Landmarks in XVA
First published:
ISBN: 9781782722939
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Smoking Adjoints: Fast Evaluation of Monte Carlo Greeks
Michael Giles and Paul Glasserman
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 efficient calculation of price sensitivities continues to be one of the greatest practical challenges facing users of Monte Carlo methods in the derivatives industry. Computing Greeks is essential to hedging and risk management, but typically requires substantially more computing time than pricing a derivative. This chapter shows how an adjoint formulation can be used to accelerate the calculation of the Greeks. This method is particularly well suited to applications requiring sensitivities to a large number of parameters. Examples include interest rate derivatives requiring sensitivities to all initial forward rates and equity derivatives requiring sensitivities to all points on a volatility surface.
The simplest methods for estimating Greeks are based on finite-difference approximations, in which a Monte Carlo pricing routine is rerun multiple times with different settings of the input parameters in order to estimate sensitivities to the parameters. In the fixed-income setting, for example, this would mean perturbing each initial forward rate and then rerunning the Monte Carlo simulation to reprice a security or a whole book. The main virtues of this method are that it is
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