DEFINITION of 'Interpolated Yield Curve  I Curve'
An interpolated yield curve (I curve) is a yield curve derived by using ontherun Treasuries. Because ontherun treasuries are limited to specific maturities, the yield of maturities that lies between the ontherun treasuries must be interpolated. This can be accomplished by a number of methodologies, including bootstrapping and regressions.
BREAKING DOWN 'Interpolated Yield Curve  I Curve'
The yield curve is the curve that is formed on a graph when the yield and various maturities of Treasury securities are plotted. The graph is plotted with the yaxis depicting interest rates, and the xaxis showing the increasing time durations. Since shortterm bonds typically have lower yields than longer term bonds, the curve slopes upwards from the bottom left to the right.
When the yield curve is plotted using data on the yield and maturities of ontherun Treasuries, it is referred to as an interpolated yield curve, or I curve. Note that ontherun Treasuries are the most recently issued U.S. Treasury bills, notes, or bonds, of a particular maturity. Conversely, offtherun Treasuries are marketable Treasury debt consisting of more seasoned issues. The ontherun Treasury will have a lower yield and higher price than a similar offtherun issue, and they only make up a small percentage of the total issued Treasury securities.
Interpolation is simply a method used to determine the value of an unknown entity. Treasury securities issued by the U.S. government are not available for every period of time. For example, you will be able to find the yield for a 1year bond, but not a 1.5year bond. To determine the value of a missing yield or interest rate in order to derive a yield curve, the missing information can be interpolated using various method including bootstrapping or regression analysis. Once the interpolated yield curve has been derived, yield spreads can be calculated from it, as few of the bonds have maturities comparable to those of the ontherun Treasuries.
The bootstrapping method uses interpolation to determine the yields for Treasury zerocoupon securities with various maturities. Using this method, a couponbearing bond is stripped of its future cash flows, that is, coupon payments, and converted into multiple zerocoupon bonds. Typically, some rates at the short end of the curve will be known. For rates that are unknown due to insufficient liquidity at the short end, interbank money market rates can be used.
To recap, first interpolate rates for each missing tenor. This can be done using a linear interpolation method. Once all the term structure rates have been determined, use the bootstrapping method to derive the zero curve from the par term structure. This is an iterative process that makes it possible to derive a zero coupon yield curve from the rates and prices of coupon bearing bonds.
Several different types of fixedincome securities trade at yield spreads to the interpolated yield curve, making it an important benchmark. For example, certain agency Collateralized Mortgage Obligations (CMOs) trade at a spread to the I curve at a spot on the curve equal to their weighted average lives. A CMO's weighted average life will most likely lie somewhere within the ontherun treasuries, which makes the derivation of the interpolated yield curve necessary.

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