The credit crunch of 2007 caused major changes in the market of interbank rates making the existing interest rate theory inconsistent. This paper puts forward one way to reconcile practice and theory by modifying the arbitrage-free condition. In this framework, the forward Libor rate is no longer considered as a risk-free rate and the credit and liquidity risks within the interbank market partly drive its dynamics. In a similar manner to the multiple-curve approach, we model the evolution of default-free rates, assimilated to overnight interest swap rates, and the default times of an interbank market segment determined by its tenor. For each segment, we use the reduced form approach to model the arrival rate of defaults with a self-exciting jump-diffusion process. Then, we deduce the dynamics of the spot forward Libor rates and provide closed-form approximation pricing formulae for options on forward Libor rates and swap rates. Even in a context of negative interest rates and compared to other forms of intensity processes such as a CIR, the self-excitation property allows a better understanding of the spread OIS-IRS and provides information about the interbank credit risk. Furthermore, our framework enables to parse the impact of the interbank credit risk on forward Libor as well as on interest rates derivatives like caps, floors, and swaptions.

中文翻译：

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具有自激跳跃过程的银行间信用风险建模

2007年的信贷紧缩导致银行同业拆借市场发生重大变化，使现有的利率理论不协调。本文提出了一种通过修改无套利条件来调和实践与理论的方法。在此框架下，远期 Libor 利率不再被视为无风险利率，银行间市场的信用和流动性风险部分推动了其动态。以与多曲线方法类似的方式，我们模拟了无违约利率的演变，类似于隔夜利率掉期利率，以及由其期限决定的银行间市场部分的违约时间。对于每个部分，我们使用简化形式的方法通过自激跳跃扩散过程对违约的到达率进行建模。然后，我们推导出即期远期 Libor 利率的动态，并为远期 Libor 利率和掉期利率期权提供封闭式近似定价公式。即使在负利率的背景下，与 CIR 等其他形式的强度过程相比，自激特性也可以更好地理解 OIS-IRS 的价差，并提供有关银行间信用风险的信息。此外，我们的框架能够分析银行间信用风险对远期 Libor 以及利率衍生品（如上限、下限和掉期期权）的影响。自激特性可以更好地理解 OIS-IRS 的价差，并提供有关银行同业信用风险的信息。此外，我们的框架能够分析银行间信用风险对远期 Libor 以及利率衍生品（如上限、下限和掉期期权）的影响。自激特性可以更好地理解 OIS-IRS 的价差，并提供有关银行同业信用风险的信息。此外，我们的框架能够分析银行间信用风险对远期 Libor 以及利率衍生品（如上限、下限和掉期期权）的影响。