Modelling, Pricing, and Hedging Counterparty Credit Exposure

A Technical Guide

By: Giovanni Cesari, Zlatko Filipovic, Niels Charpillon, John Aquilina, Ion Manda

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Hardcover | 12 January 2010

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It was the end of 2005 when our employer, a major European Investment Bank, gave our team the mandate to compute in an accurate way the counterparty credit exposure arising from exotic derivatives traded by the ?rm. As often happens, - posure of products such as, for example, exotic interest-rate, or credit derivatives were modelled under conservative assumptions and credit of?cers were struggling to assess the real risk. We started with a few models written on spreadsheets, t- lored to very speci?c instruments, and soon it became clear that a more systematic approach was needed. So we wrote some tools that could be used for some classes of relatively simple products. A couple of years later we are now in the process of building a system that will be used to trade and hedge counterparty credit ex- sure in an accurate way, for all types of derivative products in all asset classes. We had to overcome problems ranging from modelling in a consistent manner different products booked in different systems and building the appropriate architecture that would allow the computation and pricing of credit exposure for all types of pr- ucts, to ?nding the appropriate management structure across Business, Risk, and IT divisions of the ?rm. In this book we describe some of our experience in modelling counterparty credit exposure, computing credit valuation adjustments, determining appropriate hedges, and building a reliable system.

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Non-Fiction Accounting & Finance Finance Investment & Securities Mathematics Calculus & Mathematical Analysis Numerical Analysis Probability & Statistics Economics Econometrics Economic Statistics Business & Management

