Financial Risk Manager Part 1

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Explanation:

The lower bond of a one-year European call option is given by:

\text{European Call Price} \geq \max(S - \text{PV}(K) - \text{PV}(\text{Divs}), 0)

The present value of dividends, $\text{PV}(\text{Divs})$ , is
$`$ 5` \times 1.03^{-\frac{2}{12}} + 5 \times 1.03^{-\frac{4}{12}} + 5 \times 1.03^{-\frac{6}{12}} = \text{USD } 14.85

The present value of the strike price, $\text{PV}(K)$, is $`$45` \times 1.03^{-1} = \text{USD } 43.69

Thus,

\text{European Call Price} \geq \max(60 - 43.69 - 14.85, 0) = \text{USD } 1.46

Therefore, the European call option price must be at least USD 1.46.

Explanation:

The lower bond of a one-year European call option is given by:

\text{European Call Price} \geq \max(S - \text{PV}(K) - \text{PV}(\text{Divs}), 0)

The present value of dividends, $\text{PV}(\text{Divs})$ , is
$`$ 5` \times 1.03^{-\frac{2}{12}} + 5 \times 1.03^{-\frac{4}{12}} + 5 \times 1.03^{-\frac{6}{12}} = \text{USD } 14.85

The present value of the strike price, $\text{PV}(K)$, is $`$45` \times 1.03^{-1} = \text{USD } 43.69

Thus,

\text{European Call Price} \geq \max(60 - 43.69 - 14.85, 0) = \text{USD } 1.46

Therefore, the European call option price must be at least USD 1.46.

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Q.20 Suppose that the current stock price is USD 60. Suppose further that the stock is expected to pay dividends of USD 5 in two months, four months, and six months. If the risk-free rate is 3% per annum (with annual compounding) for all maturities, what is the lower bond of a one-year European call option on the stock if the strike price is USD 45?

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RRohit

Last updated: June 22, 2026 at 14:25

The European call option price must be at least USD 0.

The European call option price must be at least USD 1.46.

The European call option price must be at least USD 0.15.

The European call option price must be at least USD 0.22.