P

We have: PAR = cAn + (PAR)Dn, with An, the annuity of n periods. We can thus write:

c y D A

D D D D

R

R R

PAR par

1 1 1

1 1

1 1

( )

( )

1 1( )Rn n

ypar the yield to maturity of a par bond. Tuckman (2002) has simplifi ed the Livingston’s approach to the construction of a par-yield curve. For a bond selling at its face value, we know that the yield to maturity is equal to the coupon rate. Th erefore, to generate the par-yield curve, c, the coupon, thus satisfi es the equation: (100c/2) 2Tt=1d(t/2) + 100d(T) = 100, with d being the discount factors. Solving for c, we get: c = 2[1 − d(T)]/2Tt=1d(t/2). Th is equation can be solved for each value of T to obtain the par-yield curve (Racicot and Th éoret, 2004).