Research Technical Note

Spread Sensitivity Overhaul July 10, 2006

Eugene Sterneugene.stern@riskmetrics.com

Summary: We define the treatment of spread shifts in the sensitivity statistics in RiskManager. This includes bothspread time series and calculated spreads. Basic spread shifts are encapsulated in Generalized Stress Tests. Along theway, we also separate our current notion of risk-free curves into three separate notions (risk-free curves, base curves,non-spread curves.

1 Introduction

1.1 Credit-Related Instruments

This note describes a general treatment of spread sensitivity statistics in RiskManager. The purpose of the

statistics is to give users an informative and intuitive picture of how the value of their positions changes

when spreads move.

This subject can be confusing because it involves a number of instruments, and also, more importantly,

because it involves a number of different notions of spread. Very roughly, a spread for us will be anything

that captures the default risk of an individual obligor. Spreads impact the credit-related instruments, which

we can think of as instruments that can be affected by default risk of individual obligors. These instruments

include:

1. Bonds. This includes generic bonds, plain vanilla bonds, amortizing bonds, and convertible and

mandatory convertible bonds. We also include FRN’s, because they can be defined using the generic

bond framework.

2. Credit default swaps.

3. Synthetic CDOs.

1.2 Spread Risk Factors and Calculated Spreads

Credit-related instruments can be affected by a number of different notions of spreads. Here are some

examples:

1

Explicit Spread Risk Factors

1. Credit default swap spread time series.

2. Corporate yield curves.

3. Issuer-specific yield curves.

4. Risky sovereign curves.

Calculated Spreads

5. Bond spreads over a base curve calibrated from a bond price.

6. CDS spreads calibrated from a CDS price.

7. Bond or CDS spreads calculated using the CreditGrades model.

Strictly speaking, items 2-4 above do not represent isolated spread data, but rather both the spread and the

risk-free interest rate component tied together. However, this is not an obstacle, because we will not need to

explicitly separate the spread and the risk-free rate explicitly when we calculate spread sensitivities.

To begin to impose some order, it is useful to divide the various kinds of spread data we work with into two

classes:

1. Risk factors that include spreads. One way to think of these is as risk factors (more precisely, risk

factor time series, but we won’t harp on the distinction here) that should move when the market’s view

of the credit quality of an obligor changes. For example, a risk factor representing the 5-year CDS

spread for a particular name is clearly a “spread-related” risk factor. An issuer-specific yield curve is

another risk factor that, intuitively, incorporates a spread. Corporate curves, risky sovereign curves,

and credit indices (e.g., CDX or iTraxx) are other, slightly subtler, examples.1

2. Calculated spreads. Unlike spread risk factors, which capture the general credit quality of an obligor,

a calculated spread captures the impact of an obligor’s credit quality on a particular note. Thus, a

calculated spread is always a number (rather than a curve, as is typical for spread risk factors). There

are two kinds of calculated spreads:

• Bond spreads. These are typically calculated from a bond price and a base discounting curve as

the single number that should be added to the base curve to reproduce the price of that (partic-

ular) bond. The bond price could either be supplied by the user (in which case we speak of a

calibrated spread), or computed using some pricing model (e.g., risky yield curve or Hull-White1We do not currently maintain time series of tranche spreads. If we decide to maintain tranche spread time series in the future,

we should view them as correlation data, not spread data, and should not view them as spread risk factors in this context.

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bond pricing). A bond spread could also be supplied by the user directly in the application as

the “discount spread” above the risk-free rate.

To write the formula explicitly, suppose that P is the (dirty) price of the bond. Let t1, t2, . . . , tn

be the coupon dates. We assume that the principal is paid back on tn. Let cj be the coupon

payment made on tj .2 Let rj be the risk-free discount rate corresponding to time tj .3 Let f be

the compounding frequency according to which the rates rj are quoted. Then the bond spread is

the unique number s̃ that makes the following equation true:

P =n∑

j=1

cj ·(

1 +rj + s̃

f

)−tjf

+ N ·(

1 +rn + s̃

f

)−tnf

. (1)

We can also define a spread s in terms of continuous compounding:

P =n∑

j=1

cj · e−(rcj+s)tj + N · e−(rc

n+s)tn . (2)

• CDS spreads. Intuitively, this is the fair spread for a particular CDS on a given obligor, typically

calculated from a CDS spread curve for that obligor. For example, if the CDS spread curve

for GM includes a 1-year, a 3-year, and a 5-year spread, we can use that curve to calculate the

fair spread for a 4-year CDS on GM. The spread can also be calibrated from a market price.

