I worked them out and can post then once I figure out how to attach stuff.
So I need the best 100 trades for a currency pair. With tenor ranging from 0 to 7 years. Now at 3 months and below, gamma should be weighted higher as this will be more important to know for short dated options. Around the three month mark the weighting should be on a mixture of gamma and vega and above the three month mark the weighting should go more on the Vega instead. The answer doesn't have to be proved, it can be guessed but as long as below 3 months you get the top few gamma trades, raisins 3 months you highlight a mixture of the top gamma and vega trades and above 3 months you get the best vega trades it will be fine.
I can't see this being too difficult. My progress so far is that I have taken log of both gamma and vega and for vega have shifted the graph up by 3.3 this is so that they can both be roughly compared as before gamma is much higher than vega. Then I imagine we will have a combination of maybe exponentially of gamma and vega and maybe normalised diracs function at around 3 months for the combination of gamma and vega so that at 3 month the combination shows up for gamma and vega. Alternatively using a combination of the log normal graph and a reflection of it intersecting at around 3M.
I have some rough data which I will upload when I get home. Any ideas for the time being?
Thank you in advance
All you need is a function that changes from $0$ to $1$ the way you like. For example, $f(t)=\begin {cases} 0&0 \le t \lt 1 \\\frac 14(t-1)&1 \le t \lt 5\\1&t \ge 5 \end {cases}$
which is just a ramp from one month to five months. Now (assuming $g=$gamma and $v=$vega are scaled the same) your score is $g(1-f(t))+vf(t)$ For less than one month, $v$ is ignored, for over five, $g$ is ignored.