Mark, a risk manager from bank XYZ, is considering a 6-month American call option on a dividend paying stock ABC. The current stock price is USD 50, and the volatility is 25% p.a.. A dividend of $5 is expected in 5 months. The risk-free rate is 5% p.a. with continuous compounding. In order to find the no arbitrage price of the option with a strike price of USD 55, Mark uses a three-step binomial tree model. (Note: keep all decimal places during calculation)

(i)What is the risky component of the stock price at t=0?

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In holding the option, do you need to pay the dividend due in 5 months? Do you also need to make a total tree during your calculation in this question and if so, which nodes are affected?

In the final price tree you use to price the option in question, what should be the stock price 4 months from now after prices have kept increasing?

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What is the value of the call option 2 months from now after the stock price kept increasing?

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