XVA Modelling and Computation

This advanced three-day course gives attendees the tools to understand, implement and manage XVA’s.

The programme starts by describing pricing under CSA and multicurve; followed by building a modelling framework for implementing an efficient XVA platform. It covers CVA/DVA, Funding and Capital adjustments - from modelling and regulatory aspects to accounting choices, through to market best-practice and cutting-edge issues - with both detailed break-down and global aggregation.

Sections are devoted to Initial Margin, Collateral Currency options and other adjustments and mitigations. It concludes by describing hedging under both a strategic and an implementation point of view.

• Quants/ Financial Engineers
• Traders, Risk Managers
• Structurers
• Sales People
• Strategists, Researchers

The course is also suitable for Regulators and Academics who want to get real knowledge of market practice and modelling issues in the field of XVAs.

• The foundations of derivatives pricing
• Basic statistics and numerical methods (Monte Carlo)
• A basic understanding of Counterparty Risk and xVA's (covered in The XVA Challenge programme)

Modelling and Implementation for XVA's

• The way XVA’s are restructuring banks
• The nature of XVA’s. Netting-sets, entity specific computations, non-market parameters and hybrid hedging
• Choosing the modelling framework

The base CSA Price

• The value of collateral and OIS discounting
• The mathematics of collateral
• Negative rates and Multicurve in an XVA framework

Modelling framework for XVA

• Credit Reduced-Form Models with default intensity from flat to time dependent to stochastic. The possible addition of Jumps
• Hybrid modelling for Rates, FX,  Commodities, Equity and inflation modelling
• Wrong Way Risk and Correlated Counterparties: Multi-factor Models, PCA, Copulas, Joint Jumps
• Structural Models for Ratings and Spread
• Model Risk and Model Validation issues. Level 1, 2 and 3

Implementing CVA

• The mathematics of CVA (and DVA)
• Master Formula

Practical Examples

• Rates and Cross-currency CVA with analytics and via simulation
• Equity CVA with intensity and with structural models
• FX, Commodity and Wrong Way Risk  

Computational efficiency

• Default simulation vs exposure computation
• Full repricing vs American Monte Carlo. Technical issues and how to solve them
• Working on hardware: parallel computing, grids and GPU’s

Practical Example: Simulation fox hybrid XVA's, issues and solutions

DVA, Funding, Capital with KVA, Aggregation and Accounting DVA

• The Closeout Puzzle
• DVA as Funding Benefit

Interactions between DVA and FVA FVA

• The mathematics of funding
• The basics: valuating Collateral and Funding through discounting
• The impact of NSFR
• The interactions with Credit Risk
• Formalizing the funding strategy. Funding as replication
• The FVA debate. HW point and practical and theoretical confutation
• Implementing Funding in simulation or loan-equivalent exposures
• The optimal Funding adjustment. Market Consensus and Funding nature for competitive charge

Interactions between FVA and KVA KVA: from Regulatory Exposures to Cost of Capital

• Computing Regulatory Capital Requirements
• Modelling under the Real World measure vs Risk-Adjusted Pricing
• KVA implementation:  american and joint measure simulation
• Capital against Credit risk vs charging CVA – Two insurance strategies
• Cost of Capital

Interactions between KVA and CVA

Practical Example: aggregation without double counting

XVA Organization and Accounting

• CVA and DVA in IFRS 13. Prudent Valuation, AVAs and the choice between Fair Value and Capital. Perspectives for KVA
• FVA accounting. The approach of Albanese and Andersen. The approach of Hull and White. Variations and Examples
• EVA and other KPI. Measuring the profitability of the Derivatives Business

Practical Example: Organization, Transfer Pricing, Practical XVA Desk Interaction

Sensitivities and Hedging, Initial Margin and Collateral Options

Initial Margin Value Adjustment

• CCPs, ISDA SIMM and Bilateral Initial Margin
• Full revaluation vs Delta-gamma approximations
• Path-wise Montecarlo for the IM component of FVA
• Detecting the impact of IM in prices

Practical Example: Efficient Implementation

Other mitigations of XVA risk

• Netting and Set-off agreements
• Break-up Clauses
• Possible future: Tranching CVA and Margin Lending
• Possible future: Distributed Ledgers for efficient settlement, collateral closeout

Collateral Options

• CCS pricing and the cross-currency basis
• The mathematics of collateral currency
• The value of switching collateral currency
• The value of bond vs cash collateral

Hedging Strategies

• CVA Hedging in reality
• Different rehedging frequencies and protection of exposures
• Making use of correlations for effective hedging
• Hedging or transferring DVA

Efficient Sensitivities

• Making greeks efficient: pathwise and adjoint differentiation
• Adjoint sensitivities with credit simulation and with exposures
• Adjoint sensitivities with bootstrap and calibration

Practical Example: Hedging and Adjoint Geometry