Question

6.7. 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?

Answer 1

We shall calculate the u & d as below

where = standard deviation of volatility

t = time in years

u = upward movement

u = e^0.25*.5

= 1.1331

d= 1 /u

where d is the downward movement

d = 1 / 1.1331

= .8825

percentage up movement = 13.31%

percentage downward movement = 1 - .8825

= 11.75%

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

where R is the risk free rate

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

= 0.6285

= 62.85%

probability of a down movement in a risk-neutral world = 1 - P

= 1 - 0.6285

= 37.15%