You are given:

1. The Black-Scholes-Merton framework applies.
2. The prices of some 6-month European options on non-dividend paying Stock Y are:

   Strike Price	Price of Call Option	Price of Put Option
   525	55.92	x
   550	45.46	64.57

The continuously compounded risk-free rate is 3.25%.

Calculate x.

• 50.03
• 50.43
• 50.83
• 51.03
• 51.23

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

Key: B

Using put-call parity and the 550-strike options, we have:

[[math]] 45.46 − 64.57 = S_0 − 550e^{−0.0325*0.5} \Rightarrow S_0 = 522.0247 [[/math]]

Using the current stock price and put-call parity with the 525-strike options:

[[math]] 55.92 − x = 522.0247 − 525e^{−0.0325*0.5} \Rightarrow x = 50.43 [[/math]]

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