Close-Out Convention Tensions

Damiano Brigo and Massimo Morini

Contents

Introduction

Preface to Chapter 1

1.

Being Two-Faced over Counterparty Credit Risk

2.

Risky Funding: A Unified Framework for Counterparty and Liquidity Charges

3.

DVA for Assets

4.

Pricing CDSs’ Capital Relief

5.

The FVA Debate

6.

The FVA Debate: Reloaded

7.

Regulatory Costs Break Risk Neutrality

8.

Risk Neutrality Stays

9.

Regulatory Costs Remain

10.

Funding beyond Discounting: Collateral Agreements and Derivatives Pricing

11.

Cooking with Collateral

12.

Options for Collateral Options

13.

Partial Differential Equation Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs

14.

In the Balance

15.

Funding Strategies, Funding Costs

16.

The Funding Invariance Principle

17.

Regulatory-Optimal Funding

18.

Close-Out Convention Tensions

19.

Funding, Collateral and Hedging: Arbitrage-Free Pricing with Credit, Collateral and Funding Costs

20.

Bilateral Counterparty Risk with Application to Credit Default Swaps

21.

KVA: Capital Valuation Adjustment by Replication

22.

From FVA to KVA: Including Cost of Capital in Derivatives Pricing

23.

Warehousing Credit Risk: Pricing, Capital and Tax

24.

MVA by Replication and Regression

25.

Smoking Adjoints: Fast Evaluation of Monte Carlo Greeks

26.

Adjoint Greeks Made Easy

27.

Bounding Wrong-Way Risk in Measuring Counterparty Risk

28.

Wrong-Way Risk the Right Way: Accounting for Joint Defaults in CVA

29.

Backward Induction for Future Values

30.

A Non-Linear PDE for XVA by Forward Monte Carlo

31.

Efficient XVA Management: Pricing, Hedging and Allocation

32.

Accounting for KVA under IFRS 13

33.

FVA Accounting, Risk Management and Collateral Trading

34.

Derivatives Funding, Netting and Accounting

35.

Managing XVA in the Ring-Fenced Bank

36.

XVA: A Banking Supervisory Perspective

37.

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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