Question

The price of oil is currently at $24 but you expect it to either increase by 18 percent or decrease by 7 percent over the next 6 months. The 6-month risk-free rate of interest is 1.98 percent. What is the probability that the price will increase

Answer 1

the probability that the price will increase is 0.3592 or 35.92%

Explanation:

Given the data in the question;

risk free interest rate = 1.98 percent

expectations are ; either increase by 18 percent or decrease by 7 percent over the next 6 months

hence

increment by 18 percent; d = 1 + 18% = 1 + 0.18 = 1.18

reduction by 7 percent; u = 1 - 7% = 1 - 0.07 = 0.93

so the probability that the price of the oil will increase will is;

P = (( 1 + rate ) - u ) / ( d - u )

we substitute

P = (( 1 + 1.98% ) - 0.93 ) / ( 1.18 - 0.93 )

P = (( 1 + 0.0198 ) - 0.93 ) / 0.25

P = ( 1.0198 - 0.93 ) / 0.25

P = 0.0898 / 0.25

P = 0.3592

P = ( 0.3592 × 100 )%

P = 35.92%

Therefore, the probability that the price will increase is 0.3592 or 35.92%