Consider a stock XYZ with a current price of $30, and its put option with an exercise price of $50 and expiry in 1 year. The stock price follows a binomial process with d=0.9 and u=1.1 per six months (d and u are constant over the year). The continuously compounded risk free rate is 4.8% per annum. Find the value of the underlying stock and the value of the put option using two stage model.