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Risksvr™ Credit Curve Manager Online Help |
The Risksvr™ Credit Curve Module is a stripped down version of the Credit Curve and Default Data
Manager available in the Risksvr™ engine with the additional capability to
export intermediate data into different formats (Excel spreadsheet, XML with
user defined entity names, ASCII, etc).
Supported Credit Statistics.
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Calculation Options
Hazard Rates
Hazard rates are the probabilities of default from time t to time t+1 as seen
from time t. Hazard Rates are usually supplied as credit curve building blocks.
Hazard Rates as usually supplied for one-year intervals. If Hazard rates are
non-standard, a begin and
end dates are expected for each rate.
cf Hazard Rates in Credit-Curve
Formula guide
Cumulative Hazards
Cumulative Hazards have many useful properties and are the most important
building block of credit-curves. The Cumulative Hazard is the sum of Hazards from Time 0 to time
t for a given Credit Quality.
cf Cumulative Hazards in Credit-Curve
Formula guide
Survival Probabilities
Survival probabilities are the probability of Survival from time 0 to time t.
Survival probabilities are the opposite of expected default probabilities
The
Credit Curve can be defined from Survival probabilities, These Survival Rates
can then be transformed into Conditional Marginal Default Probabilities or
Hazard Rates and then aggregated into expected default probabilities. over
different simulation horizons.
cf Survival Probabilities in
Credit-Curve Formula guide
Marginal Conditional Default Probabilities
Marginal Conditional default probabilities define the probabilities of default from period t
up to period t+dx as seen from time 0.
For identical periods, conversion between Marginal Conditional Probabilities and Hazard rates is
trivial.
cf Marginal Conditional [No]
Default formula guide
Expected Default Frequency
Expected default probabilities or frequencies are the probabilities of default of a given counterparty with a specific rating over a
predefined period of time.
Expected default frequencies are transformed into
marginal default probabilities between each expected default frequency vertex
defined. Conversion between Survival and Expected Default Frequency is
trivial.
cf Expected
Default Probability formula guide
Transition Probabilities Migration
Transition Matrices can be used to compute credit curves over multiple horizon.
This is done by transforming the Transition
probabilities into marginal default probabilities, which are then converted into
survival or Hazard rates or expected default probabilities.
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If one single Transition Matrix is supplied and multiple time steps are defined,
then the Transition Matrix is assumed to be defined as a 1-year horizon
Transition Matrix.
Probabilities can then be scaled to each time step accord to different assumptions.
- The Transition can be assumed constant. (sic?)
- Each 1 Year Vertex gives way to Transition Multiplication and time steps
that fall between 1 year periods can be scale Transition Generator
approach can be used to scale the Matrix, by performing a spectral
decomposition on the transition
This is the approach most often used in industry.
- If multiple Transition Matrices are
provided, they must be either defined in the correct order or assigned a
simulation horizon. The simulation Horizon.
If the simulation horizon is different from the Transition Horizon, then the engine will either:
Scale the Transition Matrix to the Horizon via spectral decomposition (see Transition Generator Add-In) and then transform into marginal conditional probabilities to match the engine's horizon.
or
Transform the Transition Matrix into marginal conditional probabilities and then interpolate/ extrapolate default probability/ hazards to match the engine's horizon.
Calculation Features In Credit Curve Module
File Upload Format
File upload provides the facility to upload
Transitions files or Credit Curve File into the Credit Curve Module.
Separators: All Separators are tabs '\t'. The engine however accepts other
separators if needed.
end of lines are '\n' (dos / windows) or '\r\n' (Unix) ;
The Transition Matrix Format is assumed accordingly:
| #DECIMAL SEPARATOR:. | |||||||||||||||
| RatingSystem | From Rank | To Rank | From Rating | To Rating | Horizon In Years | Probability | Name | ||||||||
The DECIMAL SEPARATOR is a special optional keyword that is required if you use other decimal separator than the industry standard .
The Credit Curve Format is defined
accordingly:
Every row that begins with # is not considered an valid row
| Curve Name Curve Type | |||||||
| T(1) | T(2) | T(3) | T(4) | T(..) | T(..) | T(n) | |
| P(1) | P(2) | P(3) | P(4) | P(..) | P(..) | P(n) | |
Each Curve is defined as three (3) Rows:
1st Row Curve Name (Any
String) Curve Type
2nd Row Credit Curve Time Vertices
(Time 0 is optional)
3rd Row Credit Curve Probabilities.
Curve Type:
Integer (standard) or string.
1 : "Hazards"
2 : "Survival"
3 : "EDF"
4 : "Marginal" (for Marginal Conditional or "Forward
Default"
example:
File upload also accepts the generic name value pair format accordingly:
Separators: All Separators are tabs '\t'. or spaces. The engine accepts other separators if needed.
end of lines are '\n' (dos / windows) or '\r\n' (Unix) ;
All tag tokens are identical to RiskML format. They can be customized by supplying a token equivalent template or sheet file.
That is defined by supplying on each line the original token name a separator and the new token name.
The Generic Transition is defined as a standard square Matrix that contains the Migration states plus one Column with the
Default probabilities for the Default state.
A Bottom row of 0. (i.e. the Transition From Default assuming an absorbing state) can also be specified although it is often omitted.
| RATINGS R
TRANSITION
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Where R is the Rank of the Rating System used.
Transition Matrices are assumed to be defined as From/To Rating States.
To/ From Matrices can be supplied with the TRANSITONTOFROM
token instead of the standard TRANSITION
The Credit Curve Format is defined accordingly:
Every row that begins with # or ! is considered a comment and is ignored
| PERIODS P RATINGS R |
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HORIZONt(0) t(1) t(..) t(P) RATING AAA AA A BBB BB B,,
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| EDF | |||
| EDF(0,0) | EDF(1,0) | EDF(..,0) | EDF(P,0) |
| EDF(0,1) | EDF(1,1) | EDF(..,1) | EDF(P,1) |
| EDF(0,..) | EDF(1,..) | EDF(..,..) | EDF(P,...) |
| EDF(0,R) | EDF(1,R) | EDF(..,R) | EDF(P,.R) |
Simplified Format:
Except if the Time Period is Defined. Periods are assumed to be one year
intervals.
If Rating Ranks are left out, Each row is assumed to be assigned to the
corresponding Rating rank in increasing order.
i.e. row 1=rank 0, row 2=rank 1, ... from Best Rating Rank to Worset Rating Rank.
| PERIODS P RATINGS R HORIZONt(0) t(1) t(..) t(P) EDF | |||
| EDF(0,0) | EDF(1,0) | EDF(..,0) | EDF(P,0) |
| EDF(0,1) | EDF(1,1) | EDF(..,1) | EDF(P,1) |
| EDF(0,..) | EDF(1,..) | EDF(..,..) | EDF(P,...) |
| EDF(0,R) | EDF(1,R) | EDF(..,R) | EDF(P,.R) |