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XVA Modelling and Computation

Day One

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

Day Two

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

Day Three

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

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