$1.$ The short rate at time t is given by

$"$t

$=$ F$+$e$-$ke$($ro $-$ F$).$

The yield curve is given by

$(1+$ ye$)\backslash$deg $=$ E$(1+$ ro$)...(1+$re$-$i$)].$

Let $7=0\mathrm{.}03$ and k: $=0\mathrm{.}1.$ Plot the yield curve for ro $=\mathrm{.}01,$ ro $=\mathrm{.}04,$ and ro $=$ F$.$

$2.$ Suppose that ye $=0\mathrm{.}02+0\mathrm{.}06(1-$ exp$(-0\mathrm{.}10)),$ t$=1,...,$ T$,$T$=30.$ Plot the yield curve

and the implied forward rate curve f$..$

$3.$ Given f$.=0\mathrm{.}02-0\mathrm{.}08(1-$ exp$(-0\mathrm{.}1$t$))$ for t $=1,...,30.$ Plot forward rate curve f$,$ and

implied vield curve v$.$

$4.$ Suppose that the short rate r$....,1$r is known. For any time t$,$ compute the holding period

return of a coupon bond with coupon payment of c$,...,$ cr and face value of Fr$.$

Does it depend on the bond's coupon and$/$ or maturity? Does it depend on t$?5.$ A perpetuity is a bond that pays a coupon forever. Show that its duration is $(1+4)/$y$,$ where

u is the Y$\text{'}$TM$.$