The current price of a non-dividend paying stock is 40 and the continuously compounded risk-free interest rate is 8%. You are given that the price of a 35-strike call option is 3.35 higher than the price of a 40-strike call option, where both options expire in 3 months.

Calculate the amount by which the price of an otherwise equivalent 40-strike put option exceeds the price of an otherwise equivalent 35-strike put option.

• 1.55
• 1.65
• 1.75
• 3.25
• 3.35

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: A

Let C be the price for the 40-strike call option. Then, C + 3.35 is the price for the 35-strike call option. Similarly, let P be the price for the 40-strike put option. Then, P – x is the price for the 35-strike put option, where x is the desired quantity. Using put-call parity, the equations for the 35-strike and 40-strike options are, respectively,

[[math]] \begin{aligned} (C + 3.35) + 35e^{−0.02} − 40 = P − x \\ C + 40e^{−0.02} − 40 = P. \end{aligned} [[/math]]

Subtracting the first equation from the second, [math]5e^{-0.02} - 3.35 = x, x = 1.55 [/math].

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.