Consider three put options at strikes 40, 50, and 60. The price of the 40-strike option is $4 and the price of the 60-strike option is $8. Which of the following statements is most accurate? (Assume all options have the same maturity.)
A) The price of the 50-strike put is less than $10.
B) The price of the 50-strike put is less than $6.
C) The price of the 50-strike put is greater than $6.
D) The price of the 50-strike put is greater than $7.

Question

Quizplus · Accepted Answer

We can use the put-call parity formula which holds for European options:
Call - Put = Stock - Strike / (1+r)^T
Using the fact that the price of the 40-strike put is $4 and the price of the 60-strike put is $8, we can get the following equations:
Call - 4 = Stock - 40 / (1+r)^T
Call - 8 = Stock - 60 / (1+r)^T
Subtracting the first equation from the second, we get:
4 = 20 / (1+r)^T - (Call - Put)
We know that Call - Put is non-negative, because otherwise there would be an arbitrage opportunity. Therefore, we can conclude that the price of the 50-strike put, which corresponds to the average of the 40-strike and 60-strike puts, is less than $6.

Consider Three Put Options at Strikes 40, 50, and 60