市场非流动性条件下的XVA定价
XVA Valuation under Market Illiquidity
摘要：
在2008年金融危机之前，大多数金融数学研究都集中在期权定价上，而没有考虑交易对手违约的影响、流动性不足问题以及销售和回购协议（Repo）市场的作用。最近，有人提出了一些模型来解决这个问题，方法是计算衍生品的总估值调整（XVA），但没有考虑市场的潜在危机。在这篇文章中，我们包括一个可能的危机，通过使用一个交替更新过程来描述一个正常的金融制度和金融危机之间的切换。我们开发了一个框架来定价XVA的欧洲索赔在这种状态依赖的情况。将价格刻画为一个倒向随机微分方程（Besides）的解，并证明了该解的存在唯一性。在一项基于BSDEs深度学习算法的数值研究中，我们比较了不同参数对XVA估值的影响。
英文摘要：
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.
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