CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins under credit, funding and wrong-way risks: A Unified Valuation Approach

TL;DR

This paper develops a comprehensive valuation framework for CCP-cleared and bilateral trades incorporating initial/variation margins, credit, funding, and wrong-way risks, with concrete interest rate swap examples.

Contribution

It introduces a unified nonlinear valuation approach that separates interconnected risks and models nonlinearities via BSDEs, accounting for asymmetric rates and collateralization.

Findings

Initial and variation margins significantly impact valuation adjustments.

The nonlinear funding costs are isolated and analyzed through numerical BSDE schemes.

Interest rate swap case study illustrates the quantitative effects of various risks.

Abstract

The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach for pricing under CCP clearing, including variation and initial margins, gap credit risk and collateralization, showing concrete examples for interest rate swaps. Mathematically, the inclusion of asymmetric borrowing and lending rates in the hedge of a claim lead to nonlinearities showing up in claim dependent pricing measures, aggregation dependent prices, nonlinear PDEs and BSDEs. This still holds in presence of CCPs and CSA. We introduce a modeling approach that allows us to enforce rigorous separation of the interconnected nonlinear risks into different valuation adjustments where the key pricing nonlinearities are confined to a funding costs component that is analyzed through numerical schemes for BSDEs. We present a numerical case study for Interest Rate Swaps that highlights the relative size of the different valuation adjustments and the quantitative role of initial and variation margins, of liquidity bases, of credit risk, of the margin period of risk and of wrong way risk correlations.