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首页> 外文期刊>International journal of theoretical and applied finance >Pricing credit derivatives in a markov-modulated reduced-form model
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Pricing credit derivatives in a markov-modulated reduced-form model

机译：马可夫调制的简化形式模型中的信用衍生产品定价

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Numerous incidents in the financial world have exposed the need for the design and analysis of models for correlated default timings. Some models have been studied in this regard which can capture the feedback in case of a major credit event. We extend the research in the same direction by proposing a new family of models having the feedback phenomena and capturing the effects of regime switching economy on the market. The regime switching economy is modeled by a continuous time Markov chain. The Markov chain may also be interpreted to represent the credit rating of the firm whose bond we seek to price. We model the default intensity in a pool of firms using the Markov chain and a risk factor process. We price some single-name and multi-name credit derivatives in terms of certain transforms of the default and loss processes. These transforms can be calculated explicitly in case the default intensity is modeled as a linear function of a conditionally affine jump diffusion process. In such a case, under suitable technical conditions, the price of credit derivatives are obtained as solutions to a system of ODEs with weak coupling, subject to appropriate terminal conditions. Solving the system of ODEs numerically, we analyze the credit derivative spreads and compare their behavior with the nonswitching counterparts. We show that our model can easily incorporate the effects of business cycle. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low floating interest rate, high default intensity rate, and high volatility. We also model the effects of firm restructuring on the credit spread, in case of a default.
机译：金融界发生的许多事件暴露了针对相关违约时间设计和分析模型的需求。在这方面已经研究了一些模型，这些模型可以在发生重大信用事件时捕获反馈。我们通过提出具有反馈现象的新模型系列并捕获政权转换经济对市场的影响，将研究朝同一方向扩展。政权转换经济以连续时间马尔可夫链为模型。马尔可夫链也可以解释为代表我们要对其债券进行定价的公司的信用评级。我们使用马尔可夫链和风险因子过程对企业池中的默认强度进行建模。我们根据违约和损失程序的某些转换对一些单名称和多名称信用衍生产品进行定价。如果将默认强度建模为有条件仿射跳跃扩散过程的线性函数，则可以显式计算这些变换。在这种情况下，在适当的终端条件下，在适当的技术条件下，可获得信用衍生产品的价格，作为具有弱耦合的ODE系统的解决方案。通过数值求解ODE系统，我们分析了信用衍生工具利差，并将其行为与非转换对等物进行了比较。我们证明了我们的模型可以轻松地纳入商业周期的影响。我们展示了试图捕获流动性紧张状况的稀有国家的纳入对价差的影响。这些状态的特点是浮动利率低，违约强度高，波动性高。在违约的情况下，我们还模拟了企业重组对信贷利差的影响。

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