Warehousing Credit Risk: Pricing, Capital and Tax

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

Credit valuation adjustments (CVAs) apply to all counterparties with derivatives transactions that are marked to market, that is, those in the trading book. For most banks only a subset of these counterparties have liquid credit default swap (CDS) contracts available for hedging default risk (the US dollar CDS market has only about 1,600 liquid contracts), so some credit risk is inevitably warehoused. Higher credit risk requires more capital. Open risk requires pricing in the physical measure rather than the risk-neutral measure.

Here, we extend the semi-replication approach in Burgard and Kjaer (2013) and Green et al (2014) to include counterparty credit risk warehousing and taxation of any resultant profit or loss. Thus, we introduce double semi-replication, that is, partial hedging of value jump on counterparty default and tax valuation adjustment (TVA). This value jump on counterparty default must be priced in, otherwise pricing will be inconsistent with the bank’s risk appetite. The market price of jump risk can be observed (Antje et al 2005; Berg 2010), but may be different from the bank’s.

Credit risk also affects the capital a bank is required to hold under Basel III

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