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Answer: 100,100,87.34, 90
## Explanation Based on the option pricing bounds provided in the text: **Maximum Values:** - **European call**: max value = S₀ = 100 - **American call**: max value = S₀ = 100 - **European put**: max value = PV(K) = 90 × e^(-0.12×0.25) = 90 × 0.9704 = 87.34 - **American put**: max value = K = 90 **Calculation details:** - Time to expiration: 3 months = 0.25 years - Present value factor: e^(-0.12×0.25) = e^(-0.03) ≈ 0.9704 - PV(K) = 90 × 0.9704 = 87.34 Therefore, the maximum possible prices are: - European call: 100 - American call: 100 - European put: 87.34 - American put: 90 This matches option A: 100,100,87.34,90
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The current stock price of a share is USD 100 and the continuously compounding risk-free rate is 12% per year. The maximum possible prices for a 3-month European call option, American call option, European put option, and American put option, all with strike price USD 90, are:
A
100,100,87.34, 90
B
100,100,90, 90
C
97.04,100, 90, 90
D
97.04, 97.04, 87.34, 87.34