ABC is a non-dividend paying stock whose current price is $80. Its volatility is 20%. Over each of the next two 6-month periods the stock price is expected to go up by 15% or down by 13%. The risk-free interest rate is 10% per annum with continuous compounding for all maturities. There is a European call option which has a strike price of $82 and expires in 12 months.

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

(b) Use the Black-Scholes-Merton model to calculate the value of this European call option. Show your step-by-step workings.

(c) Compare the results obtained from the above two approaches and provide a brief comment.

(d) If this option is an American option rather than the European option (all else staying the same), briefly describe how you will value this option.