Question 6.3: Consider a stock whose price on 1 January is $120 and which ...

The present value of the dividends is

div_0 = 1e^{-\frac{6}{12}×12\% } + 2e^{-\frac{9}{12} \times12\% }\cong 2.77

dollars. The right-hand side of (6.4) is equal to

F(0,T)=[[S(0)-div_0]e^{rT}               (6.4)

[S(0)-div_0]e^{rT} \cong (120-2.77)e^{\frac{10}{12}\times 12\% }\cong 129.56

dollars, which is less than the quoted forward price of $131. As a result, there will be an arbitrage opportunity, which can be realised as follows:

• on 1 January 2000 enter into a short forward position and borrow $120 to buy stock;
• on 1 July 2000 collect the first dividend of $1 and invest risk-free;
• on 1 October 2000 collect the second dividend of $2 and invest risk-free;
• on 1 November 2000 close out all positions.

You will be left with an arbitrage profit of

131 − 120e^{\frac{10}{12}\times 12\% }+1e^{\frac{4}{12}\times 12\% }+2e^{\frac{1}{12}\times 12\% }\cong 1.44

dollars.