Note: For all problems where a risk-free rate or a dividend yield is given, assume that the interest rate and the dividend yield are annual and continuously compounded rates.

A stock price is currently 125. Its volatility is 30%. The risk-free rate is 4% per year, and the dividend yield on the stock is 2% per year. Calculate values for u, d, and p in the binomial model when a three-month time step is used. Assume that the option is written on 100 shares of stock.

What is the value of a 6-month European call option with a strike price of 125 using a two-step binomial tree?

What stock position should you take today to hedge the option if you sold it?

Show how you derive the stock and option binomial trees and the hedge ratio.

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