论文标题
向后的随机微分方程计算xva的注释
Notes on Backward Stochastic Differential Equations for Computing XVA
论文作者
论文摘要
X值调整（XVA）问题是数学金融方面的最新主题。首先，回顾了逐渐扩大的过滤中随机地范围的向后随机微分方程（BSDE）的基本特性。接下来，使用此类BSDE描述了可默认非处方（OTC）衍生证券的定价/对冲问题。给出了足够的条件，以确保卖方和衍生证券的买方不存在套利机会。此外，提出了一个明确的定价公式，其中XVA被解释为理论公平价格的近似校正条款。
The X-valuation adjustment (XVA) problem, which is a recent topic in mathematical finance, is considered and analyzed. First, the basic properties of backward stochastic differential equations (BSDEs) with a random horizon in a progressively enlarged filtration are reviewed. Next, the pricing/hedging problem for defaultable over-the-counter (OTC) derivative securities is described using such BSDEs. An explicit sufficient condition is given to ensure the non-existence of an arbitrage opportunity for both the seller and buyer of the derivative securities. Furthermore, an explicit pricing formula is presented in which XVA is interpreted as approximated correction terms of the theoretical fair price.
