Suppose that the price of a share varies randomly according to the probability tree shown in the following figure. Each step corresponds to 1 month and the risk-free interest rate is 10%. 55 52 50 51 5 q p 48 4 45 Figure 1: Two-period probability tree for an asset. The nodes are labelled with the share price (in $). The values of p and q are 0.6 and 0.4, respectively. It is important to notice that the increase (u) and decrease (d) factors at each branch differ. (a) Calculate the risk-free probabilities for the tree. (b) Find the prices for European and American call options (associated to this share) whose strike price (X) is $50. Suppose that the price of a share varies randomly according to the probability tree shown in the following figure. Each step corresponds to 1 month and the risk-free interest rate is 10%. 55 52 50 51 5 q p 48 4 45 Figure 1: Two-period probability tree for an asset. The nodes are labelled with the share price (in $). The values of p and q are 0.6 and 0.4, respectively. It is important to notice that the increase (u) and decrease (d) factors at each branch differ. (a) Calculate the risk-free probabilities for the tree. (b) Find the prices for European and American call options (associated to this share) whose strike price (X) is $50