Suppose that the price of a stock is $45 at the beginning of the year, the risk-free rate is 6%, and a $2 dividend is to be paid after half a year. For a long forward position with delivery in one year, find its value after 9 months if the stock price at that time turns out to be a) $49, b) $51.

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Accepted Answer

By (6.3)

[latex] F(0, T) = [S(0) − e^{−rt}div]e^{rT} .[/latex] (6.3)

the initial forward price is [latex]F(0, 1)≅ 45.72[/latex] dollars. This takes into account the dividend paid at time 1/2.

a) If S(9/12) = 49 dollars, then [latex]F(9/12, 1)≅49.74[/latex] dollars by (6.2). It follows by (6.8) that [latex]V (9/12)≅ 3.96[/latex] dollars.

[latex]F(t, T) = S(t)e^{r(T−t)}.[/latex] (6.2)

[latex]V (t) = [F(t, T) − F(0, T)]e^{−r(T−t)}[/latex]. (6.8)

b) If S(9/12) = 51 dollars, then [latex]F(9/12)≅51.77[/latex] dollars and [latex]V (9/12)≅5.96[/latex] dollars.

Question 6.7: Suppose that the price of a stock is $45 at the beginning of...

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