Example $5\mathrm{.}3$

Consider a $6-$month forward contract on an asset that is expected to provide

income equal to $2\%$ of the asset price once during a $6-$month period. The risk$-$

free rate of interest $($with continuous compounding$)$ is $10\%$ per annum. The asset

price is $$25.$ In this case, $S_0=25,r=0\mathrm{.}10,$ and $T=0\mathrm{.}5.$ The yield is $4\%$ per

annum with semiannual compounding. From equation $(4\mathrm{.}3),$ this is $3\mathrm{.}96\%$ per

annum with continuous compounding. It follows that $q=0\mathrm{.}0396,$ so that from

equation $(5\mathrm{.}3)$ the forward price, $F_0,$ is given by

$F_0=25e^{(0\mathrm{.}10-0\mathrm{.}0396)0\mathrm{.}5}=$$$25\mathrm{.}77$