Landmarks in XVA
First published:
ISBN: 9781782722939
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Backward Induction for Future Values
Alexandre Antonov, Serguei Issakov and Serguei Mechkov
Introduction
Preface to Chapter 1
Being Two-Faced over Counterparty Credit Risk
Risky Funding: A Unified Framework for Counterparty and Liquidity Charges
DVA for Assets
Pricing CDSs’ Capital Relief
The FVA Debate
The FVA Debate: Reloaded
Regulatory Costs Break Risk Neutrality
Risk Neutrality Stays
Regulatory Costs Remain
Funding beyond Discounting: Collateral Agreements and Derivatives Pricing
Cooking with Collateral
Options for Collateral Options
Partial Differential Equation Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs
In the Balance
Funding Strategies, Funding Costs
The Funding Invariance Principle
Regulatory-Optimal Funding
Close-Out Convention Tensions
Funding, Collateral and Hedging: Arbitrage-Free Pricing with Credit, Collateral and Funding Costs
Bilateral Counterparty Risk with Application to Credit Default Swaps
KVA: Capital Valuation Adjustment by Replication
From FVA to KVA: Including Cost of Capital in Derivatives Pricing
Warehousing Credit Risk: Pricing, Capital and Tax
MVA by Replication and Regression
Smoking Adjoints: Fast Evaluation of Monte Carlo Greeks
Adjoint Greeks Made Easy
Bounding Wrong-Way Risk in Measuring Counterparty Risk
Wrong-Way Risk the Right Way: Accounting for Joint Defaults in CVA
Backward Induction for Future Values
A Non-Linear PDE for XVA by Forward Monte Carlo
Efficient XVA Management: Pricing, Hedging and Allocation
Accounting for KVA under IFRS 13
FVA Accounting, Risk Management and Collateral Trading
Derivatives Funding, Netting and Accounting
Managing XVA in the Ring-Fenced Bank
XVA: A Banking Supervisory Perspective
An Annotated Bibliography of XVA
The American (or least squares) Monte Carlo method11We suggest referring to the American Monte Carlo method as the Las Vegas method for its brevity and geographical consistency. in its original formulation (see, for example, Carriere 1996; Longstaff and Schwartz 2001; see also Glasserman 2004 and the references therein) uses a backward induction to compute the continuation value of a derivative. In this chapter we generalise the backward induction to compute a future value of a derivative that corresponds to the full instrument value on future dates with effects of exercises and triggers included.
This method allows the efficient simulation of exposures (distributions of future values) in the contexts of
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- various valuation adjustments (XVA) due to counterparty risk, funding, capital, etc,
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- calculation of risk measures that use averages of future values, such as value-at-risk and expected shortfall for market risk, and potential future exposure (PFE), expected positive exposure/expected negative exposure (EPE/ENE), etc, for counterparty risk,
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- scenario generation, also in the real-world measure.
We refer to the pure backward induction
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