xVA Modelling & Management

Day One

XVA Basics

• What CVA, FVA, MVA and KVA are and why they are integral to derivative valuation

• Accounting and regulatory treatment

• Case Study 1 – CVA and FVA during financial crisis of 2007-09 – Lehman Brothers and AIG. How large were banks’ counterparty credit risk and CVA losses?

Counterparty Credit Risk

• Defining exposure – mark-to-market, replacement cost, variation margin, initial margin, netting sets and Credit Support Annexes (CSAs)

• Exposure measures, exposure distribution and exposure profile – expected (positive) exposure (EE or EPE) for CVA. Other exposure measures – expected future value (EFV) for FVA; expected negative exposure (ENE) for DVA; potential future exposure (PFE)

• CVA formula – EE, counterparty probability of default (PD), loss given default (LGD)  and discount factors (DF)

• Estimating PD from CDS, bonds and proxies

• Case Study 2 – Calculating CVA for a single derivative netting set, taking exposure profile as given. CVA sensitivity to counterparty CDS spread and to shocks to exposure profile. CVA hedging

• How has CVA been mitigated?

Exposure Modelling Via Monte Carlo Simulation – With & Without Collateral

• Process – Monte Carlo (MC) simulation of market risk factors to create exposure distributions and profiles for derivative positions priced off those risk factors

• Stochastic processes for interest rates, FX, equity, CDS, volatility

• Case Study 3 – MC simulation of interest rates to create exposure distributions and profile for an interest rate swap (IRS) – without collateral

• Case Study 4 – MC simulation of FX to create exposure distributions and profile for an FX forward – without collateral

• Exposure simulation at level of derivative netting set – allowing for correlation of stochastic processes where appropriate

• Case Study 5 – MC simulation of CDS, equity and equity volatility (all referencing same company) to create exposure distributions and profile for a netting set containing CDS, equity and equity put option (all referencing same company) – without collateral

• MC simulation to create exposure distributions and profiles with collateral and gap risk

• Variation margin vs initial margin

• Collateral overview – key CSA  terms, netting sets, rehypothecation vs segregation, initial margin requirements for non-centrally cleared OTC derivatives

• Central clearing counterparties (CCPs) overview

• Case Study 6 – Redoing MC simulations of Case Studies 3-5 including simulation of collateral

CVA

• Case Study 7 – Calculating CVA for each exposure profile created within Case Study 6 and exploring CVA sensitivities

• Regulatory capital requirements for counterparty credit risk (CCR) and CVA volatility – standardised approach for counterparty credit risk (SA-CCR) and Fundamental Review of the Trading Book (FRTB) vs Basel 2.5

• Case Study 8 – Use of proxies in measurement of counterparty PD and CVA. Which proxies, what adjustments and hedging implications?

• Case Study 9 – Calculating regulatory capital requirements for netting sets within Case Study 6

• Case Study 10 – Stress testing of counterparty credit risk within ICAAP or system-wide external, supervisor-led capital stress test

• Right and wrong way risk and directional way risk models

• Debit value adjustment (DVA)

• Case Study 11 – Accounting and regulatory capital sensitivity to CVA mark-to-market – tracking P&L, balance sheet and regulatory capital requirement for given trajectory of CVA mark-to-market

Day 2

FVA

• How funding costs and benefits arise from variation margin posting and receipt respectively

• Case Study 12 – What remuneration rates are typically received on variation margin posted in major currencies? What maturity of funding spread do banks use to measure FVA and which own funding cost do they use?

• FVA formula

• Separating FVA into funding cost adjustment (FCA) and funding benefit adjustment (FBA) using expected negative exposure (ENE) and expected positive exposure (EPE) respectively

• Case Study 13 – Calculating FVA for each exposure profile created within Case Study 6 and exploring FVA sensitivities

MVA

• Why MVA is always a cost

• Case Study 13 – major central clearers’ initial margin methodologies and clearing member default fund contributions; initial margin requirements for non-centrally cleared OTC derivatives

• Remuneration rates on initial margin and funding cost maturity used by banks to measure MVA

• Broader perspective on initial margin (IM) – CCP default fund contributions by clearing members; contingent IM for ratings downgrade triggers

• MVA formula

• Case Study 14 – Calculating expected IM at time points within MC simulation. Expected shortfall, VAR approaches and American MC approaches

• Differences in measuring expected IM between centrally cleared and non-centrally cleared netting sets

• Case Study 15 – Calculating MVA for each exposure profile created within Case Study 6 and exploring MVA sensitivities

• Role of FVA and MVA in bank funds transfer pricing

KVA

• In what ways are capital requirements for CCR (default) and CVA volatility sensitive to market risk factors? Basel 2.5, FRTB and SA-CCR perspectives

• Dealing with capital requirements on centrally cleared OTC derivatives

• Separation of market risk capital requirement from CCR (default) and CVA volatility capital requirements

• KVA formula

• Case Study 16 – Calculating KVA for each exposure profile created within Case Study 6 and exploring KVA sensitivities

• Which cost of capital to use and where does it come from?

XVA Desks – Managing & Hedging XVA

• How XVAs are priced and charged between XVA desk and trading desks and vis-à-vis customers

• Case Study 17 – Why XVA quotes from different dealers for the same new derivative can be materially different. Understanding incremental XVA for new derivative trades into two illustrative netting sets

• Using Totem to benchmark XVA pricing

• Hedging counterparty credit risk and CVA using single name CDS, index CDS and index CDS options

• Case Study 18 - Hedging CVA – hedging P&L for illustrative time series of CVA mark-to-market. Understanding negative gamma inherent in CVA and why index CDS options can be efficient hedges

• Case Study 19 – Optimising XVA from a customer perspective. Quantifying lower XVA costs from more perfected collateralisation vs cost of liquid assets to manage resulting increased contingent liquidity risk

• Case Study 20 – XVA desk management – tools to manage XVAs

• Computational requirements and relevant services for XVA pricing