MVA by Replication and Regression

Andrew Green and Chris Kenyon

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

Initial margins (IMs) are required by central counterparties (CCPs) and under Basel Committee for Banking Supervision (2013) between financials on all non-cleared derivatives. Regulatory IM is being phased in from September 2016 to September 2020 (BCBS/IOSCO 2015). IM is a cost when it must be funded, ie, when IM is one-sided (CCPs) or non-rehypothecable.11Basel Committee for Banking Supervision (2013) permits very limited rehypothecation. Usually, rehypothecation is forbidden and segregation mandated, because otherwise the risk mitigation of IM is easily lost. Here, we extend the semi-replication framework of (Burgard and Kjaer 2013) for funding and credit to include this margin valuation adjustment (MVA) alongside capital (Green et al 2014).

MVA computation requires expected IM over the lifetime of the portfolio. CCP IM can be based on historical value-at-risk (VaR) or conditional VaR (also known as expected shortfall (ES)), potentially requiring nested Monte Carlo. This can be tackled efficiently, starting from regression techniques (Longstaff and Schwartz 2001) adapted to retain accuracy for the large shocks required by VaR/ES. We introduce a simple augmentation for non

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to Risk.net? View our subscription options

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here