Question

The current price of a non-dividend-paying biotech stock is $140 with a volatility of 25%. The risk-free rate is 4%. For a three-month time step:



a) What is the percentage up movement?


b) What is the percentage down movement?


c) What is the probability of an up movement in a risk-neutral world?


d) What is the probability of a down movement in a risk-neutral world?


Use a two-step tree to value a six-month European call option and a six-month European put option. In both cases the strike price is $150.

Answer 1

Answer:

a. u = e^(0.25√0.25)

u = e^0.125

u = 1.13314845307

u = 1.1331485

The percentage up movement is 13.31%

b. d = 1/u

d = 1/ 1.1331

d = 0.88253464

d = 0.8825

The percentage downward movement = 1 - 0.8825 = 11.75%

c. Probability of upward movement(P) = (R - d) / ( u-d)

P = (1.04 - .8825) / ( 1.1331 - 0.8825)

P = 0.6285

P = 62.85%

d. Probability of a down movement in a risk-neutral world = 1 - P

= 1 - 0.6285

= 0.3715

= 37.15%