In addition to being calculated based on the CDS curve, a CDS spread can be calculated using

CreditGrades, and can also be supplied directly by the user.

To give a formula for the spread, let t1, t2, . . . , tn be the payment dates of our CDS. We assume

that the CDS matures on tn. Let P (tj) be the probability that default occurs by time tj .4 Let

cj be the length of the j-th payment period, expressed in terms of our particular day count

convention.5 Let Dj be the discount factor to time tj , obtained off the discount curve to which

we map the CDS. Let R be the recovery rate associated with the CDS. Then the fair spread s is

defined as the unique solution to the equation

0 =n∑

j=1

Dj ·((1− P (tj)) · cjs + (P (tj)− P (tj−1)) ·

(cjs

2− (1−R)

))− c1s

T − T ′

t1 − T ′. (3)

2We express the coupon payments this way to avoid having to make explicit any day count conventions — they are incorporatedin the cj .

3See Section 2 for a discussion of which “base curve” this rate should come from.4The P (tj) are typically obtained from a CDS spread curve for the obligor, though we will implement a way to derive them

from bond spreads as well. The CDS spread curve that we use to generate the P (tj) may also be adjusted, to match a given pricefor our particular CDS (calibration).

5For example, if the period is 92 days long and we are using an Actual/360 day count convention, then cj = 92360

. In general,cj depends on tj − tj−1 and the day count convention.

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Here, the term c1sT−T ′t1−T ′ that we subtract off corresponds to the accrued interest.6 Here T repre-

sents the analysis date, and T ′ represents the start of the first coupon period. We may also turn

(3) into an explicit formula for s by grouping together those terms that do and do not contain a

multiple of s.

A key point is that the spreads we are considering here all correspond to individual obligors. Thus, the fair

spread of a CDO tranche is not an example of a calculated spread that is subject to spread shifts, because it

is related to many obligors, and, perhaps more importantly, to the correlation between them. Thus, we will

always take a statement like “shift all spreads by 10 bp,” whatever else it may mean, to apply to spreads

associated with individual obligors only. This is because it usually wouldn’t make sense to shift all obligor

spreads by 10 bp and then to shift the spread of a highly leveraged (say, equity) synthetic CDO tranche

written on those obligors by the same 10 bp.

1.3 Pricing Models

Instruments and data (i.e., spread data) are linked by pricing models. Having listed both the instruments and

the different forms that the data can take, we complete the picture by listing the pricing models. We break

them up both by instrument and by the data that goes into them. As part of this survey, we briefly explain,

for each combination of instrument and pricing model, what the relevant notions of spread risk factor and

calculated spread are.

1.3.1 Bond Pricing Models

1. Pricing off a risk-free base curve plus a discount spread. No associated spread risk factor. The

calculated spread is just the discount spread.

2. Pricing off a risky yield curve. The yield curve is the spread risk factor. Calculated spread found by

calibrating the price of the bond to the base curve plus a discount spread bond pricing model.

3. Pricing using CreditGrades. This is a Hull-White pricing model. No associated spread risk factor.

Calculated spread found as above.

4. Pricing using CDS spread data. This is a Hull-White pricing model that we will implement as part

of the spread overhaul. Spread risk factor is the CDS spread curve for the obligor. Calculated spread

found as above.

6Put another way, the fair spread is the spread that makes the clean price of the CDS equal to 0.

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1.3.2 CDS Pricing Models

1. Pricing using CDS spread data. Spread risk factor is the CDS spread curve for the obligor. Calculated

spread is the fair spread of the CDS.

2. Pricing using CreditGrades. No spread risk factor. Calculated spread is the fair spread derived from

CreditGrades.

3. Pricing off a risky yield curve. Also known as pricing a CDS using bond data. This is a new type of

pricing input that we will implement as part of the spread overhaul, again based on the Hull-White

model. The yield curve is the spread risk factor. Calculated spread is the fair spread of the CDS.

4. Pricing off a risk-free yield curve plus a discount spread. Same pricing model as for a risky yield

curve. No spread risk factor. The calculated spread is the fair spread of the CDS.

1.3.3 CDO Pricing Models

1. Pricing using CDS spread data. Spread risk factors are either the CDS spread curves for each indi-

vidual obligor, or a CDS curve associated with the index (large pool model). No calculated spread, as

remarked above.

