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

Yifan Li, Ingmar Nolte, Manh Cuong Pham

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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.
Original languageEnglish
Article number105748
JournalJournal of Econometrics
Issue number2
Publication statusPublished - 30 Apr 2024


  • Mixture-of-distribution method
  • Parametric modelling
  • Risk-neutral density


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