January 23rd, 2005, 3:25 pm
Interpolation is a simple arithmetic average of the two numbers involved. YTM or the yield curve should technically denote the level of interest rates for the tenors existing in the market. For eg. if there are 10 points on the Yield curve then each of the point will denote the interest rate of the Zero Coupon bond of that tenure. However, coupon paying bonds can be seen as a bunch of zero coupon bonds. Let us assume that the market is trading a 6M and 12 M zero. We need to calculate the zero rate for 18 M given the 18 bond rate. We can calculate the zero for 18 month and use that to further calculate the 24 month zero and so on and so forth. why do we need bootstraping? because we need to discount each of the cashflows arising out of any swap at the discount factor for that tenure. The correct discount factor is calculated from the Zero coupon bond and not the coupon bearing bond of that tenure as it comprises of different cashflows arising at various times.