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.