Approximating term structure of interest rates using cubic \(L_1\) splines.

*(English)*Zbl 1141.91016Summary: Classical spline fitting methods for estimating the term structure of interest rates have been criticized for generating highly fluctuating fitting curves for bond price and discount function. In addition, the performance of these methods usually relies heavily on parameter tuning involving human judgement. To overcome these drawbacks, a recently developed cubic \(L_1\) spline model is proposed for term structure analysis. Cubic \(L_1\) splines preserve the shape of the data, exhibit no extraneous oscillation and have small fitting errors. Cubic \(L_1\) splines are tested using a set of real financial data and compared with the widely used B-splines.

##### MSC:

91B28 | Finance etc. (MSC2000) |

41A15 | Spline approximation |

65D07 | Numerical computation using splines |

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\textit{N.-C. Chiu} et al., Eur. J. Oper. Res. 184, No. 3, 990--1004 (2008; Zbl 1141.91016)

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##### References:

[1] | Bliss, R.R., Testing term structure estimation methods, Advances in futures and options research, 9, 197-232, (1997) |

[2] | Cheng, H.; Fang, S.-C.; Lavery, J.E., Univariate cubic L1 splines – a geometric programming approach, Mathematical methods of operations research, 56, 197-229, (2002) · Zbl 1029.41003 |

[3] | Cheng, H.; Fang, S.-C.; Lavery, J.E., A geometric programming framework for univariate cubic L1 smoothing splines, Annals of operations research, 133, 229-248, (2005) · Zbl 1119.65012 |

[4] | Cheng, H.; Fang, S.-C.; Lavery, J.E., Shape-preserving properties of univariate cubic L1 splines, Journal of computational and applied mathematics, 174, 361-382, (2005) · Zbl 1068.41014 |

[5] | M. Fisher, D. Nychka, D. Zervos, Fitting the term structure of interest rates with smoothing splines, Finance and Economics Discussion Series 95-1, Board of Governors of the Federal Reserve System (US), 1995. |

[6] | HolmstrĂ¶m, K., The TOMLAB optimization environment in MATLAB, Advanced modeling and optimization, 1, 47-69, (1999) · Zbl 1115.90404 |

[7] | Langetieg, T.C.; Smoot, J.S., Estimation of the term structure of interest rates, Research in financial services, 1, 181-222, (1989) |

[8] | Lavery, J.E., Shape preserving, multiscale Fitting of univariate data by cubic L1 smoothing splines, Computer aided geometric design, 17, 715-727, (2000) · Zbl 0997.65014 |

[9] | Lin, B.H., Fitting term structure of interest rates using B-splines: the case of taiwanese government bonds, Applied financial economics, 12, 57-75, (2002) |

[10] | Luo, Z.; Wahba, G., Hybrid adaptive splines, Journal of the American statistical association, 92, 107-115, (1997) · Zbl 1090.62535 |

[11] | Martellini, L.; Priaulet, P.; Priaulet, S., Fixed-income securities, (2003), John Wiley & Sons Chichester, England |

[12] | McCulloch, J.H., Measuring the term structure of interest rates, Journal of business, 44, 19-31, (1971) |

[13] | Nelson, C.R.; Siegel, A.F., Parsimonious modelling of yield curves, The journal of business, 60, 473-489, (1987) |

[14] | Peterson, E.L., Symmetric duality for generalized unconstrained geometric programming, SIAM journal on applied mathematics, 19, 487-526, (1970) · Zbl 0205.48001 |

[15] | Peterson, E.L., Geometric programming, SIAM review, 18, 1-51, (1976) · Zbl 0331.90057 |

[16] | Pittman, J., Adaptive splines and genetic algorithms, Journal of computational and graphical statistics, 11, 1-24, (2002) |

[17] | Ramponi, A., Adaptive and monotone spline estimation of the cross-sectional term structure, International journal of theoretical and applied finance, 6, 195-212, (2003) · Zbl 1079.91535 |

[18] | Rockafellar, R.T., Convex analysis, (1972), Princeton University Press Princeton, NJ · Zbl 0224.49003 |

[19] | Steeley, J.M., Estimating the gilt-edged term structure: basis splines and confidence intervals, Journal of business finance and accounting, 18, 513-529, (1991) |

[20] | Vasicek, O.; Fong, H.G., Term structure modeling using exponential splines, Journal of finance, 37, 339-356, (1982) |

[21] | Wang, Y.; Fang, S.-C.; Lavery, J.E.; Cheng, H., A geometric programming approach for bivariate cubic L1 splines, Computers and mathematics with applications, 49, 481-514, (2005) · Zbl 1083.41008 |

[22] | Wang, Y.; Fang, S.-C.; Lavery, J.E., A compressed primal-dual method for generating bivariate cubic L1 splines, Journal of computational and applied mathematics, 201, 69-87, (2007) · Zbl 1110.65015 |

[23] | Yu, S.-W., Approximating the term structure of interest rates in Japan, Applied economics letters, 6, 403-407, (1999) |

[24] | Zhang, W.; Wang, Y.; Fang, S.-C.; Lavery, J.E., Cubic L1 splines on triangular irregular networks, Pacific journal of optimization, 2, 289-318, (2006) |

[25] | Zhou, S.; Shen, X., Spatially adaptive regression splines and accurate knot selection schemes, Journal of the American statistical association, 96, 247-259, (2001) · Zbl 1014.62049 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.