Financial Risk Manager Part 1

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Explanation:

The true statement is C. The European put option on a 1.60% dividend stock with a 3.0% risk-free rate has a lower bound of zero.

For a European call on a non-dividend-paying stock, the lower bound is positive: $50.00 - 50.00 e^{-0.03\times 0.5} = $0.74.
For a European call on a dividend-paying stock, the lower bound is reduced by the dividend amount: $50.00 - $0.40 - 50.00 e^{-0.03\times 0.5} = $0.34.
For a European put on a dividend-paying stock with a 3.0% risk-free rate, the lower bound is max $0, `$0.40` + 50.00 e^{-0.03\times 0.5} - `$50.00`$ = max $0, -0.34$ = 0.
For the same put with a 0% risk-free rate, the lower bound is max $0, `$0.40` + 50.00 e^{0\times 0.5} - `$50.00`$ = $0.40.

Explanation:

The true statement is C. The European put option on a 1.60% dividend stock with a 3.0% risk-free rate has a lower bound of zero.

For a European call on a non-dividend-paying stock, the lower bound is positive: $50.00 - 50.00 e^{-0.03\times 0.5} = $0.74.
For a European call on a dividend-paying stock, the lower bound is reduced by the dividend amount: $50.00 - $0.40 - 50.00 e^{-0.03\times 0.5} = $0.34.
For a European put on a dividend-paying stock with a 3.0% risk-free rate, the lower bound is max $0, `$0.40` + 50.00 e^{-0.03\times 0.5} - `$50.00`$ = max $0, -0.34$ = 0.
For the same put with a 0% risk-free rate, the lower bound is max $0, `$0.40` + 50.00 e^{0\times 0.5} - `$50.00`$ = $0.40.

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Last updated: April 18, 2026 at 11:32

A European call option on a non-dividend-paying stock with a 3.0% risk-free rate has a lower bound of zero.

A European call option on a stock paying a 1.60% dividend with a 3.0% risk-free rate has a lower bound of zero.

A European put option on a stock paying a 1.60% dividend with a 3.0% risk-free rate has a lower bound of zero.

A European put option on a stock paying a 1.60% dividend with a 0% risk-free rate has a lower bound of zero.