论文标题
一个统一的贝叶斯框架，用于定价灾难性粘结衍生物
A Unified Bayesian Framework for Pricing Catastrophe Bond Derivatives
论文作者
论文摘要
灾难（CAT）债券市场不完整，因此仪器定价的不确定性。由于已经提出了各种定价方法，但是在统一的资产定价框架内，没有人以足够灵活且统计上可靠的方式来处理灾难发生和利率的不确定性。因此，关于猫债券的预期风险主要依据，几乎没有众所周知。本文的主要贡献是基于灾难和利率的不确定性定量，提出一个统一的贝叶斯猫键定价框架。我们的框架允许对灾难风险的复杂信念捕获灾难发生中的独特和常见模式，并且在与随机利率结合使用时，会产生一种统一的资产定价方法，并提供信息丰富的预期风险Premia。具体而言，使用改良的集体风险模型 - Dirichlet先前的层次结构贝叶斯集体风险模型（DP-HBCRM）框架 - 我们通过基于模型的聚类方法对灾难风险进行建模。利率风险被建模为贝叶斯方法下的CIR过程。由于将猫定价模型铸造到我们的框架中，我们评估了与灾难风险概况聚集的各种猫债券合同的价格和预期风险总理。数值实验表明，这些集群如何揭示猫债券价格和预期风险Premia如何与索赔频率和损失严重性有关。
Catastrophe (CAT) bond markets are incomplete and hence carry uncertainty in instrument pricing. As such various pricing approaches have been proposed, but none treat the uncertainty in catastrophe occurrences and interest rates in a sufficiently flexible and statistically reliable way within a unifying asset pricing framework. Consequently, little is known empirically about the expected risk-premia of CAT bonds. The primary contribution of this paper is to present a unified Bayesian CAT bond pricing framework based on uncertainty quantification of catastrophes and interest rates. Our framework allows for complex beliefs about catastrophe risks to capture the distinct and common patterns in catastrophe occurrences, and when combined with stochastic interest rates, yields a unified asset pricing approach with informative expected risk premia. Specifically, using a modified collective risk model -- Dirichlet Prior-Hierarchical Bayesian Collective Risk Model (DP-HBCRM) framework -- we model catastrophe risk via a model-based clustering approach. Interest rate risk is modeled as a CIR process under the Bayesian approach. As a consequence of casting CAT pricing models into our framework, we evaluate the price and expected risk premia of various CAT bond contracts corresponding to clustering of catastrophe risk profiles. Numerical experiments show how these clusters reveal how CAT bond prices and expected risk premia relate to claim frequency and loss severity.
