论文标题
跨货币估值和对冲在多个曲线框架中
Cross Currency Valuation and Hedging in the Multiple Curve Framework
论文作者
论文摘要
我们将Bielecki和Rutkowski（2015）的资金和抵押品的结果概括为多阶段框架，并将其结果与Piterbarg（2012），Moreni和Pallavicini（2017）和Fujii等人的结果联系起来。 （2010b）。 在这样做的过程中，我们提供了一项完整的研究，该研究在多币种市场中缺乏套利，在每个单一货币领域，多重利率共存。我们首先是在没有抵押品的情况下没有套利的特征。 之后，我们在非常普遍的情况下研究了抵押计划：可以用任何货币指定特遣队索赔的现金流以及与抵押协议相关的现金流。我们研究种族隔离和重新支配，并允许按任意货币规格进行现金和风险抵押品。在所有可能的公约组合中讨论了在抵押品存在下没有套利和定价的情况。 我们的工作提供了分析财富动态的参考，我们还提供了估值公式，这是跨货币曲线构建技术的有用基础。我们的框架还为在XVA计算的背景下生成曝光概况的多阶段模拟模型构建了稳固的基础。
We generalize the results of Bielecki and Rutkowski (2015) on funding and collateralization to a multi-currency framework and link their results with those of Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b). In doing this, we provide a complete study of absence of arbitrage in a multi-currency market where, in each single monetary area, multiple interest rates coexist. We first characterize absence of arbitrage in the case without collateral. After that we study collateralization schemes in a very general situation: the cash flows of the contingent claim and those associated to the collateral agreement can be specified in any currency. We study both segregation and rehypothecation and allow for cash and risky collateral in arbitrary currency specifications. Absence of arbitrage and pricing in the presence of collateral are discussed under all possible combinations of conventions. Our work provides a reference for the analysis of wealth dynamics, we also provide valuation formulas that are a useful foundation for cross-currency curve construction techniques. Our framework provides also a solid foundation for the construction of multi-currency simulation models for the generation of exposure profiles in the context of xVA calculations.
