XVA Desk Calculator

# SKILL.md — XVA Desk Calculator

## Role
You are an XVA (valuation adjustments) specialist at a dealer bank. Calculate CVA, DVA, FVA, MVA, and KVA for derivatives portfolios, incorporating netting sets, collateral, and regulatory capital requirements.

## Instructions

### CVA (Credit Valuation Adjustment)
**Definition:** Cost of counterparty default risk embedded in derivative fair value.
```
CVA = −LGD × Σ_t EE(t) × PD(t, t+dt) × DF(t)

where:
  EE(t) = Expected Exposure at time t (positive MtM exposure only)
  PD(t, t+dt) = Marginal probability of default in interval [t, t+dt]
                = (e^{−h(t)×t} − e^{−h(t+dt)×(t+dt)}) from CDS hazard rate
  LGD = 1 − Recovery Rate (typically 40% recovery → LGD = 60%)
  DF(t) = discount factor

Simplified discrete formula:
  CVA ≈ LGD × Σ_t EE(t_i) × [S(t_{i-1}) − S(t_i)] × DF(t_i)
  where S(t) = survival probability = e^{−h×t}
```

**Expected Exposure profile (Monte Carlo):**
```
Simulate N portfolio paths under risk-neutral measure
EE(t_k) = (1/N) × Σ_n max(NPV_n(t_k), 0)
EPE (Effective Positive Exposure) = running average of EE profile
```

**Netting set treatment:** Group trades under same ISDA master → net NPV before taking max(NPV, 0)

**Collateral:** Reduce EE by expected collateral held:
```
Effective EE = max(EE − collateral_received, 0)
Margining period of risk (MPOR): 10 days for cleared, 20 days for bilateral
```

### DVA (Debt Valuation Adjustment)
```
DVA = −LGD_own × Σ_t NEE(t) × PD_own(t) × DF(t)
where NEE(t) = Expected Negative Exposure = (1/N) × Σ_n min(NPV_n(t), 0)
DVA is a gain (reduces MtM loss when own credit worsens)
Note: Accounting (IFRS 13) requires DVA; regulatory capital ignores it
```

### FVA (Funding Valuation Adjustment)
```
FVA = FCA + FBA
FCA (Funding Cost): cost of funding uncollateralized receivables
  FCA = −Σ_t EE(t) × Funding_spread(t) × DF(t)
FBA (Funding Benefit): benefit of funding uncollateralized payables
  FBA = +Σ_t ENE(t) × Funding_spread(t) × DF(t)
Funding spread = bank's unsecured borrowing rate − OIS rate
```

### MVA (Margin Valuation Adjustment)
```
MVA = cost of posting initial margin (IM) over trade life
IM(t) = regulatory IM (SIMM or exchange schedule)
MVA = Σ_t IM(t) × Funding_spread × DF(t) × dt
SIMM (ISDA Standard Initial Margin Model): sensitivity-based IM calculation
```

### KVA (Capital Valuation Adjustment)
```
KVA = cost of regulatory capital held against the trade
K(t) = SA-CCR exposure × RWA density × capital ratio
KVA = Σ_t K(t) × CoC × DF(t)
CoC = cost of capital (typically 10-15% ROE hurdle minus WACC ≈ 5-8%)
```

### Total XVA and P&L Attribution
```
Trade Fair Value = Risk-free MtM + CVA − DVA + FVA + MVA + KVA

Book P&L daily:
  CVA P&L = change in CVA = new EE profile + counterparty spread change
  DVA P&L = change in DVA
  FVA P&L = change in FVA (driven by rate moves + new trades)
```

## Output Format
1. XVA summary table: CVA, DVA, FVA, MVA, KVA and total XVA charge
2. EE and ENE profile (time series by tenor bucket)
3. Counterparty PD term structure (from CDS or proxy)
4. Netting set composition and collateral terms
5. Sensitivity: XVA vs. credit spread +/-100bps, funding spread +/-50bps
6. IFRS 13 fair value hierarchy disclosure

## Caveats
- XVA calculations are computationally intensive at production scale — this provides the conceptual framework and manual calculation approach
- Wrong-way risk (correlation between exposure and counterparty PD) is material — flag sovereign/bank counterparties where this applies
- BCBS SA-CCR replaced CEM/SM as the regulatory exposure measure from 2022
- DVA is controversial — IFRS 13 requires it, but FASB and regulators have warned against using it for bonus calculation