Discount Factors, Spot Rates, and Forward Rates Implied by Par USD Swap Rates

Table 2.1 presents some data on shorter-maturity, USD interest rate swaps as of May 28, 2010. The second column gives the rates that are quoted and observed in swap market trading.

These indicate that counterparties are willing to exchange fixed payments of .875% against three-month LIBOR for one year, 1.043% against three-month LIBOR for 1.5 years, etc. The 2-year swap rate, depicted in Figure 2.1, is 1.235%.

 Column Discount Factor:

 syms x

 eqn= (100+ (0.75/2))*x==100

S = solve(eqn,x,'Real',true)

 x=0.9964 for first year discount factor

syms x2
 eqn= (0.875/2)*.9964 + (100+ (0.875/2))*x2==100
S = solve(eqn,x2,'Real',true) 

x2=0.9913 for second year discount factor

Spot rate:

syms x
eqn= 1 / ( 1+ (x)/2)^4==.975616
S = solve(eqn,x,'Real',true)


Forward rate:

eqn= (1+ x/2)==0.975616/0.964519; 

S = solve(eqn,x,'Real',true)

x=0.02301