Using the two-step binomial option pricing model calculate the price for a 2 year American PUT under the following market conditions:

• The stock is trading at $182.99 today
• The continuously compounded risk free rate is 4.3542%pa
• The strike price is $185.00
• The volatility of the stock is 21.33%pa
• The stock pays a dividend of $7.78 at the end of the first year
• The stock pays a dividend of $8.23 at the end of the second year

ECON3003 BINOMIAL.pdf

a.To four decimal places, what is the value of "u" (1 mark)

b. To four decimal places, what is the value of "d" (1 mark)

c. To four decimal places, what is the proportional increase in price of the stock at each step in the binomial tree (ie u-1) as a percentage? (0.5 marks)

d.To four decimal places, what is the proportional decrease in price of the stock at each step in the binomial tree (ie 1-d) as a percentage?(0.5 marks)

e.In percentrage terms to 2 decimal places, what is the probability that the stock increases in price? (1 mark)

f. In percentage terms to 2 decimal places, what is the probability that the stock decreases in price? (1 mark)

g. To 4 decimal places, calculate the price of the stock at each node on the binomial tree both before and after first dividend is paid

1. 1. Su (0.5 marks)
   2. Su' (0.5 marks)
   3. Sd (0.5 marks)
   4. Sd' (0.5 marks)

(Please note there is no part h)

h. To 2 decimal places, calculate the price of the stock at expiry on the binomial tree both before and after the second dividend is paid

1. 1. Suu (0.5 marks)
   2. Suu' (0.5 marks)
   3. Sud (0.5 marks)
   4. Sud' (0.5 marks)
   5. Sdu (0.5 marks)
   6. Sdu' (0.5 marks)
   7. Sdd (0.5 marks)
   8. Sdd' (0.5 marks)

(Please note there is no part j)

k. To 2 decimal places, calculate the value of the option at expiry

1. fuu (0.5 marks)
2. fud (0.5 marks)
3. fdu (0.5 marks)
4. fdd (0.5 marks)

l.To 4 decimal places, calculate the value of the option 12 months from now

1. fu (1 mark)
2. fu' (1 mark)
3. fu,max (0.5 marks)
4. fd (1 mark)
5. fd' (1 mark)
6. fd,max (0.5 marks)

m.To 2 decimal places, calculate the value of the option today (1 mark)

n.To 2 decimal places calculate the delta of the option (1 mark)