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Credit risk used to be
primarily a concern of banks, fixed income investors, and businesses that
extended credit as part of their business. The growth of
derivatives markets during the
1990s introduced new forms of credit risk, not only for the derivatives
dealers who made markets in them, but also for the
corporations who used
them.
Not all derivatives entail credit risk. For example,
futures are traded on exchanges that employ a system of
margining that virtually eliminates credit
risk. However, most OTC derivatives
entail credit risk for one or both parties to the transaction. If a dealer
sells a corporation a call option, the
corporation pays the dealer a
premium and faces the risk that the dealer may fail to perform on the
option in the event the corporation exercises it
in-the-money. If, on the
other hand, the dealer enters into an
interest rate swap with the
corporation, no premium is paid, and the swap starts off with no
market
value (except, perhaps, that due to a
bid-ask spread
charged by the dealer). Depending upon fluctuations in interest rates, the
swap could take on a positive market value for either the dealer or the
corporation. Accordingly, both face credit risk due to the possibility
that the swap might come to represent a net obligation of the other party.
OTC derivatives actually entail two forms of credit risk:
Pre-settlement risk
is the risk that a counterparty will default prior to the derivative
instrument's final settlement at expiration.
Settlement risk arises at final settlement if there are timing
differences between when each party performs on its obligations under the
contract.
Settlement risk entails a number of unique issues. In this
article, we focus on pre-settlement risk.
Many OTC derivatives are structured with termination
features. These provide for the immediate termination of the contract
should a specified trigger event occur. Trigger events might include:
Failure by a counterparty to perform on the contract or a related
contract
A downgrade of one of the counterparties'
credit ratings
A merger or acquisition of one of the counterparties
When a trigger event occurs, the contract is terminated (either
automatically or at the option of the other counterparty) and there is an
immediate cash settlement between the counterparties for any market value
of the contract.
Accordingly, a pre-settlement default might entail the following
elements:
An institution has a contract with a counterparty which has a
positive market value (the counterparty has a net obligation to the
institution for that contract).
A trigger event occurs resulting in immediate termination of the
contract.
The counterparty fails to make the settlement payment for the
contract's market value.
Unlike settlement risk, which entails exposure equal to a
counterparty's gross obligation, pre-settlement risk entails exposure
equal to a counterparty's net obligation on that contract. Suppose an
institution enters into a forward contract to exchange 1MM
GBP for 1.5MM
USD in three months. Settlement risk
exposes the institution to a possible loss of $1.5MM. Pre-settlement risk
exposes the institution to just the difference in market value between the
USD and GBP payments. If the pound were trading at 1.45 USD/GBP at the
time of a default, this would translate into a loss of just USD 50,000.
Replacement cost is a basic
metric of credit exposure due to pre-settlement risk. It is the cost that
an institution would incur if a counterparty completely defaulted on its
obligations. Effectively, it is the cost to the institution of having to
completely replace all contracts with that counterparty.
Current replacement cost (called
mark-to-market exposure)
is the replacement cost of a portfolio of contracts with a counterparty
based upon those contracts' current market values. Replacement cost is
distinct from market value for two reasons:
Replacement cost can never be negative. This reflects the fact that
an institution will never benefit from a counterparty default. Even if a
counterparty fails, obligations owed to the counterparty must be paid.
Accordingly, if a contract has a negative market value, it has a zero
replacement cost.
Unless an enforceable
netting agreement applies, offsetting
obligations will not net in a default situation. Specifically, an
institution will have to meet its obligations to a counterparty despite
that counterparty failing to perform on offsetting obligations.
For example, suppose that an institution has two contracts with a
counterparty which have the following market values:
$3MM (the counterparty owes the institution $3MM)
–$5MM (the institution owes the counterparty $5MM)
If there is not an enforceable netting agreement between the two
parties, the replacement cost of the portfolio is $3MM. This is because,
if the counterparty were to default, the institution would still have to
perform on its $5MM obligation. The only contract that would be affected
by the default would be the $3MM contract. Accordingly, the institution
has $3MM at risk.
If, on the other hand, there is an enforceable netting agreement, the
replacement cost is $0. In the event of a default, the two obligations
would be netted, and the institution would be obligated to the
counterparty for $2MM—the same net obligation it has without a default.
