Consider a two$-$step binomial tree model for the price of a stock paying no dividend. Suppose the stock price is $100$ now. The stock price may go up $20\%$ or down $10\%$ in each step. The annual interest rate is $12\%$ with continuous compounding. An American option written on the stock maturing in one year has the payoff function g$($S$)=(130$ S$)++($S $110)+.($a$)$ Determine the price of the option $[15$ marks$]($b$)$ What is the chance to early exercise in the risk$-$neutral world?