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首页> 美国政府科技报告 >Time Changed Markov Processes in Unified Credit-Equity Modeling: FDIC Center for Financial Research Working Paper, No. 2008-03
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Time Changed Markov Processes in Unified Credit-Equity Modeling: FDIC Center for Financial Research Working Paper, No. 2008-03

机译：统一信用 - 股权模型中的时间变化马尔可夫过程：FDIC金融研究中心工作文件，第2008-03号

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This paper develops a novel class of hybrid credit-equity models with state-dependent jumps, local-stochastic volatility and default intensity based on time changes of Markov processes with killing. We model the defaultable stock price process as a time changed Markov diffusion process with state-dependent local volatility and killing rate (default intensity). When the time change is a Levy subordinator, the stock price process exhibits jumps with state-dependent Levy measure. When the time change is a time integral of an activity rate process, the stock price process has local-stochastic volatility and default intensity. When the time change process is a Levy subordinator in turn time changed with a time integral of an activity rate process, the stock price process has state-dependent jumps, local-stochastic volatility and default intensity. We develop two analytical approaches to the pricing of credit and equity derivatives in this class of models. The two approaches are based on the Laplace transform inversion and the spectral expansion approach, respectively. If the resolvent (the Laplace transform of the transition semigroup) of the Markov process and the Laplace transform of the time change are both available in closed form, the expectation operator of the time changed process is expressed in closed form as a single integral in the complex plane.

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