2. Pricing using CreditGrades. No spread risk factors, and no calculated spread. The only way to move

the price of such an instrument would be to shift equity prices for obligors in the collateral pool,

and to pass the shift on to CreditGrades spreads for the obligors (see Section 3.4). This isn’t a great

treatment, but it’s unlikely that users will want to model CDO’s this way anyway.

3. Pricing off a risky yield curve. The yield curve is the spread risk factor. No calculated spread.

4. Pricing off a risk-free yield curve and a discount spread. No spread risk factors, and no calculated

spread. To move the price of such an instrument, we would have to shift all interest rates.

Note that for a CDO priced with the granular model, we can mix input models (map some obligors to CDS

curves, others to CreditGrades, and still others to bond data).

1.4 General Approach to Spread Shifts

Our general goal is to work out what it should mean when a user asks to shift all spreads by, say, 100 bp,

and to apply the shift to a certain group of instruments.7

7The instruments to apply the shift to are selected via tagging. See Section 3.1.

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The first part of the answer, already laid out, is that the shift is meant to apply to individual obligors, or to

proxies for them. Thus, a user who wants to shift spreads by 100 bp would want the shift to apply to, say,

bond spreads or even swap spreads, but not to, say, CDO tranche fair spreads.8

The next part of the answer is that we could shift spread risk factors or calculated spreads. As we have seen

above, many instruments have both spread risk factors and a calculated spread associated with them, and we

would typically be unable to apply the shift to both simultaneously in a consistent fashion. This is because

calculated spreads typically depend on spread risk factors, but not always through a direct translation of the

form S 7→ S + k.

Consequently, when we are defining spread sensitivity statistics, we will give users a choice of applying

a shift to either spread risk factors or calculated spreads.9 A calculated spread will be available for every

credit-related instrument.10 Spread risk factors will be available for many, but not all, instruments. For

example, a bond priced using CreditGrades, or off a risk-free curve plus a discount spread, will not be

impacted by any spread risk factors, and thus will not show any sensitivity to spread risk factor moves.

Because of this, the default option for spread shifts should be to shift calculated spreads.

2 Risk-Free Curves

Currently, the system admits a single risk-free curve per currency. This curve, which is preset and cannot be

modified by the user, is used in three distinct ways:

1. Option pricing. The curve is used to calculate discount rates for option pricing models.

2. Interpreting spreads. In other words, spreads are viewed as spreads over the risk-free curve.

3. Identifying spread risk factors. When we do spread shifts in calculating Generalized PVBP or in

Generalized Stress Tests, we shift all yield curves that are not risk-free.

To see that these are completely separate applications of the notion of risk-free curve, note that it would

make perfect sense to view bond spreads as spreads over USD Govt, to discount at USD Swap in pricing

options, and to shift neither USD Swap nor USD Govt when we apply a shift to all spread curves. Thus, we

also observe that while the first and second application require us to have a single risk-free curve for each

currency, the third really doesn’t.11

8While this is reasonable while we are modeling synthetic CDO’s only, we may want to model cash flow CDO’s in the future.In that case, users may want to shock tranche spreads.

9This will be somewhat similar to the current distinction between “spread shifts” and “credit spread shifts” in the currentimplementation of Generalized Stress Tests.

10For synthetic CDOs, we will shift the calculated spreads of the underlying names and not the tranche spread.11In fact, because we treat on-the-run and off-the-run curves as two separate curves, we should expect to have more than one

“non-spread” curve per currency.

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Thus, to enable a proper treatment of spreads and of options pricing, we will separate out these three notions,

and will also allow users to set their own risk-free curves in each context. The three notions are:

1. Risk-free curves. Used to discount in all option pricing formulas. Can be set by the user, but defaults

to the risk-free curve assigned to each currency today.

2. Base curves. Used to calculate bond spreads. That is, if a bullet bond has price P , we calculate the

bond spread s by the formula (2), where the rj are taken from the base curve. Can be set by the user,

but defaults to the risk-free curve assigned to each currency today.

3. Curves without credit risk. These are the yield curves which we leave alone when we apply spread

shifts to spread risk factors. Multiple curves per currency are possible. Can be set by the user, but

defaults to just a single curve — the risk-free curve assigned to each currency today.

Currently, at the position level, discount curves can be supplied for option pricing and discounting bond

coupons. To complete the picture above, a risk-free curve base curve will be added for bond instruments

and as a new input for the bond spread model. Let’s consider the generic bond. Users will be able to specify

both the discount and base curves. When both are present, the former will be treated as a risky curve so that

whenever a credit risky yield curve shift is applied, the specified discount curve will then be shifted.12 If the

same discount curve happens to used in option pricing, say for a CDS, it will not be shifted under a credit

risky curve shift.

