Mr. In-the-Money, research analyst at worked all day yesterday valuing a stock option by the binomial pricing method. This morning when he came to work, he discovered that a bandicoot (a large tropical rodent) had chewed through most of his work. He has a presentation in an hour and would like you to help him redo his work (and possibly save his job!). For your convenience he has provided below all the facts and pictures that he can salvage and/or remember.

Option type: American Call

Expiration: Six months

Exercise price: 60

Current stock price: 60

Dividend: One known dividend with the ex-dividend date in exactly 4.5 months

Volatility of underlying stock (annualized): 30%

No. of steps in binomial tree: 2

Risk-free rate of interest (annual, continuous compounding): 5%

Mr. In-the-money is following the method we discussed in class to generate a recombining tree in the presence of dividends. Also, following Hull, he is not making a volatility correction to draw the tree for the risky portion of the stock. Part of the tree he has drawn for the risky part of the stock price (which survived the bandicoot) is shown below:

a)Draw the complete tree for the stock price (including dividends), and show the option values at expiration on this tree. Show all calculations in detail.

b) Work backward to derive the value of the American call, showing the call valuation at each intermediate node. Does it ever make sense to exercise this call earlier than expiration? If so, when and why?

Mr. In-the-money is following the method we discussed in class to generate a recombining tree in the presence of dividends. Also, following Hull, he is not making a volatility correction to draw the tree for the risky portion of the stock. Part of the tree he has drawn for the risky part of the stock price (which survived the bandicoot) is shown below: Risky stock tree a) (10 points) Draw the complete tree for the stock price (including dividends), and show the option values at expiration on this tree. Show all calculations in detail