Workshop 2

Fair Value

Fractional Years

We can even use exponents to figure out fractional years. If the underlying is $50 and risk-free interest rates are 7%, how much would each of the following be selling for?

• 15-month contract
• Six-month contract
• 27-day contract

We just need to convert the months to years and realize that 15 months is the same as 15 / 12 = 1.25 years. Therefore, a 15-month futures contract would be selling for $50 x (1.07)1.25 = $54.41.

A six-month contract represents of a year (0.5), so $50 x (1.07)^0.5 = $51.72.

A 27-day contract represents 27 / 360 = .075 years, so $50 x (1.07)^.075 = $50.25. Note that we used 360 as the number of days in a year. This is just a matter of convention although many institutions use 365 when calculating fair value since it is more accurate.

Okay, here's some more for you to try using fractional exponents

If the underlying is $70 and the risk-free rate is 8%, what would you expect an 8-month futures contract to be trading for?