Substitution risk measurement:

“Substitution risk”
Msc in Finance
Rocco Letterelli
Marco Ticciati
Substitution risk
“ risk of greater cost sostitution of the asset afforded
by one part if the couterpart makes a default before the
settlement date”
In the financial lecterature there is relationships with
Pre-settlement risk
Conterparty risk
Substitution risk
It is a kind of risk which we have in
hedging positions
 It is observable to OTC derivative markets
 Need for mark-to-market monitoring of
financial position
Substitution risk
2 questions:
If a counterparty was to default today,
what would it cost to replace the
derivatives transaction (i.e., what is the
current exposure)?
If a counterparty defaults at some point
in the future, what is a reasonable
estimate of the potential replacement
cost (i.e., what is the potential
Substitution risk:
1) the first answer is quite intuitive and it is represented
by mark-to-market value of the underlying contract.
Example: 5y swap
 fixed rate 6%
 floating rate of LIBOR.
 The mark-to-market value is zero at t0
Suppose that t=0,5 the swap rate for a 4.5-year swap is
5.50%. If the counterparty paying the fixed rate of 6.00%
defaults, the nondefaulting counterparty receiving the
fixed rate (and paying the floating rate) will be forced to
replace it with a 5.50% swap and will thereby suffer a
replacement cost equal to 0.50% per annum for the
remaining 4.5 years
Substitution risk:
2) The second question is more difficult to answer in
that it asks for an assessment of what the replacement
cost could be in the future
Dealers use Monte Carlo or historical simulation studies,
option valuation models, and other statistical techniques
to assess potential exposure. These techniques are
often used to generate two measures of potential
exposure: expected exposure; and maximum or "worst
case" exposure
2 important measures:
• Expected exposure at any point during the life of the
swap is the mean of all possible probability-weighted
replacement costs, where the replacement cost in any
outcome is equal to the mark-to-market present value if
positive and zero if negative.
• The maximum potential exposure is calculated as an
estimate of "worst case" exposure at any point in time
This shape is due to 2 different effects:
Diffusion effects: as the time progresses the probability to
have MKT far from zero increases (volatility of underlying)
Amortization effect: the reduction in years of cash flows that
need to be replaced
Substitution risk
before the
crises(basilea I
and II)
Regulation after
Substitution risk
According to basel I there are two
approaches to estimate counterparty risk
 Basel II treated CCR loss as credit risk
The second one accounts for substitution
FPE(future potential expusure)
 It is based on
CE(current expusure
LEE(loan equivalent expusure)
Substitution risk
the CE is given by the current market value (MV) of the OTC
contract, that is, by the cost the bank would face to replace
the contract (“substitutioncost”) with an identical one, if
the counterparty were to default. If the market value is
negative, then there is no current exposure to credit risk,
and CE is set to zero. To this CE, an estimate of FPE must
be added, given by a fixed percentage (p) of the notional
(N). The value of p, also called the “add-on” factor, depends
on the underlying asset and increases with the maturity of
the contract.
LEE = CE + FPE = max(0,MV ) + p ·N
Substitution risk
After the crisis…
Basel III
Basel III has incorporated credit value
adjustment (CVA) that is the risk
premium from the counterparty to be
compensated for the risk of the
counterparty defaulting , in calculations of
regulatory capital for counterparty credit
risk (CCR)
Substitution risk
Basel III applies a hybrid approach in terms
of CCR regulation by treating default risk
and credit migration risk differently: the
default risk is treated as creditrisk under
the ASRF framework (with capital horizon
H = 1 year and confidence level q =
99.9%), while the credit migration risk is
treated as market risk
Substitution risk
Therefore, in the last regulation framework

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