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Account for why pricing counterparty risk is wanted and what makes it hard.

FRM® Part II · Credit Risk Measurement and Management · CVA · FRM2.CR.20.a

The idea

Pricing counterparty risk matters because a derivative is not risk free. The counterparty may default when it owes the bank money, and that expected loss is a real cost that should be charged in the price, not only controlled with limits. Fair-value accounting expects the credit adjustment, and Basel III charges capital for the volatility of the adjustment. Much of the crisis loss came from the counterparty spread widening, not from defaults. Pricing is hard because exposure is stochastic, two-sided and depends on the whole netting set, so the charge is not additive across trades. It also needs a default probability for counterparties with no traded CDS. And because the exposure moves, hedging with fixed-notional CDS is imperfect. Exam point: name both the reason and the difficulty.

A practice question

From the question bank, with the reason each wrong option is wrong.

Why did dealers move from controlling counterparty credit risk only through exposure limits to also pricing it into derivative trades?

  1. Expected credit losses and their hedging cost are a real economic cost, and the mark-to-market swings in that cost caused large losses in 2007-09 without any default. - correct
  2. Pricing the risk makes netting agreements and collateral terms unnecessary, because the charge fully replaces them and removes the need for credit mitigants.Why not: Treats a price as a substitute for risk mitigants; netting and collateral remain and reduce the charge itself.
  3. Once a derivative is collateralized, it has no market risk left, so a credit charge is the only remaining risk that needs to be priced into it.Why not: Confuses collateral with the removal of market risk; collateral cuts credit exposure, it does not remove the risk of the trade.
  4. Accounting standards require a derivative to be carried at its risk-free value until the counterparty actually defaults, with no credit adjustment before that.Why not: Reverses the accounting rule: fair value is meant to reflect counterparty credit quality before any default.

Counterparty risk is a cost that exists from day one (expected loss plus the cost of hedging and capital). The crisis showed that much of the loss came from deteriorating counterparty credit quality marked to market, not only from defaults, so the cost has to be priced and managed, not just limited.

A harder one

A trader proposes pricing the credit charge for a new trade by calculating its CVA on a standalone basis and adding it to the price. The counterparty already has several trades with the bank under a single netting agreement. What is the main problem with this approach?

  1. Standalone CVA always understates the charge, because netting concentrates the exposure on the existing trades of the counterparty.Why not: Gets the sign of netting wrong; netting can only reduce or leave unchanged the exposure of a set of trades.
  2. The new trade's CVA would be computed with the bank's own default probability and loss given default, not those of the counterparty.Why not: Confuses CVA with DVA: CVA uses the counterparty default probability, so that is not the problem with standalone pricing.
  3. Netting and collateral apply to the whole set, so the new trade's charge depends on the existing portfolio and differs from its standalone CVA. - correct
  4. CVA is not defined for a single trade, only for a counterparty with at least ten trades in a documented netting agreement.Why not: Invents a minimum-trade rule; CVA can be computed for a single trade, it just is not additive across trades.

Because exposure is the positive part of the netted portfolio value, CVA is not a sum of trade-level numbers. The relevant charge is the change (or an allocation) at netting-set level.

The hardest tier

A dealer charges a client an upfront CVA and hedges it by buying single-name CDS on the client for a fixed notional equal to today's expected exposure. Six months later interest rates have moved sharply and the swap's expected exposure has doubled while the client's spread is unchanged. Which statement best describes the dealer's position?

  1. The dealer is fully hedged, since a CDS on the client covers any change in the swap's exposure automatically.Why not: Assumes a plain CDS is a contingent instrument; its notional does not follow the swap's exposure.
  2. The dealer is under-hedged and must rebalance, because the CDS notional is fixed while the exposure it protects moves with the market. - correct
  3. The hedge is unaffected because CDS notional is determined by the client's recovery rate, not the exposure.Why not: Confuses what sets the hedge size; the notional is chosen from the exposure to be protected, and recovery only scales the loss.
  4. The dealer is over-hedged, because a higher expected exposure reduces the CVA that the fixed CDS notional was sized to cover.Why not: Wrong sign: higher expected exposure raises CVA, so the original hedge notional is too small, not too large.

A plain CDS has a fixed notional, while CVA depends on a moving exposure. Hedging spread risk with CDS therefore leaves a residual market-exposure risk that needs rebalancing, one reason CVA is hard to hedge.

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