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XVA Analytics Library

XVA Analytics Library contains the Utilities to generate various Valuation Adjustments (Collateral VA/CVA/DVA/FBA/FCA/FVA/MVA/XVA).

Documentation

Document Link
Technical Specification Latest Previous
User Guide
API Javadoc

Component Projects

  • XVA => Valuation Adjustments that account for Collateral, CC Credit/Debt and Funding Overhead.

Coverage

  • Collateral Agreements and Derivative Valuation
    • Background
    • Introduction and Motivation
    • Two Collateralized Assets
    • Setup of the Collateral Curve Dynamics
    • Collateralized Black-Scholes Formulation
    • Collateralization and Funding Derivative Valuation
    • Collateral PDE Formulation
    • Forward Contract Valuation
    • European Style Options
    • Cross-Currency Model
    • Collateral Choice Model
    • References
  • Cross Asset Random Number Generator
    • Introduction
    • Centralized Random Number Generator
    • Data Structures
    • Factor Model for Correlation Handling
    • Variance Reduction
    • Implementation - The Scope of the Risk Factors
    • Implementation - The Correlation Matrix
    • Testing
    • Random Number Generators
    • Multi-Stream RNG's
  • Core CVA/DVA Model
    • Abstract and Synopsys
    • Introduction
    • General Framework for CVA/DVA Pricing
    • Recovery Rate Map
    • CVA/DVA Model for Interest Rate Products
    • CVA/DVA Valuation of a Single Swap
    • Approximate Computation of the Convexity Based Adjustment for Contracts based on Averaging Index
    • Hull White Model Calibration
    • CVA/DVA of Portfolio of Swaps, Caps, Floors, and Swaptions
    • Risk Participation Swap (RPS) Valuation
    • CVA for Swaps with Prepay Risk
    • Negative Rates Distribution
    • Portfolio Specific Calibration of CVA/DVA for Interest Rates Products
    • Portfolio Construction for the Calibration
    • Portfolio NPV and NPV Option Valuation
    • Bootstrapping the Volatility Term Structure
    • Margin Period of Risk for CVA/DVA
    • Exposure Interpolation
    • CVA/DVA of MUNI FPA Product
    • CVA/DVA Model for Portfolio of Cross-Currency Swaps
    • Cross-Currency Swaps with MTM Legs for Notional Rates
    • FX Delta and Gamma Calculation and PnL
    • Negative Rate Distribution in XCCY swap CVA Model
    • CVA/DVA of Credit Products
    • An Approximate Method to combine Credit Exposure Profiles with a given Correlation
    • References
  • Cross Asset CVA Modeling, Testing, and Validation
    • Executive Summary of the Framework
    • Features of the LOB CVA Models
    • Cross Asset CVA Model Features
    • Overview
    • Overview of the Mathematical Definitions – CVA
    • Overview of the Mathematical Definitions – DVA
    • Collateral
    • Summary of Model Inputs
    • Summary of Model Outputs
    • Centralized Random Number Generator
    • Factor Model for Correlation Handling
    • Market Generation and Monte Carlo Simulation
    • General Scope of the Simulation
    • Correlations in Monte Carlo Simulations
    • Credit Risk Factors Simulation
    • FX Risk Factors Simulation
    • Equity Risk Factors Simulation
    • Commodity Risk Factors Simulation
    • IR Risk Factors Simulation
    • Simplified Stochastic Volatility Model
    • Interpolation in Monte Carlo Simulation
    • Trade Valuation
    • Sparse Grid or Sub-Sampling
    • Replication Model with Risks or Scenario Values
    • Proxy Pricer
    • Basel Notional Conversion Factor Based Proxy Pricer
    • NPV Based Proxy Pricer
    • Testing, Monitoring, Conservative Measures, and Materiality Analysis
    • Exposure Valuation and Aggregation
    • Exposure Interpolation
    • Conservative Measures
    • Portfolio Level Conservative Measure for Cross-Asset or Cross-System Portfolios
    • Monitoring and Materiality Analysis
    • CVA/DVA Valuation
    • Overview of Wrong-Way and Right-Way Risks
    • Specific Wrong-Way and Right-Way Risks
    • General Wrong-Way and Right-Way Risks
    • Extreme Wrong-Way Risks
    • Methodology Survey of WWR and RWR Models
    • Identification and Monitoring of WWR and RWR CPs
    • Mathematical Modeling of Wrong-Way and Right-Way Risks
    • A Simple WWR/RWR Model Based on the Convexity Adjustment to the CP Portfolio Value
    • A Simple WWR/RWR Model with Approximated CP Probability Distribution
    • A Simple CVA Model with Approximated CP Collateral under Stress Scenarios
    • A Simple Specific WWR and RWR Model with Approximated Exposures upon CP Default
    • Default and Market Risk Metrics
    • Martingale Resampling and Testing
    • At the Underlying Trade Level
    • Known Limitations of the CVA Models
    • Materiality Criteria
    • CVA-PV-Underlying-PV Test
    • One Cash Flow Test
    • Swap-Forward-Swap Test
    • Swap Swaption Test
    • Swap Forward Swaption Test
    • Cash Flow Martingale Target
    • Vega Based Error Analysis
    • At the State Variable Level
    • Portfolio Based Testing
    • Materiality Analysis of Unmodeled or Failed Trades
    • Materiality Analysis Based on P&L
    • CVA/DVA Testing
    • Stress/CCAR Testing
    • Back Testing
    • Quantile Based Exposure Testing
    • Simplified Back Testing
    • References
  • Exposure Aggregation and XVA Calculation in Cross-Asset Model
    • Introduction
