This is my question from Financial Modelling course, could you help me to solve this question:

2. Carsales.com Limited (CAR) is an Australian company that (unsurprisingly) owns the online marketplace www.carsales.com.au. At the time of writing, the share price of CAR is $18.86. Assume this is time zero. You wish to compare premium prices of a European call calculated with the BlackScholes model, with premium prices calculated with a binomial model. The call has strike price K = $20, and expires in 90 days so T = 90/365 years. The yearly volatility of CAR shares is estimated to be = 2.55 . Assume the continuously compounding interest rate is r = 3% pa.

(a) Calculate the call premium using the Black-Scholes model.

(b) Consider a three-step binomial CRR model.

(i) Assuming interest rates are constant over the life of the call, 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 in this three-step model. (iv) Construct a three-step binomial pricing tree for the call and calculate its premium.

(c) Consider a ten-step binomial CRR model.

(i) Assuming interest rates are constant over the life of the call, calculate the return R over one time step.

(ii) Calculate the up and down factors u and d in this ten-step model.

(iii) Calculate the risk neutral probability in this ten-step model.

(iv) Construct a ten-step binomial pricing tree for the call and calculate its premium.

(d) Compare the premiums calculated with the three-step and ten-step binomial models with the premium calculated with the Black-Scholes model. You should find that the premium calculated from the ten-step model is closer to the Black-Scholes solution than the premium calculated from the three-step model. Why?