Cooking with Collateral

Vladimir Piterbarg

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

An economy without a risk-free rate has been considered in the past (see Black 1972), but traditional derivatives pricing theory (see, for example, Duffie 2001) assumed the existence of such a rate as a matter of course. Until the global financial crisis, this assumption worked well, but since the crisis even government bonds cannot be considered credit risk-free. Hence, using a risk-free money-market account or a zero-coupon bond as a foundation for asset pricing theory needs revisiting. While some of the standard constructions in asset pricing theory could be reinterpreted in a way consistent with the developments of this chapter, there is significant value in going through the steps of derivations to show how they should be adapted to the prevailing market practice. This is the programme we carry out here.

What comes closest to a credit risk-free asset in a modern economy, in our view, is an asset fully collateralised on a continuous basis. Of course, possible jumps in asset values and practicalities of collateral monitoring and posting do not allow for full elimination of credit risk, but we will neglect this here.

A collateralised asset is fundamentally different from the

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