We introduce the notion of a regime switching affine process. Informally this is a Markov process that behaves conditionally on each regime as an affine process with specific parameters. To facilitate our analysis, specific restrictions are imposed on these parameters. The regime switches are driven by a Markov chain. We prove that the joint process of the Markov chain and the conditionally affine part is a process with an affine structure on an enlarged state space, conditionally on the starting state of the Markov chain. Like for affine processes, the characteristic function can be expressed in a set of ordinary differential equations that can sometimes be solved analytically. This result unifies several semi-analytical solutions found in the literature for pricing derivatives of specific regime switching processes on smaller state spaces. It also provides a unifying theory that allows us to introduce regime switching to the pricing of many derivatives within the broad class of affine processes. Examples include European options and term structure derivatives with stochastic volatility and default. Essentially, whenever there is a pricing solution based on an affine process, we can extend this to a regime switching affine process without sacrificing the analytical tractability of the affine process.

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体制转换仿射过程及其在金融中的应用

我们介绍了一种政权转换仿射过程的概念。非正式地，这是一个马尔可夫过程，在每个过程中有条件地表现为具有特定参数的仿射过程。为了方便我们的分析，对这些参数施加了特定的限制。体制切换由马尔可夫链驱动。我们证明了马尔可夫链和有条件仿射部分的联合过程是一个在状态空间上，以马尔可夫链的起始状态为条件的，具有仿射结构的过程。像仿射过程一样，特征函数可以用一组常微分方程表示，有时可以通过解析来求解。该结果统一了文献中针对特定状态切换过程在较小状态空间上的导数进行定价的几种半分析解决方案。它还提供了一个统一的理论，使我们可以在广泛的仿射过程类别中将制度转换引入许多衍生产品的定价中。例子包括具有随机波动率和违约的欧洲期权和期限结构衍生产品。本质上，只要有基于仿射过程的定价解决方案，我们都可以将其扩展到体制转换仿射过程，而不会牺牲仿射过程的分析可处理性。