[Question based on textbook Introduction to Quantitative Finance by Stephen Blyth, Chapter 8]

Stock A and stock B both have current price 100; neither pays dividends. In one year's time, stock A is worth 120 with probability 0.9 and 90 with probability 0.1; stock B is worth 125 with probability 0.2 and 90 with probability 0.8. The one-year annually compounded interest rate is 10%.

(a) Prove by replication that the one-year 110-strike call on stock A has price 600/99; and that the one-year 110-strike call on stock B has price 600/77. (In particular, the call on stock B is more valuable.)

(b) Calculate the risk-neutral probability of stock B being worth 125 at T = 1.