Efficient XVA Management: Pricing, Hedging and Allocation

Chris Kenyon and Andrew Green

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

Banks must calculate and manage valuation adjustments (XVA) across their entire trading portfolio. XVA includes the effects of credit (CVA, DVA), funding (FVA, MVA) (Burgard and Kjaer 2013; Green and Kenyon 2015), capital (KVA) (Green et al 2014) and tax (TVA) (Kenyon and Green 2015).11Abbreviations are as follows: VA is for valuation adjustment, where takes the following values and meanings: C, credit; D, debit; F, funding; M, margin; K, capital; T, tax; X, all, including those that have not yet been identified. XVA management includes allocation, hedging and pricing. Allocation refers to the allocation of XVA, and XVA hedging costs, to desks. Hedging costs require the computation of both first-order sensitivities and second-order sensitivities, such as interest rate-credit cross-gamma. Incremental allocation is required for daily trading.

Here, we provide an analytically rigorous method for managing XVA efficiently, which combines three elements: trade-level regression, analytic computation of sensitivities and global conditioning. Regression has been demonstrated in MVA to speed things up by one-to-two orders of magnitude, even on vanilla instruments for medium-sized

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