A while ago, I interviewed for a trader role and was given the below assignment (I didn't get the job). I wanted to revisit the questions to learn from my mistakes and be better prepared next time. Generally speaking, I have a good understanding of options and greeks but for some reason I'm having a hard time applying it here.
Question 1 Based on the P&L profile below please calculate a 25bps gamma profile for the up and down shocks.
I'm not sure what's meant by gamma profile or why the +/-50bp values are highlighted. I see that the changes in P&L are non-linear and asymmetrical, similar to the payoff diagram of a long put.
I know that
$\\P\&L$ = $\delta$ * $\Delta$S + $\frac{1}{2}$ * $\Gamma$ * ($\Delta S^2$)
but I'm not sure how to isolate the delta and gamma. Any pointers would be appreciated!
Question 2 The desk would like to purchase 5k of 25bps gamma with a goal of remaining delta and vega neutral. Utilizing the trades below develop the most cost efficient (cheapest 1m carry) way to achieve this goal.
To calculate 25bps Gamma, I used the following formula:
$\Gamma_{25}$ = $\frac{Dn_{25} + Up_{25} - 2 * Base}{2 * Base * 0.0025^2}$
which gives me the following values:
1m/10y = 102,204
3m/10y = 32,932
6m/10y = 16,095
1y/10y = 7,515
2y/10y = 3,671
I thought I should be able to re-calculate the Delta (10bp) as $\\Up_{10} - Base$ but the results don't make sense.
Can you confirm that my delta/gamma calculations are correct or tell me where I went wrong?
Finally, I tried to find a combination of straddles where the Gamma ~= 5k and Delta and Vega are close to 0 but I'm having a hard time finding a feasible solution, which makes me think my Gamma calculations might be incorrect.