Regulatory-Optimal Funding

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

Trading desks that require funding typically must pay above the risk-free rate. This has led some to add a funding valuation adjustment (FVA) to derivatives prices, and to a heated debate over the legitimacy of this practice (Hull and White 2012). At the time of writing some firms were starting to report explicit FVA line items. However, the FVA literature treats the funding curve as an input to the model (Burgard and Kjaer 2011; Morini and Prampolini 2011). This can vary from the firm’s senior unsecured debt to internally set curves.

Few studies have examined how a bank can fund itself in practice, but banks have long been engaged in the practice of maturity transformation, receiving funding sources such as deposits of uncertain maturity while making long-term loans. This maturity transformation, while central to banking activities, is a source of risk, and this has attracted regulatory attention.

Tougher regulatory requirements for liquidity buffers, such as those proposed by the UK Financial Services Authority in 2009 and implemented by its successor, the Prudential Regulatory Authority (PRA), put constraints on the minimum funding levels banks can have (Financial Services

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