You have been tasked by your line manager to prepare supporting calculations in your report for a presentation to be made before MPF’s management. These calculations should essentially demonstrate derivative pricing using the No Arbitrage Principle. To do so, you choose to demonstrate the pricing of futures and options contracts using Apple’s stock. The line manager also wants to understand more about the challenges to BSM in the real world in pricing call and put options and any alternatives. 

Required: 

Estimate the fair price of an equity futures on Apple’ stock expiring in 6 months’ time using the cost of carry model. You are required to cover the following too:
provide (select and make assumptions) any missing inputs.
explain all the inputs in your pricing model and justify each.
compare the price from your cost of carry model against the actual price of the stock in the spot market at the day close to determine if it in contango or backwardation.             (8 marks)

1). Estimate the prices of both Apple’s call and put options trading on CBOE using two and three period binomial option pricing models as well as the BSM model. You must cover the following:
provide (select and make assumptions) any missing inputs.
explain all the inputs in your pricing model and justify each.
evaluate whether the call and the put options are over or under-valued based on the price estimates from your calculations compared to their actual prices at the end of trading day on CBOE.            (12 marks)

2). For the two period binomial model, demonstrate that the estimated price of the call is fair using the hedge portfolio calculations over the two period and adjusting the hedge ratio accordingly.         (4 marks)

Estimate the value of the risk free bonds from the put-call parity using first the prices of calls and puts from the BSM model in 2 above and then the actual prices of calls and puts available from OPRA in Eikon for the same calls and puts. Discuss the factors that could explain the differences in pricing across the two put-call parity calculations.            (6 marks)

Explain why the BSM may not hold in the real world. Identify and discuss the factors that challenge BSM in practice and if there are any alternatives to BSM.please sir do it urjent please please