A stock is priced at $100. It pays a continuous dividend of 2% per year. The riskless rate is 3% per year continuously compounded. The volatility of the stock is 23% per year.

1.

Compute the price of an American call option with strike $90 that expires in six months. Show the option prices at each node of the lattice and indicate the nodes where the option should be exercised.

2.

Compute the price of an European call option on the stock with strike 90 for the above problem. Establish the initial replicating portfolio for the European call. Show your calculations and demonstrate that this portfolio does indeed replicate the payout of the European call option over the first period.