R31.P1.T4- Tuckman Chapter 2- Discount Factors, given Swap Rates

[gargi.adhikari]

In reference to R31.P1.T4- Tuckman Chapter 2- Discount Factors, given Swap Rates and also Learning Spreadsheet-P1.T4.c XLS Bundle-Sheet/Tab -"SwapRates " :-

The discount factor d(1) has been calculated considering the FV to be $100
d(.5) * .44 + d(1) * 100( 1+ .875%/2 ) = 100
My question is that , isn't the FV greater than the initial Par Value...? Shouldn't the price at each period be given instead of the assumption of the initial Par value of 100 $...?

 

[ShaktiRathore]

Hi,
FV is the face value which is nothing but the par value only.The price at each period is the par value only ,here we are given the swap rates such that when the price is par value the coupon rate is the same as the swap rate.
For T=.5 yr maturity Bond,Price=100=d(.5)*(1+.00705/2)*100, the coupon rate is .705% same as the swap rate.=>d(.5)=0.9965
For T=1 yr maturity Bond,Price=100=d(.5)*(.00875/2)*100 + d(1)*(1+(.00875/2))*100 and the coupon rate is .875% same as the swap rate when price is same as the par value of 100.
=> 100=0.9965*0.4375+ d(1)*(1.004375)*100 =>d(1)=.9913
thanks

 

[gargi.adhikari]

@ShaktiRathore Thanks Shakti....oh yea...I forgot and overlooked the fact that when coupon rate = swap rate/ yield etc.., price = par value....thanks again for the quick reminder. ..