Accordingly, depending upon whether there is a netting agreement, the
replacement cost is either $3MM or $0. Each result is different from the
portfolio's market value of –$2MM.
Replacement cost can also be measured prospectively. Future replacement
cost is the discounted value of the replacement cost of a portfolio of
contracts with a counterparty, based upon what those contracts' market
values would be under a specified market scenario. Obviously, the result
depends upon the assumed scenario. Statistical risk measures such as
expected credit exposure summarize what future replacement cost may be
based upon the entire probability distribution of possible market
scenarios.
Suppose an institution is about to enter into a foreign
exchange forward contract with a counterparty. With such a contract, the
initial market value is zero—except, perhaps for a bid-ask spread.
Accordingly, its current replacement cost (or mark-to-market credit
exposure) is zero. This, however, gives no indication of the potential
credit exposure from the contract. As the underlying exchange rate
fluctuates, the contract could take on a positive replacement cost.
Indeed, if the exchange rate moves significantly in the institution's
favor, the replacement cost could become quite large.
When that happens, it will be too late for the institution to start
managing its credit exposure to the counterparty. The time to do so is
now—while the institution is still negotiating the contract. Only now can
the institution decide whether or not to enter into the contract. Only
now, can it incorporate credit
enhancements into the deal. The institution cannot base its actions on
the mark-to-market credit exposure of the contract, which is zero.
Somehow, it must analyze the potential credit exposure.
There are two statistical measures of potential credit exposure that
are commonly used. They are closely related:
Expected exposure
is the expected value (mean) of the probability distribution for
replacement cost at a specified point in the future.
Maximum likely exposure
(also called worst-case exposure)is a quantile of the probability distribution for replacement cost at a
point in the future.
Let's consider our example of the institution which is about to enter
into a foreign exchange forward. Exhibit 1 illustrates the probability
distribution for the replacement cost, one month from today, for the
contract.
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For the foreign exchange forward example,
this exhibit illustrates the probability distribution of replacement
cost one month from today. The distribution is actually a mixed
distribution—with both a discrete and a continuous part. There is a
positive probability that replacement cost will be zero. This is
depicted by the rectangle of probability on the best above 0. If
replacement cost turns out to be positive, the actual value is
continuously distributed. This is depicted by the tail of
probability density trailing off to the right. |
The probability distribution in Exhibit 1 is a mixed distribution
having two components. The first component is a discrete block of
probability corresponding to a zero replacement cost. This probability
arises from the possibility that the exchange rate may move against the
institution over the next month. In that event, the institution will owe
the counterparty money on the contract, and the replacement cost will be
precisely zero.
The second component of the distribution is continuously distributed,
starting at a zero replacement cost and extending beyond USD 1MM. This
corresponds to the possibility that the exchange rate may move in the
institution's favor. If this happens, the contract will have a positive
replacement cost equal to the present value of its market value.
Exhibit 2 illustrates both expected exposure and maximum likely
exposure
(calculated as a .975-quantile of replacement cost) for this example.
Expected exposure is simply the mean of the distribution. The maximum
likely exposure is the dollar value such that there is a 97.5% probability that
the replacement cost will be less than that value—it is the "maximum
likely exposure" in the sense that there is a 97.5% probability that replacement
cost will not exceed it.
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Expected exposure, for a given horizon, is
the mean of the distribution of replacement cost at that horizon.
Maximum likely exposure is a quantile of the replacement cost at that
horizon—in this case, a .975-quantile. |
Obviously maximum likely exposure is not literally the maximum
value that the replacement cost could possibly take on. For example, when
it is measured as a .975-quantile, there is a 2.5% probability that the
replacement cost will actually exceed the maximum likely exposure.
The term potential
exposure is used to refer to expected exposure, maximum likely
exposure or any similar metric of possible future exposure.
In complex portfolios, with multiple contracts maturing or
paying cash flows on various dates, potential credit exposure can vary
significantly from one horizon to the next.
Specifically, this means that expected exposure and maximum likely
exposure
are horizon-specific notions. A portfolio does not have a single expected
exposure or maximum likely exposure. Instead, those measures of exposure will
vary for a portfolio depending upon which horizon they are calculated
over. Accordingly, exposure is typically calculated for multiple horizons.
In our example, we analyzed potential credit exposure at the one-month
horizon. Suppose, however, that the forward contract in that example is
going to mature in 6 months. Exhibit 3 illustrates how our analysis might
be performed for each monthly horizon, out to 6 months.
