Basics on CVA and DVA
Chapter 9
J. Hull: Options, Futures, and Other Derivatives (10th ed)
Credit risk in derivatives
 Derivatives valuation assumes that neither side of the
contract will default
 Credit risk is generally taken into account by a separate
calculation
 The default of the counterparty in a derivative contract
may cause a loss if the early termination happens when
the derivative has a positive value
 The no-default value of a derivative is adjusted to take
into account the default probability of the two parties
involved in the contract
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CVA
 Consider a derivative contract between party A and the
counterparty B with maturity Tn
 Assume that Ci, i = 1, 2, …, n, is the present value of the
expected loss to A if counterparty B defaults at time Ti
 Assume that πB is the (constant) probability of default of B
 The Credit Value Adjustment (CVA) is the estimate of the
present value of the expected cost to A of a B default
n
CVA    B  Ci
i 1
T0
CVA
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T1
C1
T2
C2
………
………
Tn
Cn
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DVA
 However, party A itself might default before maturity Tn
and, in that case, counterparty B will incur a loss
 Assume that Di, i = 1, 2, …, n, is the present value of the
expected loss to counterparty B if A defaults at time Ti
 Assume that πA is the (constant) probability of default of A
 The Debit Value Adjustment (DVA) is the estimate of the
present value of the expected gain to A from its own default
n
DVA    A  Di
i 1
T0
DVA
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T1
D1
T2
D2
………
………
Tn
Dn
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Adjusted value of derivative
 Define fnd as the no-default value of the derivative to A,
i.e., the value of the derivative to A under the assumption
that neither side will default
 Therefore, the value of the derivative to A adjusted for
credit risk is
f adj  f nd  CVA  DVA
T0
CVA
DVA
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T1
C1
D1
T2
C2
D2
………
………
………
Tn
Cn
Dn
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