The stock price is currently at $50 per share. A European call option with 2 year to maturity and a strike price $60 is trading on this stock. Risk-free asset pays 5% interest rate per year. In one year, it is estimated that the stock price will either go up to $80 per share or go down to $31.25 per share.The stock price is currently at $50 per share. A European call option with 1 year to maturity and a strike price $60 is trading on this stock. Risk-free asset pays 5% interest rate per year. In one year, it is estimated that the stock price will either go up to $80 per share or go down to $31.25 per share.

1.

Find the terminal option prices c_uu, c_ud, and c_dd.

2.

Using the binomial formula, find c_u, c_d, and c.

3.

Compare c that you calculated in this problem to c that you calculated in the previous problem. What is the difference? How do you explain it?

4.

Find option delta in every node of the tree.

5.

You write 100 call contracts today. How should you hedge this position?

6.

In the up state one year from now, how should you adjust your hedge? Show that the value of your hedge after the adjustment will be exactly equal to the option value in that state.

7.

In the down state one year from now, how should you adjust your hedge? Show that the value of your hedge after the adjustment will be exactly equal to the option value in that state.