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Maximum likely exposure is calculated at multiple
horizons. Six probability distributions are depicted, each for
replacement cost at a different horizon. The .975-quantile of each
is calculated, creating a curve of maximum likely exposures across
horizons. |
Exhibit 3 analyzes maximum likely exposure at each horizon (expected exposure
could be calculated similarly). At each horizon, the probability
distribution for the contract's replacement cost is determined. For
example, the distribution for the one-month horizon is precisely the
distribution we constructed in Exhibit 1 above. Here, we are just
expanding that analysis to multiple horizons.
In Exhibit 3, as the horizon increases, the continuous component of
each distribution becomes flatter and more spread out. This reflects the
increasing uncertainty in the future value of the contract's underlying
exchange rate over greater horizons.
The .975-quantile is determined for each distribution, and the results
are plotted on a graph. That graph, expanded in Exhibit 4, plots maximum
likely exposure as a function of horizon. As we might expect, the
potential exposure from the contract increases with horizon.
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Based upon the analysis of Exhibit 3,
maximum likely exposure is plotted as a function of horizon. |
In Exhibit 4, maximum likely exposure peaks out at $2.3MM at 6 months—just
prior to the maturity of the contract. This reflects the fact that
exchange rates are likely to move more over 6 months than over a shorter
interval.
Exhibit 5 shows a similar analysis for a 5-year interest rate swap. The
evolution of maximum likely exposure is very different from that of the foreign
exchange forward.
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Maximum likely exposure is plotted as a
function of horizon for a hypothetical 5-year interest rate swap.
The jagged pattern is created by the periodic payment of net
interest on the swap. At any point in time, if replacement cost is
positive, payment of net interest reduces replacement cost by an
equal amount. |
Two competing forces shape the evolution of exposure in Exhibit 5:
Diffusion: Over time, the contract's replacement cost is determined
by interest rates. These are likely to vary more over longer horizons
than over shorter horizons, thus tending to make exposure increase with
horizon.
Amortization: Every six months, there is a net
coupon payment under
the swap. Each payment reduces the market value of the swap by the
amount of the payment. This tends to reduce exposure with horizon,
causing a shark-tooth pattern of exposure.
Actually calculating potential exposure can be an involved process that
often requires some form of Monte Carlo simulation. The process is made
more complicated by the fact that credit exposures are not additive. It is
not possible to calculate exposure for the individual instruments in a
portfolio, and then sum the results.
For example, suppose an institution has two foreign exchange forward
contracts with a counterparty, and that the 3-month expected exposure
under each is USD 5MM. Without knowing anything more about the situation,
we cannot judge what the total 3-month exposure is for the two contracts.
The answer could range from USD 0MM to USD 10MM—or anywhere in between.
For example, if there is a netting agreement, and the two contracts are
identical, one long and the other short, then their credit exposures
cancel, and the total exposure is USD 0MM. On the other hand, if they are
both long, the total exposure is USD 10MM. A more complex situation would
be if one contract were linked to the
EUR
and the other to the GBP. Taking into account the correlations between the
two exchange rates, the total exposure might be USD 8MM. Accordingly, when
Monte Carlo simulation is used to measure credit exposure, it must be
applied to the entire portfolio at once.
In practice, OTC derivatives are often
collateralized, with one or both parties posting collateral whenever
they have a net obligation on the derivative. Collateral is typically
adjusted daily so that its market value always exceeds that of the
derivative. With such an arrangement, net expected exposure and net
maximum likely exposure can both be assumed to be zero.
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collateral
Assets held to secure an obligation.
credit derivative A
derivative instrument designed to transfer credit risk from one
party to another.
credit risk
Risk due to uncertainty in a counterparty's ability to
meet its obligations.
credit enhancement
Any methodology that reduces the credit risk of a transaction with
a counterparty.
derivative instrument
An instrument which derives its value from the value of other
financial instruments.
forward contract
A trade that is agreed to at one point in time but will
take place at some later time.
netting The offsetting of cash flows or other obligations against each
other.
settlement
risk
Risk
that a counterparty will default on a derivative instrument at its
final settlement. |
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Ads by Contingency Analysis
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Das (2003)
offers an in-depth discussion of derivatives pre-settlement risk.
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