non-dividend-paying stock is trading at S0 = 100, and the interest rate is 6 ln(1.01).
(a) Use a two-period binomial model with up and down factors u = 1.16, d = 0.91
and up probability p = 0.7 to price a European put option with strike K = 110
and maturity T in eight months.
[ 5 marks ]
(b) Price an American put option with the same strike (and maturity). What is the
probability that you will exercise early?
[ 5 marks ]
(c) Suppose the stock has suddenly become 10% more volatile, and the company
announced that it will pay a one-off cash dividend of $5 per share six months
from now. Explain how this new development can be captured in the model
above. Make appropriate adjustment to your model parameters, price the
European and American put option in part (a) and part (b) using an 8 step
binomial tree. Discuss the results.
[ 10 marks ]
(d) Your colleague uses the Black-Scholes model to price the European put option
and gets a different answer. How can you improve your model to try to match
with theirs? Demonstrate in Excel how a closer match can be achieved.
[ 10 marks ]