# A unified approach to xVA with CSA discounting and initial margin

## TL;DR

This paper advances xVA modeling by integrating initial margin with defaults, addressing discount curve inconsistencies, and analyzing portfolio aggregation effects, thereby improving valuation accuracy and consistency.

## Contribution

It introduces a unified BSDE framework incorporating initial margin, resolves discount curve inconsistencies between front-office and xVA desk, and examines portfolio aggregation impacts.

## Key findings

- Enhanced xVA models include initial margin with defaults.
- Resolved discounting inconsistencies between trading and xVA desks.
- Analyzed non-linearity effects from portfolio aggregation.

## Abstract

In this paper we extend the existing literature on xVA along three directions. First, we enhance current BSDE-based xVA frameworks to include initial margin in presence of defaults. Next, we solve the consistency problem that arises when the front-office desk of the bank uses trade-specific discount curves (CSA discounting) which differ from the discount rate adopted by the xVA desk. Finally, we clarify the impact of aggregation of several sub-portfolios of trades on the xVA-valuation of the resulting global portfolio and study related non-linearity effects.