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目录
Part I Methodology
1 Introduction ................................ 3
1.1 Basic Concepts ............................ 3
1.2 PreliminaryExamples........................ 4
1.2.1 Vanilla Interest-Rate Swap ................. 4
1.2.2 Cancellable Swap . . . ................... 5
1.2.3 Managing Credit Risk—Collateral, Credit Default Swap . . 8
1.3 Why Compute Counterparty Credit Exposure? . . ......... 10
1.4 Modelling Counterparty Credit Exposure .............. 10
1.4.1 Definition .......................... 10
1.4.2 RiskMeasures........................ 12
1.4.3 Netting and Aggregation ................... 12
1.4.4 Close-OutRisk........................ 13
1.4.5 Right-Way/Wrong-Way Exposure .............. 14
1.4.6 CreditValuationAdjustment:CVA ............. 14
1.4.7 ASimpleCreditQuantificationExample .......... 15
1.4.8 Computing Credit Exposure by Simulation ......... 17
1.4.9 Implementation Challenges ................. 18
1.4.10 An Alternative Approach: The AMC Algorithm ...... 19
1.5 WhichArchitecture?......................... 20
1.6 WhatNext? ............................. 21
2 Modelling Framework .......................... 23
2.1 Counterparty Credit Exposure Definition .............. 23
2.2 Process Dynamics .......................... 26
2.3 InterestRate:SingleCurrency.................... 27
2.3.1 Simple Specifications . ................... 29
2.3.2 HJMFramework....................... 31
2.3.3 Libor Market Models . ................... 32
2.4 Multiple Currencies and Foreign Exchange ............. 33
2.5 Inflation ............................... 37
2.6 Equity ................................ 37
2.7 Credit ................................ 38
2.7.1 Default Probabilities from par CDS Spreads ........ 39
2.7.2 Stochastic Default Probabilities ............... 41
2.7.3 LossSimulation ....................... 42
3 Simulation Models ............................ 45
3.1 Interest-Rate Models ......................... 45
3.1.1 Separable Volatility . . ................... 46
3.1.2 Example: Hull-White (Extended Vasicek) . ......... 50
3.2 Equity and FX Models ........................ 52
3.2.1 Black Model ......................... 53
3.2.2 Local Volatility ....................... 54
3.2.3 Stochastic Volatility . . ................... 58
3.2.4 Jump Models ......................... 60
3.2.5 Extension to Stochastic Interest Rates . . . ......... 60
3.2.6 A Simpler Approach: Independent Interest Rates ...... 63
3.2.7 Different Models for Different Markets . . ......... 63
3.3 Credit Models ............................ 65
3.3.1 Simulation of Single-Name Default Probabilities and
DefaultTimes ........................ 66
3.3.2 Inter-Name Default Dependence .............. 69
3.3.3 Technical Note: Recursion .................. 72
3.3.4 Properties of the Loss Distribution: Large Homogeneous
Portfolio ........................... 73
3.3.5 CalibrationofCorrelation.................. 75
3.4 Choice of Model ........................... 75
4 Valuation and Sensitivities ........................ 79
4.1 American Monte Carlo: Mathematical Notation and Description . . 80
4.1.1 MathematicalFormulation.................. 80
4.1.2 PracticalExamples...................... 83
4.1.3 Backward Induction Algorithm ............... 85
4.2 AMCEstimationAlgorithms .................... 88
4.2.1 Tilley’s Algorithm . . . ................... 88
4.2.2 Longstaff-Schwartz Regression ............... 89
4.2.3 BiasesofEstimates ..................... 90
4.2.4 An AMC Algorithm to Compute Credit Exposure ..... 91
4.3 Post-ProcessingofthePriceDistribution .............. 93
4.4 PracticalExamplesRevisited .................... 93
4.5 Computing Price Sensitivities . ................... 94
4.5.1 The Classical Approach ................... 95
4.5.2 Price Sensitivities through Regression . . ......... 95
4.5.3 RemovingCorrelation.................... 96
4.6 Extensions .............................. 98

Part II Architecture and Implementation
5 Computational Framework .......................101
5.1 AMCImplementationandTradeRepresentation ..........101
5.1.1 Examples...........................102
5.1.2 ExpressionTrees.......................103
5.2 A Portfolio Aggregation Language .................103
5.2.1 PALExamples........................105
5.3 The Concept of Scenarios . . . ...................108
5.4 The Concept of Super-Product . ...................108
5.4.1 An Example of Super-Products: The C-CDS ........109
6 Implementation ..............................111
6.1 Spot and Forward Statistics . . ...................111
6.1.1 LiborRatesandBondPrices ................112
6.1.2 Annuity ...........................113
6.1.3 SwapRate ..........................113
6.2 Path Dependent Statistics . . . ...................114
6.2.1 Extremum ..........................114
6.2.2 Average ...........................115
6.2.3 In Range Fraction . . . ...................116
6.2.4 CreditLoss..........................116
6.3 Monte Carlo Stepping ........................117
6.4 Technical Notes ...........................120
6.4.1 SDE Integration Schemes ..................120
6.4.2 Milstein 2 Scheme . . . ...................121
6.4.3 MartingaleInterpolation...................122
6.4.4 DistributionofMaximaandMinima ............123
6.5 ErrorAnalysis ............................125
6.5.1 Choice of Model: Scenario and Exposure Analysis .....125
6.5.2 AMCError..........................129
6.5.3 NumericalErrors ......................130
6.5.4 Approximations:ArbitrageConditions ...........131
7 Architecture ................................135
7.1 Requirements ............................136
7.1.1 Functional, Non-Functional Requirements, and Design
Principles ..........................136
7.2 Conceptual View: Methodology ...................137
7.3 LogicalView.............................139
7.3.1 Portfolio Manager Components ...............139
7.3.2 State of the World Components ...............141
7.3.3 Quantification Components .................141
7.4 PhysicalView ............................142
7.5 Alternative Approaches .......................144

