In this article, we develop a semi-analytical solution for a structural model that combines jump and regime switching risk. We use an Esscher transform that is applicable to regime switching double exponential jump diffusion to move from the historical world to the risk-neutral world. Further, we define and implement a matrix Wiener–Hopf factorization associated with the latter process, allowing us to price the various components of balance sheet. We illustrate the model with a study of a bank that issues contingent convertible bonds (CoCos). Thus, we obtain valuation formulas for the bank’s equity, debt, deposits, CoCos, and deposit insurance. We also show in an illustration the respective effects of the jump risk and of regime switching on the values of all of a bank’s balance sheet components.

中文翻译：

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CoCos 和存款保险的结构性定价与体制转换和跳跃

在本文中，我们为结合跳跃和状态转换风险的结构模型开发了一个半解析解。我们使用适用于状态转换双指数跳跃扩散的埃舍尔变换从历史世界转移到风险中性世界。此外，我们定义并实施了与后一个过程相关的矩阵 Wiener-Hopf 分解，使我们能够对资产负债表的各个组成部分进行定价。我们通过对发行或有可转换债券 (CoCos) 的银行的研究来说明该模型。因此，我们获得了银行股权、债务、存款、CoCos 和存款保险的估值公式。我们还在插图中展示了跳跃风险和制度转换对银行所有资产负债表组成部分价值的各自影响。