本文開發了一個創新的資產定價框架，將投資者對極端災難的信念整合至跳躍擴散期權定價模型中。我們將信念過程定義為經濟處於穩定體制的條件概率，並將其視為透過連續貝式學習演變的潛在狀態變量。在該模型中，投資者因無法直接觀測底層體制，必須從市場跳躍中推斷經濟狀態，進而產生顯著的信息反饋循環：單一災難事件會觸發信念的立即下修，導致跳躍強度與風險溢價內生性飆升；反之，在市場平靜期，信念的恢復則極其緩慢。透過重要性重採樣粒子濾波（SIR Particle Filter）並結合 S&P 500 指數與選擇權截面數據進行估計，實證結果顯示，這種信念驅動的動態機制在解釋變異數風險溢價與隱含波動率期限結構上，明顯優於傳統的隨機強度模型。研究強調，投資者信念的修正而非外部波動率衝擊，才是金融市場危機期間尾部風險與非線性行為的主要驅動力。

This paper develops a novel asset pricing framework that investor beliefs regarding rare disasters within a jump-diffusion option pricing model. We formalize the belief process as the conditional probability that the economy resides in a stable regime, treating it as a latent state variable that evolves through continuous Bayesian learning. In our model, investors do not observe the underlying regime directly; instead, they must infer the state of the economy from realized market jumps.This mechanism generates a significant informational feedback loop: single catastrophic event triggers an immediate downward revision of investor beliefs, leading to an endogenous spike in jump intensity and risk premium. Conversely, the recovery of beliefs is characterized by a slow process during periods of market calm. Estimating the model with S&P 500 index returns and a cross-section of option prices via a Sequential Importance Resampling Particle Filter, we demonstrate that this belief-driven dynamics provides a superior fit for the variance risk premium and the term structure of implied volatility compared to traditional stochastic intensity models. Our findings suggest that the revision of investor beliefs rather than exogenous volatility shocks is the primary driver of tail risk and the non-linear behavior observed in financial markets during crises.

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