A month ago, the price of an IBM stock was $110 and its volatility was 28%. Today, its price is still $110 but its volatility has gone up to 40%. If the one-month interest rate has not changed over the last month and IBM stock does not pay any dividends (i.e., there are no costs or benefits of carry,) then:
A) The one-month forward prices of IBM today equals the one-month forward price a month ago
B) The one-month forward price of IBM today is greater than the one-month forward prices a month ago by $10
C) The one-month forward prices of IBM today is lower than the one-month forward price a month ago by $10
D) The one-month forward price of IBM today is $44

Question

A month ago, the price of an IBM stock was $110 and its volatility was 28%. Today, its price is still $110 but its volatility has gone up to 40%. If the one-month interest rate has not changed over the last month and IBM stock does not pay any dividends (i.e., there are no costs or benefits of carry,) then: 
A) The one-month forward prices of IBM today equals the one-month forward price a month ago
B) The one-month forward price of IBM today is greater than the one-month forward prices a month ago by $10
C) The one-month forward prices of IBM today is lower than the one-month forward price a month ago by $10
D) The one-month forward price of IBM today is $44

Quizplus · Accepted Answer

The one-month forward price of a stock is calculated as the current spot price multiplied by the exponent of [(interest rate - dividend yield) x time to expiration - 0.5 x volatility^2 x time to expiration]. Since the interest rate and dividend yield are assumed to be constant, the only factor that affects the one-month forward price is the change in volatility. In this case, the stock price has remained the same, so the forward price a month ago and today must also be the same. Therefore, the answer is A.

A Month Ago, the Price of an IBM Stock Was