A different European put has strike price K = $35 and expires in 30 days. The underlying asset is currently selling for S = $33 . The yearly volatility of the underlying is estimated to be σ = 0.42, and the interest rate is r = 7% pa. (a) Calculate the put premium using the Black–Scholes model. (b) Now consider calculating the value of the put using a three-step binomial model. i. Assuming interest rates are constant over the life of the put, calculate the return R over one time step. ii. Calculate the up and down factors u and d in this three step model. iii. Calculate the risk neutral probability π in this three-step model. iv. Calculate the premium of the put using the three-step binomial model (either by constructing a binomial pricing tree or by calculating the state prices). (c) Now consider a ten-step binomial model. Calculate the return R over one time step, the up and down factors u and d and the risk neutral probability π for the ten-step model. Thuscalculate the premium of the put using the ten-step binomial model. (d) Compare the premiums calculated with the three-step and ten-step binomial models with the premium calculated with the Black–Scholes model. Which is closer to the Black–Scholes solution? Explain why this result is expected.