What is TVA (Total Valuation Adjustment), and how does a dealer aggregate all XVA components into a single pricing framework?

TVA (Total Valuation Adjustment) represents the aggregate impact of all valuation adjustments applied to a derivative's risk-free price. While conceptually it is the sum of individual XVAs, practical aggregation requires careful treatment of overlaps, netting effects, and allocation methodologies.\n\nTVA Framework:\n\nTVA = CVA - DVA + FVA + MVA + KVA + ColVA\n\nWhere ColVA (Collateral Valuation Adjustment) captures optionality in collateral posting (currency choice, securities vs. cash).\n\nAll-In Price = Risk-Free Mid-Market Price - TVA\n\nSign Conventions:\n- CVA > 0: cost (counterparty might default)\n- DVA > 0: benefit (you might default -- controversial)\n- FVA: cost if uncollateralized (funding), benefit if you receive excess collateral\n- MVA > 0: cost (funding initial margin)\n- KVA > 0: cost (capital consumption)\n- ColVA: can be positive or negative\n\nWorked Example -- Full XVA Pricing:\n\nSilverleaf Capital prices a new $400M 10-year cross-currency swap with Kensington Corp (BBB+, no CSA):\n\n| XVA Component | Amount | Calculation Basis |\n|---|---|---|\n| Risk-free mid-market | +$1,250,000 | Standard swap valuation |\n| CVA | -$485,000 | Kensington default risk |\n| DVA | +$62,000 | Silverleaf default risk |\n| FVA | -$720,000 | 10Y uncollateralized funding |\n| MVA | -$0 | No IM (no CSA) |\n| KVA | -$1,180,000 | SA-CCR + CVA capital |\n| ColVA | +$35,000 | Collateral optionality |\n| TVA | -$2,288,000 | |\n| All-In Price | -$1,038,000 | Mid-market minus TVA |\n\nThe trade that appeared profitable at $1.25M mid-market becomes a $1.04M loss after XVA adjustments. Silverleaf must charge at least $2.29M in spread to break even.\n\nAggregation Challenges:\n\n1. Path dependency: CVA and FVA are computed on different exposure measures (positive exposure for CVA, funding exposure for FVA). They cannot be simply summed from independent simulations.\n\n2. Correlation effects: Joint default of the counterparty and rate movements creates wrong-way risk that affects CVA but not FVA or MVA independently.\n\n3. Incremental vs. standalone: Each XVA should ideally be computed incrementally against the existing portfolio, but this requires full portfolio re-simulation for every new trade.\n\n4. Allocation across trades: TVA is a portfolio-level number. Allocating it to individual trades for pricing requires Euler allocation or Shapley value methods.\n\nMost dealers run a unified Monte Carlo simulation engine that computes all XVA components simultaneously, sharing the same scenario paths to capture correlation effects correctly.\n\nDeepen your understanding of TVA in our FRM Part II course.