关于计算XVA的倒向随机微分方程的注记
Notes on Backward Stochastic Differential Equations for Computing XVA
摘要：
对金融数学中的一个新课题--X值调整问题进行了研究和分析。首先，回顾了逐步扩大滤过中具有随机时域的倒向随机微分方程的基本性质。接下来，违约场外（OTC）衍生证券的定价/对冲问题，使用这样的BSDES。给出了一个明确的充分条件，以确保不存在套利机会的卖方和买方的衍生证券。此外，一个明确的定价公式，其中XVA被解释为近似的理论公允价格的修正项。
英文摘要：
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.
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