Term Structure Modeling Using Exponential Splines

Vasicek, Oldrich A; Fong, H. Gifford

doi:10.1111/j.1540-6261.1982.tb03555.x

Cited by 264 publications

(62 citation statements)

References 13 publications

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“…This method was developed in Vasicek and Fong (1982), and Fisher, Nychka, and Zervos (1995). It is based either on a fixed or variable grid and an optimization procedure that minimizes some penalty functions.…”

Section: Methods Of Calculating Zero-coupon Yield Curvesmentioning

confidence: 99%

The estimation of nominal and real yield curves from government bonds in Israel

Wiener

Pompushko²

2006

The Journal of Risk Finance

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We develop and test a mathematical method of deriving zero yield curve from market prices of government bonds. The method is based on a forward curve approximated by a linear (or piecewise constant) spline and should be applicable even for markets with low liquidity. The best fitting curve is derived by minimizing the penalty function. The penalty is defined as a sum of squared price discrepancies (theoretical curve based price minus market closing price) weighted by trade volume and an additional penalty for non-smoothness of the yield curve. We apply this method to both nominal and CPI linked bonds traded in Israel (some segments of these markets have low liquidity). The resulting two yield curves are used for derivation of market expected inflation rate. The main problems are low liquidity of some bonds and imperfect linkage to inflation in the CPI linked market. Usage of forward curves as the state space for the minimization problem leads to a stable solution that fits the data very well and can be used for calculating forward rates.

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Section: Methods Of Calculating Zero-coupon Yield Curvesmentioning

confidence: 99%

The estimation of nominal and real yield curves from government bonds in Israel

Wiener

Pompushko²

2006

The Journal of Risk Finance

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“…It is clear that B n (x) ∈ C n−2 is a piecewise polynomial of degree n − 1. One may find more details on the splines and B-splines in [9]- [13] and [14] and some applications in [15] and [16]. In [17], Dyn and Ron considered periodic exponential B-splines defined by weight functions w i (u) = e aiu r i (u) with r i (u + 1) = cr i (u), a i ∈ R, and showed these Bsplines possess a significant property of translation invariant and satisfy a generalized Hermite-Genocchi formula.…”

Section: 4)mentioning

confidence: 99%

Eulerian polynomials and B-splines

2012

Journal of Computational and Applied Mathematics

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Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, Bsplines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann zeta function values at odd integers are given. The relation between Eulerian numbers and B-spline values at knot points are also discussed.

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“…Classic approaches to estimating yield term structures from data sets of bond prices include the spline methods of McCulloch (1971) and McCulloch (1975). McCulloch's approaches have been modified and extended by Shea (1984), Vasicek and Fong (1982) and Nelson and Siegel (1987) amongst others. Surveys and comparative analysis of different techniques are provided by Bliss (1997) and Ferguson and Raymar (1998).…”

Section: Credit Term Structure Fitsmentioning

confidence: 99%

Determinants of Asset-Backed Security Prices in Crisis Periods

Perraudin

2008

SSRN Journal

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Term Structure Modeling Using Exponential Splines

Cited by 264 publications

References 13 publications

The estimation of nominal and real yield curves from government bonds in Israel

The estimation of nominal and real yield curves from government bonds in Israel

Eulerian polynomials and B-splines

Determinants of Asset-Backed Security Prices in Crisis Periods

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