Exercise $1(10$ points$)$

Three bonds are traded on the market:

A: risk$-$free bond, zero coupon, maturity $4$ months, market price $99\mathrm{.}70$

B: risk$-$free bond, maturity $1$ year and $4$ months, annual coupon $2\%,$ market price $($clean price$)100\mathrm{.}92$

C: risky bond, maturity $1$ year and $4$ months, annual coupon $4\%,$ market price $($clean price$)100\mathrm{.}89$

Compute:

Accrued interest and dirty price for bonds B and $C$

Yield to maturity for the three bonds

Some points of the interest rate term structure

The average spread of bond $C($defined as the average differential return offered by the bond at the different

maturities compared to risk free bonds$)$

The duration of the three bonds

Show on a Cartesian graph the relationship between the theoretical equilibrium price of bond $C(y$ axis$)$ and the value of

the spread defined as in # $4.($x axis$)$