On discrete rational least squares approximation

Pomentale, T.

doi:10.1007/bf02170995

Cited by 6 publications

(2 citation statements)

References 7 publications

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“…Moreover, it can be shown that when discrete conditions are imposed at sufficiently many locations, the condition is implied in between all locations [36]. Unfortunately, the theoretical number of discrete conditions needed for this implication to hold is often too high to be of practical use.…”

Section: Rational Interval Interpolation (Rii) Approachmentioning

confidence: 98%

Determining and benchmarking risk neutral distributions implied from option prices

Celis

Liang

Lemmens

et al. 2015

Applied Mathematics and Computation

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a b s t r a c tRisk neutral probability density functions (RNDs) play a central role in assessing models for stock market behavior. However, it remains challenging to distill a realistic estimate for the RND from empirical data. In this work we introduce a novel method to infer a RND estimate from observed option prices. Our method efficiently yields a realistic rational function approximation to the RND, it is flexible w.r.t. the shape of the underlying distribution and robust in the presence of noise. To show this, we first investigate how well a method can actually retrieve a known distribution from noisy option prices. Then we consider real market data and show how our method can be used to derive a single continuously differentiable RND estimate from empirical call and put option price data.

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Section: Rational Interval Interpolation (Rii) Approachmentioning

confidence: 98%

Determining and benchmarking risk neutral distributions implied from option prices

Celis

Liang

Lemmens

et al. 2015

Applied Mathematics and Computation

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show abstract

“…Very little has been known about this problem so far (e.g. [9,8,14,18]). Before iterative minimization, it is still necessary to ask whether the best l p estimate exists.…”

Section: Introductionmentioning

confidence: 98%

On the existence of the best discrete approximation inlpnorm by reciprocals of real polynomials

Jukić

2009

Journal of Approximation Theory

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For the given data (w i , x i , y i ), i = 1, . . . , M, we consider the problem of existence of the best discrete approximation in l p norm (1 ≤ p < ∞) by reciprocals of real polynomials. For this problem, the existence of best approximations is not always guaranteed. In this paper, we give a condition on data which is necessary and sufficient for the existence of the best approximation in l p norm. This condition is theoretical in nature. We apply it to obtain several other existence theorems very useful in practice. Some illustrative examples are also included.

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Algorithms for Rational Discrete Least Squares Approximation Part I: Unconstrained Optimization

Spellucci

1976

Moderne Methoden Der Numerischen Mathematik

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On discrete rational least squares approximation

Cited by 6 publications

References 7 publications

Determining and benchmarking risk neutral distributions implied from option prices

Determining and benchmarking risk neutral distributions implied from option prices

On the existence of the best discrete approximation inlpnorm by reciprocals of real polynomials

Algorithms for Rational Discrete Least Squares Approximation Part I: Unconstrained Optimization

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