A non-dividend paying stock currently trades at 37 per share. There is a six-month European call option

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Question:

A non-dividend paying stock currently trades at £37 per share. There is a six-month European call option on the stock with exercise price of £30. The stock can either rise by 10% or fall by 8% in each of the next three months’ period. The risk free rate is 1%. Answer the following questions: Calculate the price of this option using the two steps binomial option pricing model explaining clearly every step you make. [20 marks]

Using the same two steps binomial pricing model, what would be the price of this option if it were an American put option instead of a European option? Explain when (if ever) it would be optimal to exercise the option in the context of the model. 10 marks