Q$2$ Suppose the following bonds are trading in the market.

In addition to the bonds above, you also observe the $1-$year forward rate in $2$ year's time $2f_3$ is

$5\mathrm{.}40\%.$ You wish to price Bond $H,$ which is $4-$year $10\%$ coupon bond with a face value of $$100.$

Assume all bonds $($and the forward rate$)$ are risk$-$free and that Bond F and Bond $H$ are annual

coupon bonds.

a$.$ Infer the term structure of interest rates: $y_1,y_2,y_3$ and $y_4($i$.$e$.$ derive the pure yield curve for

years $1-4).$

b$.$ Price Bond $H$ of the pure yield curve.

c$.$ Based on the pure yield curve, infer the $2-$year forward rate commencing in $2$ year's time $2f_4.$

d$.$ Assume the Liquidity Preference Hypothesis holds and the annual liquidity premium is flat at

$0\mathrm{.}50\%$ for all $t.$ What is the expected future $1-$year spot rate $($i$.$e$.$ the short rate$)$ in $3$ year's time

$E(3y_4)?$

e$.$ Assume the Expectations Hypothesis holds. What is the expected $1$ year future spot rate $($i$.$e$.$

the short rate$)$ in $1$ year's time $E(t{y}_2)?$