The prices of stocks or other financial instruments are often modeled with a lognormal distribution. An investor is considering purchasing stock in one of two companies, A or B. The price of a share of stock today is $1 for both companies. For company A, the value of the stock one year from now is modeled as lognormal with parameters μ = 0.05 and σ = 0.1. For company B, the value of the stock one year from now is modeled as lognormal with parameters μ = 0.02 and σ = 0.2.

a. Find the mean of the price of one share of company A one year from now.

b. Find the probability that the price of one share of company A one year from now will be greater than $1.20.

c. Find the mean of the price of one share of comp any B one year from now.

d. Find the probability that the price of one share of company B one year from now will be greater than $1.20.

Solution

Step 1 of 5

Let X is the price of the company A share

Here X follows the lognormal distribution with parameters and

Let Y is the price of the company B share

Here Y follows the lognormal distribution with parameters and