Type of Document	Dissertation
Author	Jerassy-Etzion, Yaniv
Author's Email Address	yaniv@yjecpa.com
URN	etd-01132010-124541
Title	Stripping The Yield Curve With Maximally Smooth Forward Curves
Degree	Doctor of Philosophy
Department	Economics, Department of
Advisory Committee	Advisor Name Title Paul Beaumont Committee Chair David Rasmussen Committee Member Stefan Norrbin Committee Member Gershon Tenenbaum University Representative
Keywords	Interpolation US Treasuries Genetic Programming Yield Curve Forward Curve
Date of Defense	2010-01-07
Availability	unrestricted
Abstract Continuous discount functions and forward rate curves are needed for nearly all asset pricing applications. Unfortunately, forward curves are not directly observable so they must be constructed from existing fixed-income security prices. In this paper I present two algorithms to construct maximally smooth forward rate and discount curves from the term structure of on-the-run U.S. treasury bills and bonds. I use on-the-run treasuries to get the most recent and liquid prices available. The maximum smoothness criterion produces more accurate prices for derivatives such as swaps and ensures that no artificial arbitrage will be introduced when using the constructed forward curve for pricing out-of-sample securities. When coupon bonds are included among the securities it is necessary to both strip the coupon payments and interpolate the spot curve. To be consistent, these steps must be done simultaneously but this complication usually leads to highly nonlinear algorithms. The first method I describe uses an iterated, piecewise, quartic polynomial interpolation (IPQPI) of the forward curve that only requires the solution of linear equations while maintaining minimal pricing errors and maximum smoothness of the interpolated curves.The second method uses a genetic programming (GP) algorithm that searches over the space of diferentiable functions for maximally smooth forward curves with minimal pricing errors. I nd that the IPQPI method performs better than the GP and other algorithms commonly used in industry and academics.
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