Part III Products
8 Interest-Rate Products ..........................149
8.1 Interest-RateSwaps .........................149
8.1.1 Swaps in Advance and in Arrears ..............150
8.1.2 Capped and Floored Swaps .................152
8.1.3 Cancellable Swaps . . . ...................152
8.1.4 Cross-CurrencySwaps....................153
8.2 Constant-Maturity Swaps and Steepeners ..............154
8.3 Range Accruals ...........................155
8.4 Interest-RateOptions ........................156
9 Equity, Commodity, Inflation and FX Products ............159
9.1 ForwardsandOptions ........................159
9.1.1 ForwardsContracts .....................160
9.1.2 Vanilla and Digital Options .................162
9.1.3 Bermudan and American Options ..............162
9.1.4 AsianOptions ........................164
9.1.5 BarrierOptions .......................164
9.2 AssetSwaps .............................166
9.2.1 AbsoluteReturnSwaps ...................166
9.2.2 RelativeReturnSwaps....................167
9.2.3 Cliquets ...........................168
9.2.4 Target Redemption Swaps ..................169
10 Credit Derivatives ............................171
10.1CreditDefaultSwaps ........................171
10.2CollateralDebtObligations .....................172
11 Structures .................................175
11.1 Sinking Funds ............................175
11.2 Accelerated Share Re-Purchase ...................176
11.3CallableDailyAccrualNotes ....................178
11.4CallSpreadOverlays ........................179
Part IV Hedging and Managing Counterparty Risk
12 Counterparty Risk Aggregation and Risk Mitigation .........183
12.1RiskMeasures............................184
12.2ChoiceofMeasure..........................186
12.3PortfolioRiskAggregation .....................187
12.3.1 Reference Currency . . ...................188
12.3.2 Netting and No-Netting Agreements . . . .........188
12.3.3BreakClauses ........................189
12.4CollateralAgreements........................190
12.4.1 Counterparty Exposure of Collateralised Counterparties . . 191
12.4.2Examples...........................192
12.5Close-OutRisk............................194
12.6RiskAllocation ...........................195
12.6.1NaiveAllocation.......................196
12.6.2EulerAllocation.......................196
12.6.3ComparisonwithNaiveAllocation .............197
12.6.4 Contribution Calculation of Collateralised Transactions . . 199
13 Combining Market and Credit Risk ..................201
13.1 Change of Measure: Practical Implementation . . .........202
13.2 Exposure under Real-World Measure ................203
13.3StressTesting ............................204
13.4 Right-Way/Wrong-Way Exposure ..................205
13.4.1 Right-Way/Wrong-Way Exposure: Merton Approach . . . 206
13.4.2TheInverseProblem.....................209
13.4.3Example1:CallOptiononStock ..............210
13.4.4Example2:CallPutStructureonOil ............212
13.4.5Example3:Cross-CurrencySwaponUSD-GBP......212
13.4.6 Comparison with the Change of Measure Approach ....212
14 Pricing Counterparty Credit Risk ....................215
14.1 Credit Valuation Adjustment and Static Hedging . .........216
14.2 Contingent Credit Default Swap ...................217
14.2.1AmericanMonteCarloValuation..............218
14.2.2Example ...........................218
14.3 Dynamic Hedging of Counterparty Risk ..............219
14.4 Optimal Static Hedging .......................220
14.5 CVA Sensitivities ..........................221
14.6CollateralAgreements........................223
14.7 Right-Way/Wrong-Way Risk . ...................224
14.8Examples...............................224
14.8.1 C-CDS on a Vanilla Interest-Rate Swap . . .........224
14.8.2 Impact of Discretization Schedule ..............225
14.8.3CollateralisedEquitySwap .................226
Concluding Remarks .............................231
A Approximations ..............................233
A.1 Maximum Likely Exposure . . ...................233
A.1.1 MLE of Equity and FX Products ..............233
A.1.2 MLEofSwaps........................234
A.2 Expected Positive Exposure . . ...................235
A.2.1 EPEandCVAofEquityOptions ..............235
A.2.2 RelationbetweenMLE,EPE ................235
A.3 CVAofSwaps............................236
B Results from Stochastic Calculus and Finance .............239
B.1 BrownianMotionandMartingales .................239
B.2 Replication of Contingent Claims: Martingale Representation . . . 241
B.3 Change of Numeraire ........................243

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