CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins Under Credit, Funding and Wrong-Way Risks: A Unified Valuation Approach

52 Pages Posted: 17 Jan 2014

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Date Written: January 16, 2014

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.

Keywords: Central Counterparty Clearing, Credit Support Annex, ISDA, Interest Rate Derivatives, Funding Costs, Bilateral Counterparty Risk, Credit Valuation Adjustment, CVA, Collateral Modeling, Initial Margin, Variation Margin, Close-Out, Re-hypothecation, Gap Risk, Margin Period of Risk, Backward Stochastic

JEL Classification: G12, G13

Suggested Citation

Brigo, Damiano and Pallavicini, Andrea, CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins Under Credit, Funding and Wrong-Way Risks: A Unified Valuation Approach (January 16, 2014). Available at SSRN: https://ssrn.com/abstract=2380017 or http://dx.doi.org/10.2139/ssrn.2380017

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Andrea Pallavicini (Contact Author)

Banca IMI ( email )

Largo Mattioli 3
Milan, MI 20121
Italy
+39 02 7261 (Phone)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

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