Consider an American-style put option written on a stock share that does not pay dividends. The continuously compounded risk-free rate is 3%. The option matures in nine months and its strike is \($60.\) The current stock price is \($50\) and its annualized drift and volatility are 10% and 50%, respectively. Price the option using a time step of three months. If we had to price a European-style Asian option, would the lattice calibration or anything else change?