Question

Suppose that firm D's shares are currently selling for $50. After six months it is estimated that the share price will either rise to $56.00 or fall to $44.75. If the share price rises to $56.00 in six months, six months from that date (1 year from today) the price is estimated to either rise to $62.72 or fall to $50.12. If the share price falls to $44.75 in six months, six months from that date (1 year from today) the price is estimated to either rise to $50.12 or fall to $40.05. The six month risk free rate is 2.5%.

Based on the two stage binomial model, what should the value of a put option with exercise price $55 be today?

Multiple Choice

· $3.54

· $2.77

· $4.81

· $1.63

Answer 1

50-------56.00 or 44.75

If 56.00----------62.72 or 50.12

If 44.75----------50.12 or 40.05

Exercise price = $ 55

u = 56/50 = 1.12,

d = 44.75/50 = 0.895

r = 1.025

p = (r-d)/(u-d)

= (1.025-0.895)/(1.12-0.895)

= 0.5778

Puu = Max [0, 55-62.72] = 0

Pud = Max [0, 55-50.12] = $ 4.88

Pdd = Max [0, 55-40.05] = $ 14.95

Pu = {(0.5778*0)+(1-0.5778)*4.88}/1.025 = $ 2.01

Pd = {(0.5778*4.88)+(1-0.5778)*14.95}/1.025 = $ 8.9089

P0 = {(0.5778*2.01)+(1-0.5778)*8.9089}/1.025 = $ 4.81