Landmarks in XVA
First published:
ISBN: 9781782722939
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Close-Out Convention Tensions
Damiano Brigo and Massimo Morini
Close-Out Convention Tensions
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
When a default event happens to one of the counterparties in a deal, it is stopped and marked-to-market: the net present value (NPV) of the residual part of the deal is calculated. The recovery rate is applied to this close-out value to determine the default payment. While modelling the recovery is known to be a difficult task, the calculation of the close-out amount has never been the focus of extensive research. Before the credit crunch, and actually up to the Lehman Brothers’ default in 2008, the close-out amount was usually calculated as the expectation of the future payments discounted back to the default day by a Libor-based curve of discount factors.11Libor is the London Interbank Offered Rate.
At the time of writing, however, things are not so trivial. We are aware that discounting a deal that is default-free and backed by a liquid collateral should be performed using a default-free curve of discount factors, based on overnight quotations, whereas a deal that is not collateralised and is thus subject to default risk should be discounted taking liquidity costs into account and include a credit value adjustment. NPV should be calculated in different ways even for equal
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