2.2. The price of a commodity is 45. Its volatility is 20% and the risk-free rate of interest is 3% per annum with continuous compounding (for all maturities). Use a three-step binomial tree to value (i) a nine-month European call option with strike 45 and (ii) a nine-month American put option with strike 48. Up and down movement can be calculated using volatility and expiration date (9 month call option).