GNI is a non-dividend paying stock whose current price is $50. Its volatility is 12%. Over each of the next two 6-month periods the stock price is expected to go up by 9% or down by 8%. The risk-free interest rate is 6% per annum with continuous compounding for all maturities. There is a European put option which has a strike price of $53 and expires in 12 months.

(a) Use a two-step binomial tree to calculate the value of this European put option. Show your step-by-step workings.