The following table lists three financial instruments and their deltas, gammas, and vegas for each $1 million notional amount 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 amount long position in the three-year call option, an $8 million notional amount short position in the three-year swap, and an $11 million notional amount long position in the FRA. Each derivative is based on the 90-day LIBOR.

a. As described earlier, 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 amounts that would make your overall position be delta hedged, gamma hedged, and vega hedged?

Instrument Delta Gamma Vega 3-year call option with exercise $40 1,343 $5.02 rate of 0.12 3-year swap with fixed rate of 0.1125 $152 -$678 S0 2-year FRA with fixed rate of 0.11 S72 $390 S0