If the volatility of a stock is 20% per annum and a risk-free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter p for a tree with a three-month time step?

A) 0.50

B) 0.54

C) 0.58

D) 0.62

B. 0,54

Explanation:

Step 1. Given information.

Volatitlity = 20% Time = 3/12 =.25 Interest rate = 5%

Step 2. Formulas needed to solve the exercise.

u = e volatiltiy * (time).5

a = e rate * time

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

Step 3. Calculation.

u = e 0.2 * (.25).5

u = 1.105170918

d = 1/u

d =.904837418

a = e rate * time

a = e 0.05 *.25

a = 1.012578452

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

p = (1.012578452 - 0.904837418) / (1.105170918 - 0.904837418)

p =.538 =.54

Option B