Question

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

Answer 1

Answer:

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