Xiaomi Inc. is currently trading at $100 per share. After examining the stock of Xiaomi, you have determined that in one year time its price will either increase to $130 with probability 55% or decrease to $90 with probability 45%. Xiaomi does not pay any dividend. A European call option on Xiaomi with an exercise price of $100 is currently trading at $8.82.

Required:

a) What are the implied risk-neutral probabilities and the implied one-year risk-free rate in the economy? If unable to solve the relevant equations, check that the implied risk-neutral probability of seeing an increase in the stock price is 30% and the risk-free rate is 2% per annum.

b) Determine the replicating portfolio of the call option.

c) What is the arbitrage free price of a European put option with an exercise price of $95?