Figure 1 shows the binomial tree of prices for assets a and b. At each node in the tree, a pair (Pa: Pb) of asset prices is shown, the first of which is the price of asset a at the node, the second of which is the price of asset b. t=0 t=1 t=2 (100, 150) UU u (98, 100) ud (100, 75) (Pa = 95, p. = 85) (100, 80) du (95,80) dd * (100,90) Figure 1: Binomial tree with asset prices i). Derive the one-period risk-free rates at nodes u, re, and d, r. (4 points) i). Derive the one-period risk-free rate at t = 0, 70. (8 points) iii). Derive the price at t = 0 of a European call option on asset b, with strike price 80 and expiration day at t = 2. (9 points) iv). Derive the price at t = 0) of a European put option on asset b, with strike price 90 and expiration day at t = 2. (9 points) Figure 1 shows the binomial tree of prices for assets a and b. At each node in the tree, a pair (Pa: Pb) of asset prices is shown, the first of which is the price of asset a at the node, the second of which is the price of asset b. t=0 t=1 t=2 (100, 150) UU u (98, 100) ud (100, 75) (Pa = 95, p. = 85) (100, 80) du (95,80) dd * (100,90) Figure 1: Binomial tree with asset prices i). Derive the one-period risk-free rates at nodes u, re, and d, r. (4 points) i). Derive the one-period risk-free rate at t = 0, 70. (8 points) iii). Derive the price at t = 0 of a European call option on asset b, with strike price 80 and expiration day at t = 2. (9 points) iv). Derive the price at t = 0) of a European put option on asset b, with strike price 90 and expiration day at t = 2. (9 points)