Using the two-step binomial option pricing model calculate the price for a 1 year American call option for a stock trading at $61.89 today, under the following market conditions:

• The continuously compounded risk free rate is 2.4693%pa
• The number of periods is 2, each of 0.5 year
• The strike price is $60
• The volatility of the stock is 40.25%pa
• The stock pays a dividend of $0.75 at the end of the first 6 months
• The stock pays a dividend of $0.78 at the end of the second 6 months
• Binomial diagram is available here: 200079 BINOMIAL.pdf

Calculate

1. To four decimal places, what is the proportional increase in price of the stock at each step in the binomial tree?
2. To four decimal places, what is the proportional decrease in price of the stock at each step in the binomial tree?
3. In percentrage terms to 2 decimal places, what is the probability that the stock increases in price?
4. To 4 decimal places, calculate the price of the stock at the first node up and down on the binomial tree both before and after the first dividend is paid as depicted in the diagram
   1. Su
   2. Su'
   3. Sd
   4. Sd'
5. To 2 decimal places, calculate the price of the stock at expiry of the option both before and after the second dividend is paid as depicted in the diagram
   1. Suu
   2. Suu'
   3. Sud
   4. Sud'
   5. Sdu
   6. Sdu'
   7. Sdd
   8. Sdd'
6. To 2 decimal places, calculate the value of the option at expiry (ie 12 months from now)
   1. fuu
   2. fud
   3. fdu
   4. fdd
7. To 4 decimal places, calculate the value of the option six months from now
   1. fu
   2. fu, max
   3. fd
   4. fd, max
8. To 2 decimal places, calculate the value of the option today
9. To 2 decimal places calculate the delta of the option