The following table lists three financial instruments and their deltas, gammas, and vegas for each $1 million notional principal under the assumption of a long position. (Long in a swap or FRA means to pay fixed and receive floating.)
Assume that you hold a $12 million notional principal long position in the three-year call option, an $8 million notional principal short position in the three-year swap, and an $11 million notional principal long position in the FRA. Each derivative is based on the 90-day LIBOR.
a. As described above, you have three instruments currently in your portfolio. Determine your current portfolio delta, gamma, and vega. Describe in words the risk properties of your portfolio based on your calculations.
b. Assume that you have to maintain your current position in the call option but are free to increase or decrease your positions in the swap and FRA and you can add a position in a one-year call with a delta of $62, a gamma of $2,680, and a vega of $2.41.
Find the combination of notional principals that would make your overall position be delta hedged, gamma hedged, and vega hedged.