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TCQ Corporation's current share price is 31. Assume you want to write a call option on the company's share with a strike price of 29 and 6 months until expiry. The risk-free rate per 3 months is 1.8% compounded quarterly and is constant in the next 6 months. You cannot find a similar call option in the market, so you have to calculate the option price yourself. The company is not expected to pay any dividend in the next 6 months. Part 1 (13 marks): Use the replicating portfolio method and answer questions (a) and (b). For this part only, assume that in any 3 months, the share price can either go up or down by $5. (a) Draw the two-period binomial tree. In the diagram, label the corresponding time period, the share price at each node and the option payoffs in the last period. (b) Calculate the value of the call option at t=0 using the replicating portfolio method. Part 2 (7 marks): (c) Assume the standard deviation of the company's asset is 0.35. Use the Black Scholes Option Pricing Model to price the same call option