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Name and account for the costs attached to an OTC derivative.

FRM® Part II · Credit Risk Measurement and Management · Counterparty Risk and Beyond · FRM2.CR.15.g

The idea

An OTC derivative carries costs beyond its risk-free value, and a dealer builds them into the price. The counterparty credit cost is CVA, the expected loss from the client's default. The funding cost, FVA, arises because an uncollateralised client trade is hedged with collateralised market trades that require cash to be posted. The capital cost, KVA, is the return required on regulatory capital held for the position over its life. The margin cost, MVA, is the cost of funding initial margin posted on margined or cleared trades. A price also reflects ordinary hedging and transaction costs. Each charge is estimated over the life of the trade, so the dealer quotes the following. Price = risk-free value + CVA + FVA + KVA + MVA. Exam point: these charges are expected values over the whole life, not one-year amounts, and each has its own driver.

Formulas

Dealer's price for an OTC derivative

Dealer price = RFV + CVA + FVA + KVA + MVA

RFV
the risk-free value
CVA
the credit charge for the client's default
FVA
the funding charge
KVA
the capital charge
MVA
the cost of funding initial margin

Each charge is an expected value over the whole life of the trade, not a one-year amount.

Capital valuation adjustment, undiscounted

KVA = EAD × RW × 0.08 × k × T

EAD
the exposure at default
RW
the regulatory risk weight
k
the hurdle rate on capital a year
T
the life of the trade in years

Ignores discounting and the interest earned on capital. Leaving out the risk weight overstates it.

Margin valuation adjustment, undiscounted

MVA = IM × s × T

IM
the average initial margin posted
s
the funding spread over the rate earned on the margin, a year
T
the life of the trade in years

A financing cost that arises whether or not anyone defaults. Use the spread over the rate earned on the margin, not the full funding rate.

A practice question

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

Which cost of an OTC derivative reflects the return the dealer must earn on the regulatory capital held against the position?

  1. Capital value adjustment (KVA) - correct
  2. Credit value adjustment (CVA)Why not: CVA is the expected default loss, not the cost of holding capital.
  3. Funding value adjustment (FVA)Why not: FVA covers the cost of funding collateral and uncollateralised positions, not capital.
  4. Margin value adjustment (MVA)Why not: MVA is the cost of funding initial margin, which is not the same as holding regulatory capital.

KVA is the present value of the cost of capital over the trade's life: capital held times the hurdle rate. It is separate from credit, funding and margin costs.

A harder one

A dealer's risk-free value for a derivative it sells to a client is USD 2.00 million. It adds a credit charge of USD 0.45 million, a funding charge of USD 0.30 million, a capital charge of USD 0.25 million and a margin charge of USD 0.10 million. The price the dealer should quote is:

  1. USD 2.45 millionWhy not: Adds only the credit charge and omits the funding, capital and margin charges.
  2. USD 0.90 millionWhy not: Subtracts all the charges from the risk-free value, treating them as discounts rather than costs.
  3. USD 2.85 millionWhy not: Omits the capital charge (KVA) from the total.
  4. USD 3.10 million - correct

Dealer price = risk-free value + CVA + FVA + KVA + MVA = 2.00 + 0.45 + 0.30 + 0.25 + 0.10 = 3.10. Each charge is a cost the dealer must recover from the client.

The hardest tier

A dealer holds an OTC derivative with a constant exposure at default of USD 40 million and a regulatory risk weight of 50% over a four-year life. Regulatory capital is 8% of risk-weighted assets, and the dealer's cost of capital (hurdle rate) is 12% a year. Ignoring discounting and the interest earned on capital, the capital valuation adjustment is closest to:

  1. USD 1.54 millionWhy not: Omits the 50% risk weight and applies the capital ratio to the full exposure.
  2. USD 0.77 million - correct
  3. USD 0.19 millionWhy not: Counts only one year of the capital charge instead of the full four-year life.
  4. USD 1.60 millionWhy not: Reports the capital held (40 x 50% x 8%) itself, ignoring both the hurdle rate and the four-year life.

Capital held = 40 x 50% x 8% = 1.6. Annual charge = 1.6 x 12% = 0.192. Over four years: 0.768, so about 0.77. Forgetting the risk weight doubles it.

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