Management & Management Techniques Applied Mathematics Stochastics

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Paperback

Published: 1st March 2012

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Methodology
Introduction	p. 3
Basic Concepts	p. 3
Preliminary Examples	p. 4
Vanilla Interest-Rate Swap	p. 4
Cancellable Swap	p. 5
Managing Credit Risk—Collateral, Credit Default Swap	p. 8
Why Compute Counterparty Credit Exposure?	p. 10
Modelling Counterparty Credit Exposure	p. 10
Definition	p. 10
Risk Measures	p. 12
Netting and Aggregation	p. 12
Close-Out Risk	p. 13
Right-Way/Wrong-Way Exposure	p. 14
Credit Valuation Adjustment: CVA	p. 14
A Simple Credit Quantification Example	p. 15
Computing Credit Exposure by Simulation	p. 17
Implementation Challenges	p. 18
An Alternative Approach: The AMC Algorithm	p. 19
Which Architecture?	p. 20
What Next?	p. 21
Modelling Framework	p. 23
Counterparty Credit Exposure Definition	p. 23
Process Dynamics	p. 26
Interest Rate: Single Currency	p. 27
Simple Specifications	p. 29
HJM Framework	p. 31
Libor Market Models	p. 32
Multiple Currencies and Foreign Exchange	p. 33
Inflation	p. 37
Equity	p. 37
Credit	p. 38
Default Probabilities from par CDS Spreads	p. 39
Stochastic Default Probabilities	p. 41
Loss Simulation	p. 42
Simulation Models	p. 45
Interest-Rate Models	p. 45
Separable Volatility	p. 46
Example: Hull-White (Extended Vasicek)	p. 50
Equity and FX Models	p. 52
Black Model	p. 53
Local Volatility	p. 54
Stochastic Volatility	p. 58
Jump Models	p. 60
Extension to Stochastic Interest Rates	p. 60
A Simpler Approach: Independent Interest Rates	p. 63
Different Models for Different Markets	p. 63
Credit Models	p. 65
Simulation of Single-Name Default Probabilities and Default Times	p. 66
Inter-Name Default Dependence	p. 69
Technical Note: Recursion	p. 72
Properties of the Loss Distribution: Large Homogeneous Portfolio	p. 73
Calibration of Correlation	p. 75
Choice of Model	p. 75
Valuation and Sensitivities	p. 79
American Monte Carlo: Mathematical Notation and Description	p. 80
Mathematical Formulation	p. 80
Practical Examples	p. 83
Backward Induction Algorithm	p. 85
AMC Estimation Algorithms	p. 88
Tilley's Algorithm	p. 88
Longstaff-Schwartz Regression	p. 89
Biases of Estimates	p. 90
An AMC Algorithm to Compute Credit Exposure	p. 91
Post-Processing of the Price Distribution	p. 93
Practical Examples Revisited	p. 93
Computing Price Sensitivities	p. 94
The Classical Approach	p. 95
Price Sensitivities through Regression	p. 95
Removing Correlation	p. 96
Extensions	p. 98
Architecture and Implementation
Computational Framework	p. 101
AMC Implementation and Trade Representation	p. 101
Examples	p. 102
Expression Trees	p. 103
A Portfolio Aggregation Language	p. 103
PAL Examples	p. 105
The Concept of Scenarios	p. 108
The Concept of Super-Product	p. 108
An Example of Super-Products: The C-CDS	p. 109
Implementation	p. 111
Spot and Forward Statistics	p. 111
Libor Rates and Bond Prices	p. 112
Annuity	p. 113
Swap Rate	p. 113
Path Dependent Statistics	p. 114
Extremum	p. 114
Average	p. 115
In Range Fraction	p. 116
Credit Loss	p. 116
Monte Carlo Stepping	p. 117
Technical Notes	p. 120
SDE Integration Schemes	p. 120
Milstein 2 Scheme	p. 121
Martingale Interpolation	p. 122
Distribution of Maxima and Minima	p. 123
Error Analysis	p. 125
Choice of Model: Scenario and Exposure Analysis	p. 125
AMC Error	p. 129
Numerical Errors	p. 130
Approximations: Arbitrage Conditions	p. 131
Architecture	p. 135
Requirements	p. 136
Functional, Non-Functional Requirements, and Design Principles	p. 136
Conceptual View: Methodology	p. 137
Logical View	p. 139
Portfolio Manager Components	p. 139
State of the World Components	p. 141
Quantification Components	p. 141
Physical View	p. 142
Alternative Approaches	p. 144
Products
Interest-Rate Products	p. 149
Interest-Rate Swaps	p. 149
Swaps in Advance and in Arrears	p. 150
Capped and Floored Swaps	p. 152
Cancellable Swaps	p. 152
Cross-Currency Swaps	p. 153
Constant-Maturity Swaps and Steepeners	p. 154
Range Accruals	p. 155
Interest-Rate Options	p. 156
Equity, Commodity, Inflation and FX Products	p. 159
Forwards and Options	p. 159
Forwards Contracts	p. 160
Vanilla and Digital Options	p. 162
Bermudan and American Options	p. 162
Asian Options	p. 164
Barrier Options	p. 164
Asset Swaps	p. 166
Absolute Return Swaps	p. 166
Relative Return Swaps	p. 167
Cliquets	p. 168
Target Redemption Swaps	p. 169
Credit Derivatives	p. 171
Credit Default Swaps	p. 171
Collateral Debt Obligations	p. 172
Structures	p. 175
Sinking Funds	p. 175
Accelerated Share Re-Purchase	p. 176
Callable Daily Accrual Notes	p. 178
Call Spread Overlays	p. 179
Hedging and Managing Counterparty Risk
Counterparty Risk Aggregation and Risk Mitigation	p. 183
Risk Measures	p. 184
Choice of Measure	p. 186
Portfolio Risk Aggregation	p. 187
Reference Currency	p. 188
Netting and No-Netting Agreements	p. 188
Break Clauses	p. 189
Collateral Agreements	p. 190
Counterparty Exposure of Collateralised Counterparties	p. 191
Examples	p. 192
Close-Out Risk	p. 194
Risk Allocation	p. 195
Naive Allocation	p. 196
Euler Allocation	p. 196
Comparison with Naive Allocation	p. 197
Contribution Calculation of Collateralised Transactions	p. 199
Combining Market and Credit Risk	p. 201
Change of Measure: Practical Implementation	p. 202
Exposure under Real-World Measure	p. 203
Stress Testing	p. 204
Right-Way/Wrong-Way Exposure	p. 205
Right-Way/Wrong-Way Exposure: Merton Approach	p. 206
The Inverse Problem	p. 209
Example 1: Call Option on Stock	p. 210
Example 2: Call Put Structure on Oil	p. 212
Example 3: Cross-Currency Swap on USD-GBP	p. 212
Comparison with the Change of Measure Approach	p. 212
Pricing Counterparty Credit Risk	p. 215
Credit Valuation Adjustment and Static Hedging	p. 216
Contingent Credit Default Swap	p. 217
American Monte Carlo Valuation	p. 218
Example	p. 218
Dynamic Hedging of Counterparty Risk	p. 219
Optimal Static Hedging	p. 220
CVA Sensitivities	p. 221
Collateral Agreements	p. 223
Right-Way/Wrong-Way Risk	p. 224
Examples	p. 224
C-CDS on a Vanilla Interest-Rate Swap	p. 224
Impact of Discretization Schedule	p. 225
Collateralised Equity Swap	p. 226
Case Study	p. 226
Concluding Remarks	p. 231
Approximations	p. 233
Maximum Likely Exposure	p. 233
MLE of Equity and FX Products	p. 233
MLE of Swaps	p. 234
Expected Positive Exposure	p. 235
EPE and CVA of Equity Options	p. 235
Relation between MLE, EPE	p. 235
CVA of Swaps	p. 236
Results from Stochastic Calculus and Finance	p. 239
Brownian Motion and Martingales	p. 239
Replication of Contingent Claims: Martingale Representation	p. 241
Change of Numeraire	p. 243
References	p. 245
Index	p. 249
Table of Contents provided by Ingram. All Rights Reserved.

Modelling, Pricing, and Hedging Counterparty Credit Exposure

A Technical Guide

At a Glance

Hardcover

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Defective items

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