Landmarks in XVA
First published:
ISBN: 9781782722939
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Bilateral Counterparty Risk with Application to Credit Default Swaps
Damiano Brigo and Agostino Capponi
Introduction
Preface to Chapter 1
Being Two-Faced over Counterparty Credit Risk
Risky Funding: A Unified Framework for Counterparty and Liquidity Charges
DVA for Assets
Pricing CDSs’ Capital Relief
The FVA Debate
The FVA Debate: Reloaded
Regulatory Costs Break Risk Neutrality
Risk Neutrality Stays
Regulatory Costs Remain
Funding beyond Discounting: Collateral Agreements and Derivatives Pricing
Cooking with Collateral
Options for Collateral Options
Partial Differential Equation Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs
In the Balance
Funding Strategies, Funding Costs
The Funding Invariance Principle
Regulatory-Optimal Funding
Close-Out Convention Tensions
Funding, Collateral and Hedging: Arbitrage-Free Pricing with Credit, Collateral and Funding Costs
Bilateral Counterparty Risk with Application to Credit Default Swaps
KVA: Capital Valuation Adjustment by Replication
From FVA to KVA: Including Cost of Capital in Derivatives Pricing
Warehousing Credit Risk: Pricing, Capital and Tax
MVA by Replication and Regression
Smoking Adjoints: Fast Evaluation of Monte Carlo Greeks
Adjoint Greeks Made Easy
Bounding Wrong-Way Risk in Measuring Counterparty Risk
Wrong-Way Risk the Right Way: Accounting for Joint Defaults in CVA
Backward Induction for Future Values
A Non-Linear PDE for XVA by Forward Monte Carlo
Efficient XVA Management: Pricing, Hedging and Allocation
Accounting for KVA under IFRS 13
FVA Accounting, Risk Management and Collateral Trading
Derivatives Funding, Netting and Accounting
Managing XVA in the Ring-Fenced Bank
XVA: A Banking Supervisory Perspective
An Annotated Bibliography of XVA
In the valuation space, bilateral features are quite relevant for counterparty risk and often can be responsible for seemingly paradoxical statements. For example, Citigroup in its press release on the first quarter 2009 revenues11See http://www.citigroup.com/citi/news/2009/090417a.htm. reported a positive mark-to-market due to its worsened credit quality:
Revenues also included… a net $2.5 billion positive CVA [credit valuation adjustment] on derivative positions, excluding monolines, mainly due to the widening of Citi’s CDS [credit default swap] spreads.
In this chapter we explain precisely how such a situation may originate. Previous research on arbitrage-free valuation of counterparty risk adjustments (or CVAs) with dynamical models for commodities, rates and credit (see Brigo and Chourdakis (2009) for a summary and references) assumed the party computing the valuation adjustment to be default-free. Bielecki and Rutkowski (2001) present a formula for vulnerable claims with bilateral risk, but focus on the application to interest rate swaps.
We introduce here the general arbitrage-free valuation framework for CVAs in the presence of bilateral default risk, including
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