The FVA Debate

John C Hull and Alan D White

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

When valuing European options in the early 1970s, Fischer Black, Myron Scholes and Robert Merton (BSM) showed that, over any short period of time, an investment in an option could be replicated with a portfolio of stock and risk-free debt. This observation allowed them to calculate the economic value of the option by solving a differential equation. Subsequent analysis showed the economic value of the option could also be determined by discounting the expected payoff on the option in a risk-neutral world at the risk-free rate of interest. The calculated value is “economic” in the sense that, if the option price were different from this value, an investment in the option would dominate an investment of equivalent risk in a portfolio of debt and equity. The BSM analysis also showed that if it were possible to borrow and lend at the risk-free rate of interest, the replicating portfolio could be used as a hedge for the option.

Prior to the credit crisis that started in 2007, the London Interbank Offered Rate (Libor) was thought to be the best proxy for the risk-free rate, and it was assumed banks could borrow and lend at that rate, allowing them to carry out the replicating trading

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