3 General Spread Shifts

In general, spread sensitivity statistics are intended to capture what happens to instrument or portfolio prices

when spreads move by a controlled amount. Thus, by “shifting spreads,” we will mean taking spread data

that gives rise to a price for an instrument, adjusting that data to move the spreads up or down, and repricing

the instrument.

It is worth emphasizing again that the initial state before a spread shift consists of both spread data and a

price, with the two being linked by a pricing model. In many cases, the pricing model is used to derive the

price from the spread data. However, in some cases, the process is reversed: we start with a price (either

supplied by the user or coming from some pricing model), and then calibrate spread data that corresponds

to that price according to the “linking” pricing model. In this case, the linking model may be completely

different from the model that gave rise to the initial price.

The output of a spread shift typically communicates the change in price coming from the spread shift.

However, in some cases, we simply convey the new prices rather than the change.12We see that the risky curve at the position level for the generic bond acts as an override to the current global definition of risky

curves.

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Until Section 3.4, we assume that CreditGrades are turned off for every instrument in the portfolio.

3.1 Generalized Stress Tests

Currently, we implement shifts in classes of risk factors in two ways: through the Generalized PVBP statis-

tic, and through Generalized Stress Tests. This is confusing for clients, and forces us to maintain more

infrastructure. Going forward, we should keep only one of these two frameworks.

The advantage of Generalized PVBP is that it requires fewer steps to use: all we need to do is define the

statistic, rather than defining a Generalized Stress Test and then defining a statistic. The advantages of

Generalized Stress Tests are that we can save and reuse them, that we can stress by tags, and that viewing

spread (and other) shifts as stresses is probably more conceptually coherent.

In our redesigned framework, we will focus on our stress testing functionality, and enhance it so that stress

tests can be run right away without having to separately define an associated statistic. This means that going

forward, we can capture the main benefits of Generalized PVBP, and have lots more functionality besides,

with Generalized Stress Tests. In this note, we will take spread shifts to be implemented via Generalized

Stress Tests. Because it is confusing to have the same functionality in two places, Generalized PVBP should

be phased out over time (but existing reports that include it should continue to run).13

As discussed above, we will implement two versions of spread shifts. One is shifting spread risk factors,

while the other (the default) is shifting calculated spreads. Users will have a choice of which type of spread

shift they want to apply, and shifting calculated spreads will be the default. Thus, we will eliminate the

current dichotomy between spread shifts and credit spread shifts, and classify everything as a spread shift.

Credit spread shifts in existing Generalized Stress Tests should be interpreted as shifts in calculated spreads.

Spread shifts in existing tests should be interpreted as shifts in spread risk factors. If an existing test has

both, interpret it as a shift in calculated spreads (because this way we will be sure that all instruments get

impacted).

3.2 Shifting Spread Risk Factors

There are two kinds of spread risk factor curves:

1. Credit-risky yield curves. As stated above, these are all the yield curves that have not been labeled

as yield curves without credit risk by the user. Typically, the credit-risky yield curves will include at

least the corporate curves, issuer-specific curves, and credit-risky sovereign curves.

13Note that we have other statistics (e.g., Generalized Greeks) that are currently implemented in terms of Generalized PVBP.As we phase out Generalized PVBP, we should redefine and extend (e.g., to spreads) those statistics in terms of Generalized StressTests.

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2. CDS spread curves. This includes CDS spread time series for individual names, as well as for credit

indices.14 Currently used to price CDS and CDO, and could also be used to price bonds through

Hull-White bond pricing.

We allow shifts of spread risk factor curves in basis points (bp), but not in percent for credit risky yield

curves. One reason for not allowing percentage shifts is that we may not be able to apply such a shift to the

term structure in a consistent way. Another is that applying a percentage shift to a risky yield curve would

apply to the risk-free component of the risk factor as well.

To apply spread risk factor shifts to individual instruments, we reprice those instruments (instruments priced

off of either risky yield curves or CDS spread risk factors) based on the shifted risk factors. We then display

either the new price or the delta between the old price and the new price. We apply the same pricing model

to calculate the old and new price; while this may seem obvious, it is worth keeping in mind in comparing

with the treatment of calculated spread shifts in the next subsection.15

Note that before shifting the values of spread risk factors, we may have to adjust them to match market prices

(calibration). For example, suppose that we price a bond using a risky yield curve, that we have supplied

a price of P for the bond, and that we want to apply a shift of ∆ basis points. Suppose that we need to

apply a parallel shift of ∆′ to the yield curve to recover the original price P . Then the new price should be

calculated by applying a shift of ∆′ + ∆ to the yield curve, and using the bond pricing model.

