Consider a nine-month American put option on a non-dividend paying stock where the stock price is 3.25, the exercise price is 3.50, the risk-free interest rate is 2% per annum and the volatility is 28% per annum.

(i) Use a three-time-step tree to calculate the option price.

(ii) Estimate and interpret the delta of the option at the first timestep from the constructed binomial tree.

(iii) Estimate and interpret the gamma of the option at the second time-step from the constructed binomial tree