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Question

To compute prices of a 6-month American call option, future prices of the underlying stock are modeled with a

2-period binomial tree with 3 month periods.

You are given:

(i) In each period, the price of the stock are either multiplied by 1.1 or multiplied by 0.9. (ii) The initial stock price is 40.

(iii) The stock pays continuous dividends proportional to its price. The dividend yield is 0.03. (iv) The continuously compounded risk-free interest rate is 0.05.

Determine the least upper bound of strike prices for which early exercise is optimal at least at one node.

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