Today is November $8,2006.$ You have been retained to suggest an effective hedging strategy to an investor, who invested in callable bonds. In particular, the bond portfolio is long in $5\%,10-$year AAA rated corporate coupon bonds $($par $=500$ million$),$ which will become callable in exactly three years. The investor is worried about prepayment risk, and your job is to set up an effective hedging strategy using American swaptions. The current LIBOR and swap rates are in Table $12\mathrm{.}13.$

From the LIBOR and swap rates compute the semi$-$annual discount curve Z$(0,$ T$)$ up to T $=10.$Table $12\mathrm{.}13$ LIBOR and Swap Rates on November $8,2010-$year swap

$5\mathrm{.}1690\%$

Source: Bloomberg. $\backslash$table$[[3$ month libor,$5\mathrm{.}37442\%$