1. Suppose that a second traded option has a delta, gamma, and vega of -0.4, 0.9, and 0.5 respectively, and costs $0.04 (per Euro). What position in the two traded options, Euros and risk-free assets would make the portfolio in problem 2 delta neutral, and reduce gamma and vega by half?

a. Use RMFI software to calculate the price, delta, gamma, vega, theta, and rho for a European call option on a stock with S₀ = $100, a strike price of $105, and a volatility of 20%. The risk-free rate is 2% and the exercise date is in 6 months from now.

b. Compare these exact calculations for the Greeks to approximations that are produced with S = 0.1, = .01 (i.e., 1%), r = 0.005 and t = 0.05 (in years). Use RMFI software for the prices you will need.