Type of Document Dissertation Author Jerassy-Etzion, Yaniv Author's Email Address email@example.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
- US Treasuries
- Genetic Programming
- Yield Curve
- Forward Curve
Date of Defense 2010-01-07 Availability unrestricted AbstractContinuous 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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