Abinary call option pays $1 at expiry if the value of the underlying asset is greater than the strike price, and $0 otherwise. the current interest rate is 3% pa.
(a) calculate the return r over one month.
(b) calculate all state prices at expiry for a ten-step binomial model where each time step is one month and the underlying asset is s=20, k=19, u=1.090, d=0.9173. that is, calculate all λ(10, j) for j = 0, 1, . . , 10 .
(c) use the state prices in part (b) to calculate the the premium of a binary call option with strike price k = $16 and k =$35, expiry in ten months
(d) use the state prices in part (b) to calculate the the premium of an option which pays $1 at expiry if the value of the underlying asset is greater k1 = $16 but less than k2 = $35 .