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ABy Admin
May 14'23
Exercise
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.
ABy Admin
May 14'23
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.