N°25-61: Pricing News and No News with Heterogeneous Beliefs

We study a general-equilibrium economy where agents trade assets and derivatives with heterogeneous beliefs along two dimensions: news intensity and content. When intensity disagreement dominates, implied volatility is persistent: quiet periods shift wealth toward calm-world believers, compressing risk-neutral tail probabilities and raising prices. The information structure of the news process governs the persistence of intensity disagreement: in a Poisson limit, intensity disagreement lasts, whereas in a Brownian limit it is eliminated. When content disagreement dominates, volatility is mean-reverting: news shifts wealth between optimists and pessimists. Our framework rationalizes the implied volatility smirk and derivative positions across subjective return beliefs.