Parametric Risk-Neutral Density Estimation via Finite Lognormal-Weibull Mixtures

Li, Yifan and Nolte, Ingmar and Pham, Manh (2024) Parametric Risk-Neutral Density Estimation via Finite Lognormal-Weibull Mixtures. Journal of Econometrics, 241 (2): 105748. ISSN 0304-4076

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Abstract

This paper proposes a new parametric risk-neutral density (RND) estimator based on a finite lognormal-Weibull mixture (LWM) density. We establish the consistency and asymptotic normality of the LWM method in a general misspecified parametric framework. Based on the theoretical results, we propose a sequential test procedure to evaluate the goodness-of-fit of the LWM model, which leads to an adaptive choice for the number and type of mixture components. Our simulation results show that, in finite samples with various observation error specifications, the LWM method can approximate complex RNDs generated by state-of-the-art multi-factor stochastic volatility models with a few (typically less than 4) mixtures. Application of the LWM model on index options confirms its reliability in recovering empirical RNDs with a heavy left tail or bimodality, which can be incorrectly identified as bimodality or a heavy left tail by existing (semi)-nonparametric methods if the goodness-of-fit to the observed data is ignored.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Econometrics
Uncontrolled Keywords:
Research Output Funding/yes_externally_funded
Subjects:
?? yes - externally fundednohistory and philosophy of scienceeconomics and econometricsapplied mathematics ??
ID Code:
218016
Deposited By:
Deposited On:
15 Apr 2024 09:20
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Nov 2024 00:40