Out-of-sample density forecasts with affine jump diffusion models

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7 Scopus citations


We conduct out-of-sample density forecast evaluations of the affine jump diffusion models for the S&P 500 stock index and its options' contracts. We also examine the time-series consistency between the model-implied spot volatilities using options & returns and only returns. In particular, we focus on the role of the time-varying jump risk premia. Particle filters are used to estimate the model-implied spot volatilities. We also propose the beta transformation approach for recursive parameter updating. Our empirical analysis shows that the inconsistencies between options & returns and only returns are resolved by the introduction of the time-varying jump risk premia. For density forecasts, the time-varying jump risk premia models dominate the other models in terms of likelihood criteria. We also find that for medium-term horizons, the beta transformation can weaken the systematic effect of misspecified AJD models using options & returns.

Original languageEnglish
Pages (from-to)74-87
Number of pages14
JournalJournal of Banking and Finance
Issue number1
StatePublished - Oct 2014


  • Affine jump diffusion
  • Beta transformation
  • Density forecasts
  • Particle filters
  • Time-series consistency
  • Time-varying jump risk premia


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