英文标题：
《Wrong-Way Risk Models: A Comparison of Analytical Exposures》
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作者：
Fr\\\'ed\\\'eric Vrins
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最新提交年份：
2016
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英文摘要：
In this paper, we compare static and dynamic (reduced form) approaches for modeling wrong-way risk in the context of CVA. Although all these approaches potentially suffer from arbitrage problems, they are popular (respectively) in industry and academia, mainly due to analytical tractability reasons. We complete the stochastic intensity models with another dynamic approach, consisting in the straight modeling of the survival (Az\\\'ema supermartingale) process using the $\\Phi$-martingale. Just like the other approaches, this method allows for automatic calibration to a given default probability curve. We derive analytically the positive exposures $V^+_t$ \"conditional upon default\" associated to prototypical market price processes of FRA and IRS in all cases. We further discuss the link between the \"default\" condition and change-of-measure techniques. The expectation of $V^+_t$ conditional upon $\\tau=t$ is equal to the unconditional expectation of $V^+_t\\zeta_t$. The process $\\zeta$ is explicitly derived in the dynamic approaches: it is proven to be positive and to have unit expectation. Unfortunately however, it fails to be a martingale, so that Girsanov machinery cannot be used. Nevertheless, the expectation of $V^+_t\\zeta_t$ can be computed explicitly, leading to analytical expected positive exposure profiles in the considered examples.
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中文摘要：
在本文中，我们比较了在CVA背景下建模错误路径风险的静态和动态（简化形式）方法。尽管所有这些方法都可能存在套利问题，但它们（分别）在工业界和学术界广受欢迎，主要是由于分析的可处理性原因。我们用另一种动态方法完成了随机强度模型，包括使用$\\ Phi$-鞅直接建模生存（Az¨ema supermartingale）过程。与其他方法一样，此方法允许对给定的默认概率曲线进行自动校准。我们通过分析得出，在所有情况下，与FRA和IRS的典型市场价格过程相关的正风险敞口V^+\\U t$“有条件违约”。我们进一步讨论了“默认”条件与测量技术变化之间的联系。以$\\tau=t$为条件的$V^+\\u t$预期等于无条件的$V^+\\u t\\zeta\\u t$。过程$\\zeta$是在动态方法中明确推导出来的：它被证明是积极的，并且具有单位期望值。然而，不幸的是，它不是鞅，所以Girsanov机制不能使用。然而，可以明确计算$V^+\\u t\\zeta\\u t$的预期值，从而在所考虑的示例中得出分析预期的正暴露曲线。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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