In the Balance

Christoph Burgard and Mats Kjaer

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

Funding costs and the bilateral counterparty credit risk of derivatives positions have become increasingly hot topics since the beginning of the credit crisis in 2008. It has become standard practice to adjust derivatives prices for the counterparty risk. Similarly, funding costs are increasingly incorporated into derivatives prices one way or another, but the conceptual foundations for such funding adjustments are much less well understood.

Piterbarg (2010) showed how the funding costs of delta hedging affect derivatives pricing. Subsequently, Burgard and Kjaer (2011) developed a unified framework that combines funding costs and bilateral counterparty credit risk. This framework specifies how a positive cash account related to the hedging strategy of an uncollateralised derivative can be used to fund the repurchase of the issuer’s own bonds in order to hedge its own credit risk. This demonstrates that the debit value adjustment (DVA) is equivalent to a funding benefit adjustment and justifies its inclusion in a bilateral counterparty value adjustment. The framework also includes the funding costs associated with a negative cash account, and yields a corresponding additional

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