A simple and general approach to fitting the discount curve under no-arbitrage constraints

Fengler, Matthias R.; Hin, Lin-Yee

doi:10.1016/j.frl.2015.08.006

Cited by 6 publications

(3 citation statements)

References 32 publications

(41 reference statements)

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“…Leitenstorfer and Tutz (2007) considered the use of monotone B-splines in generalized additive models. For other applications of monotone B-splines, one can refer to Kanungo, Gay, and Haralick (1995) and Fengler and Hin (2014). In addition, Eilers and Marx (1996) proposed a flexible class of P-splines.…”

Section: Related Literaturementioning

confidence: 99%

Semiparametric Models for Accelerated Destructive Degradation Test Data Analysis

et al. 2017

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Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials' long term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition.Motivated by this challenge, we propose a semi-parametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonically decreasing).Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and accelerating variable, allowing for extrapolation to the use conditions. We develop an efficient procedure to estimate model parameters. We also use simulation to validate the developed procedures and demonstrate the robustness of the semi-parametric model under model misspecification. Finally, the proposed method is illustrated by multiple industrial applications.

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Section: Related Literaturementioning

confidence: 99%

Semiparametric Models for Accelerated Destructive Degradation Test Data Analysis

et al. 2017

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“…This has been investigated by among other Barzanti and Corradi (1999), Ramponi (2003), Chiu et al (2008). The relationship of shape and monotonicity restrictions with no-arbitrage conditions is detailed for example in the recent literature, see Laurini and Moura (2010) and Fengler and Hin (2015). Additional motivations of the use of monotonicity constraints will be developed in the numerical Section 5.4.…”

Section: Kriging Under Additional Monotonicity Constraintsmentioning

confidence: 99%

Kriging of financial term-structures

Cousin

Maatouk

Rullière

2016

European Journal of Operational Research

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Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The proposed method is based on a generalization of kriging models with linear equality constraints (market-fit conditions) and shape-preserving conditions such as monotonicity or positivity (no-arbitrage conditions). We define the most likely curve and show how to build confidence bands. The Gaussian process covariance hyper-parameters under the construction constraints are estimated using cross-validation techniques. Based on observed market quotes at different dates, we demonstrate the efficiency of the method by building curves together with confidence intervals for term-structures of OIS discount rates, of zero-coupon swaps rates and of CDS implied default probabilities. We also show how to construct interest-rate surfaces or default probability surfaces by considering time (quotation dates) as an additional dimension. JEL classification C63; E43; G12

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“…Barzanti and Corradi (1998) use tension splines where the tension in the spline is increased manually until problematic behaviour is avoided. Chiu et al (2008), Laurini andMoura (2010), andFengler andHin (2015), among others, impose shape constraints on the B-splines used to represent the discount function. The discount curve produced by our method is not guaranteed to be positive or monotonic non-increasing, however we did not find this to be a problem in the numerical examples we have explored.…”

Section: Introductionmentioning

confidence: 99%

Exact Smooth Term-Structure Estimation

Filipović¹,

Willems²

2016

Preprint

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We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is easy to implement and requires only basic linear algebra operations. We provide a full theoretical framework as well as several practical applications.

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A simple and general approach to fitting the discount curve under no-arbitrage constraints

Cited by 6 publications

References 32 publications

Semiparametric Models for Accelerated Destructive Degradation Test Data Analysis

Semiparametric Models for Accelerated Destructive Degradation Test Data Analysis

Kriging of financial term-structures

Exact Smooth Term-Structure Estimation

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