The following is a portfolio of over-the-counter options on the Euro (each option is on 125,000 Euro, and * below is a reminder that Greeks are quoted for the long option, and per unit of underlying (per 1)):

Type Position (#options) Delta of Option* Gamma of Option* Vega (per .01) of Option*

Call 400 0.50 1.9 1.3

Call -3000 0.70 0.7 0.5

Put 2000 -0.60 1.3 0.8

Put -1400 -0.70 1.5 1.2

a. What is the delta, gamma, and vega of this portfolio?

b. There are two exchange traded options on the Euro. One has a delta, gamma, and vega of 0.6, 1.2, and 0.6 (per .01) respectively, and costs $0.05 (per Euro), the other has Greeks of -0.4, 0.9, and 0.5 respectively, and costs $0.04 (per Euro). Again, each option is on 125,000 and * above applies. What position in these two traded options, Euros and risk free assets would make this portfolio delta neutral, and reduce gamma and vega by half? Note 0 = $1.20.