论文标题
XVA估值在市场不足之下
XVA Valuation under Market Illiquidity
论文作者
论文摘要
在2008年的金融危机之前，大多数金融数学研究都集中在定价方案上，而无需考虑交易对手的默认效果，流动性不足问题以及销售和回购协议（Repo）市场的作用。最近，提出了通过计算衍生物的总价值调整（XVA）来解决这一问题的模型。但是，不考虑市场上的潜在危机。在本文中，我们通过使用交替的续签流程来描述正常金融体制与金融危机之间的转换，包括可能的危机。我们开发一个框架，以这种依赖州依赖的情况为欧洲主张的XVA定价。价格的特征在于向后的随机微分方程（BSDE），我们证明了该解决方案的存在和独特性。在基于BSDE的深度学习算法的数值研究中，我们比较了不同参数对XVA评估的影响。
Before the 2008 financial crisis, most research in financial mathematics focused on pricing options without considering the effects of counterparties' defaults, illiquidity problems, and the role of the sale and repurchase agreement (Repo) market. Recently, models were proposed to address this by computing a total valuation adjustment (XVA) of derivatives; however without considering a potential crisis in the market. In this article, we include a possible crisis by using an alternating renewal process to describe the switching between a normal financial regime and a financial crisis. We develop a framework to price the XVA of a European claim in this state-dependent situation. The price is characterized as a solution to a backward stochastic differential equation (BSDE), and we prove the existence and uniqueness of this solution. In a numerical study based on a deep learning algorithm for BSDEs, we compare the effect of different parameters on the valuation of the XVA.
