A non-dividend paying stock has a current price of S. The continuously compounded risk-free interest rate is 2.75%.

The price of the stock over a six-month period follows a binomial model with u = 1.2903 and d = 0.7966. A six-month European put option on the stock with a strike price of ( S − 4.50) has a price of 2.482.

Calculate S.

• 44.22
• 45.72
• 46.97
• 49.11
• 50.24

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

Key: A

The risk-neutral probability of an increase is:

[[math]] 1-q = \frac{e^{0.0275*0.5}-d}{u-d} = 0.44003 [[/math]]

Then

[[math]] 2.482 = e^{−0.0275*0.5} ((1 − q)*0 + q *( S − 4.5 − 0.7966S )) \Rightarrow S = 44.22 [[/math]]

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