Consider the S&P/ASX 200 option contracts that expire on 17th September 2020, with a strike price of 6050. On 24th July 2020, the S&P/ASX 200 index was priced at 6019.8. The annual standard deviation of S&P/ASX 200 stocks is 26%. The risk-free rate is 2.25% with annual compounding. Assume no dividends are paid on any of the underlying securities in the index. 1) Using a three-step binomial tree model, calculate theoretical prices for

a) a September American call option,

b) a September American put option,

c) a September European call option, and

d) a September European put option on S&P/ASX 200. Draw the trees and show all calculation workings at each node.