    • Netting and Aggregation
    • Aggregation for Trades Priced in Proxy Models
    • Three Points Brownian Bridge Interpolation
    • XVA Calculation
  • Prudent Adjustments
    • Abstract
    • Fair Valuations
    • Wealth Transfers and Prudent Valuation
    • Loss in Translation
    • References
  • CVA And Funding Adjustments PDE
    • Counterparty Risk and Funding Costs
    • Motivation, Literature Scan, and Approach
    • Notation, Symbology, and Key PDEs
    • Model Setup and the Derivation of the Bilateral Risky PDE
    • Using $\hat{V}$ (T, s) As Mark-to-Market at Default
    • Using V (T, S) As Mark-to-Market at Default
    • Funding and Default Payoff Examples
    • Counterparty Funding and PDE Extensions
    • Balance Sheet and Funding Cost Management
    • Unified Framework for Bilateral Counterparty Risk and Funding Adjustments
    • Simple Model for the Impact of Derivative Asset on Balance Sheet and Funding
    • Balance Sheet Management to Mitigate Funding Costs
    • Funding Strategies and Costs Impact
    • Generalized Semi-Replication and Pricing PDE
    • Semi-Replication
    • Examples of Different Bond Portfolios
    • Perfect Replication – The FCA Vanishes
    • Semi-Replication with No Shortfall at Own-Default
    • Set-offs
    • Semi-Replication with a Single Bond
    • Burgard and Kjaer (2013) Case Study
    • References
  • Accounting for OTC Derivatives: Funding Adjustments and Rehypothecation Option
    • Status of Current FCA/FBA Accounting
    • Comparison Between FCA/FBA and FDA/FVA
    • References
  • Funding and Re-Hypothecation Adjustment - Motivation
    • OTC vs. Repo Markets
    • Modus Operandi of Funding Desks
    • MMT And Asset-Liability Symmetry
    • Rigorous Framework For Funding Costs
    • Funding Set VM RHO Computation
    • Shortcomings of Traditional CVA Systems
    • Addressing the Shortcomings of FCA/FBA Accounting
    • References
  • Albanese and Andersen (2014) Results Summary
    • Valuation Adjustment Estimation Framework Setup
    • OTC Books Funding Set Decomposition
    • Inconsistent Booking Under the FCA/FBA
    • Improvements Offered by the FVA/FDA Accounting
    • References
  • CET1 Capital Deductions in Basel III and Capital Structure Considerations
    • CET1 Deductions
    • “Going Concern” or Defaultable Banks?
    • Categorization of Cash-flow Streams
    • References
  • Accounting Principles, Units of Accounts, and Valuation Adjustment Metrics
    • Accounting Rules
    • Contra-Asset and Contra-Liability Accounting for Credit Risk
    • Contra-Asset and Contra-Liability Accounting for Funding
    • References
  • Accounting Cash Flows
    • Accounting Cash Flow Setup Framework
    • Cash Flows Related to VM Funding
    • Cash Flows at Counterparty Default
    • Cash Flows at Bank Default
    • References
  • Credit and Funding Valuation Adjustments
    • Introduction
    • CVA and DVA
    • FVA and FDA
    • FCA and FBA
    • CA and CL Adjustments
    • Own Credit Sensitivities
    • References
  • Triggers and Close-out Adjustments
    • Introduction
    • Collateral Triggers and Close-outs
    • Incorporating ISDA 1992 Close-outs
    • VM Rehypothecability Across Funding Sets
    • References
  • Entry Prices, Exit Prices, and Trade FTP
    • Trade and Portfolio FTP Estimation
    • FTP For FCA/FBA Accounting
    • FTP For FVA/FDA Accounting
    • Exit Prices and Fair Valuation
    • FVA/FDA Accounting
    • FCA/FBA Accounting
    • References
  • Liquidity Spreads, Asset Liability Symmetry, and Alternative Allocations for Excess Collateral
    • Motivation
    • Working Capital Management and Operations
    • Equity Gain and Debt Gain
    • Liquidity Based Analysis and Treatment
    • Problems with the Gain Accounting
    • References
  • Albanese and Andersen (2014) Case Study
    • Case Study Setting and Purpose
    • Scenario Estimation of the XVA Metrics
    • Product and Scenario Threshold Type Scenarios
    • XVA Metric Errors and Incrementals
    • Estimation of the FCA/FBA – FVA/FDA Mismatch
    • References
  • Conclusions with Funding Adjustments with RHO
    • Traditional Challenges with Derivative Accounting
    • Problems with FCA/FBA Accounting
    • FVA/FDA as FCA/FBA Enhancement
    • Trading Staff Point of View
    • Challenges with the XVA Metric Estimation
    • Shortfalls of the FVA/FDA Scheme
    • Alternate Specialized Value Adjustment Metrics
    • References
  • The FVA Puzzle: Accounting, Risk Management, and Collateral Trading
    • Abstract
    • Introduction
    • CVA/DVA Accounting
    • The FBA/FCA Method
    • FVA/FDA Accounting
    • Funds Transfer Pricing
    • FCA/FBA Accounting
    • FVA/FDA Accounting
    • Notes on Exit Pricing and Asset-Liability Symmetry
    • Extensions
    • Balance Sheet Simulations and Reverse-Stress Testing
    • Strategies for Exploiting Funding Arbitrage
    • References
  • Derivatives Funding, Netting, and Accounting
    • Introduction, Motivation, Scope, and Synopsis
    • Model Setup and Asset Dynamics
    • Balance Sheet Dynamics under Semi-Replication
    • Economic Values
    • Derivation of the Coupled Solutions
    • Fair Values
    • Funding Strategies
    • Derivation of $\hat{V}$IV
    • Proof of the Statement FCAIV < FCAIII < FCAI
    • Discussion
    • References

DROP Specifications