The price of a share is currently 100 and in each of the next two 3-month periods it is expected to go up by 10% or down by 20%. The risk-free interest rate is 10% per annum (continuously compounded. Let S_t be the market price of the share at any given time t. Consider a derivative on the share with the following payoff at any given time t:

(a) Using a two-step binomial tree, calculate the theoretical price of the option in case it is of European style

(b) Recalculate the price of the option in case it is of American style.

\\( V_{t}=\\left\\{\\begin{array}{cc}100, & S_{t}>100 \\\\ \\max \\left\\{0,2 \\cdot S_{t}-S_{0}-64\ ight\\}, & S_{t} \\in[70,100] \\\\ 0, & S_{t}