Another point worth noting is that when we shift a credit-risky yield curve, we shift it only for the purpose

of pricing fixed-income instruments. If the same curve happens to be used as a discount curve in, say, CDS

or option pricing, we use the unshifted curve there. For example, say we use USD Swap as a discount curve

for CDS and CDO pricing, but have classified it as a credit risky curve for spread shifts. Then, when we

shift USD Swap, we use the shifted curve for discounting cash flows from bonds that use it as a discount

curve, but we use the unshifted curve for discounting spread or loss payments in CDS or CDO pricing.

Finally, note that this last aspect of the treatment is different from spread changes in either historical or

user-defined stress tests. For example, when we shift USD Swap according to either a historical scenario or

a user-defined move, we use the shifted curve in every application of USD Swap. In the example above, we

would use the shifted curve both to discount both bond and CDS cash flows.

14Credit index data is currently labeled as CDS data, so the inclusion of credit indices should come for free.15In particular, when we analyze a bond with Hull-White pricing based on CDS spread curves, we calculate the original price

using Hull-White pricing with the original CDS spread curve, and the new price using Hull-White pricing with the new CDS spreadcurve. While this may seem obvious, it is different from the treatment of effective duration; see Section ??.

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3.3 Shifting Calculated Spreads

Calculated spreads are either bond spreads on top of a base curve (associated with the currency) or CDS

spreads. Thus, it always makes sense to shift them either in basis points or in percent.16

The way we shift calculated spreads follows the discussion of credit spread shifts in [1]. It is useful to

distinguish between bond spreads and CDS spreads. The general framework for shifting bond spreads, and

repricing based on the new spread, is:

1. Calculate the bond price, based on whichever model we ordinarily use to price the bond. (If the user

supplies a price, we just use that.)

2. Calibrate a spread to the bond price. To do this, we plug the price into the bond math model (based

on a base curve plus a spread) given by equation (2). The base curve (i.e., the collection of rj) comes

from the currency, as discussed above.

3. Shift the spread.

4. Plug the shifted spread back into (2) and calculate a new bond price.

The treatment of CDS spreads is roughly similar. It is based on the idea that a CDS pricing model can be

viewed as a way of going back and forth between present value (clean MTM) and fair spreads.17 More

specifically, the framework for shifting CDS spreads is:

1. Calculate the PV and the fair spread of the CDS. If one is already known, then use the CDS pricing

model to calculate the other.

2. Shift the fair spread.

3. Use the CDS pricing model to calculate the new PV based on the new fair spread.

A useful conceptual distinction to keep in mind is that for bond spreads, we apply the shift in terms of a

fixed pricing model (basic bond math applied to a base yield curve plus a spread), regardless of how we are

16As discussed previously, we’ll need to single out CDO’s for special treatment. The problem is that shifting all spreads istypically interpreted as shifting spreads for individual obligors, not, for, say a CDO tranche, which depends on multiple obligors.Thus, if the user has specified a 50 bp shift to calculated spreads, we would want to apply a 50 bp shift to individual obligors, whilethe calculated spread corresponding to the instrument is a tranche spread.

In this case, we will stick to applying a shift to the CDS fair spreads for the individual obligors.17If we have neither a PV nor a fair spread, the pricing model will calculate both. If we have a PV, we adjust the pricing model

inputs (for now, this means spread curves; in the future, it could mean something like hazard rates) so that the CDS pricing modelcomes up with that PV, and then calculate the fair spread based on the adjusted inputs. Similarly, if we have a fair spread, we adjustthe pricing model inputs so that the CDS pricing model comes up with that spread, and then calculate the PV based on the adjustedinputs.

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pricing the bond. By contrast, for CDS spreads, we apply the shift in terms of the specific model we use to

price the CDS.

One more difference between spread risk factors and calculated spreads is that we never connect shifts in

calculated spreads to any kind of predictive stress test framework. For example, if we are interested in

shifting a corporate curve or a CDS spread curve for a particular obligor, we can pass the effect of this

shift on to other risk factors if we model the shift using the predictive stress testing framework rather than

Generalized Stress Tests. (Shifts in spread risk factors modeled via Generalized Stress Tests are analogous

to simple stress tests: we shift only the factors we have chosen, without applying any impact on other,

correlated risk factors.) However, there is no analogous way to pass a shift in a calculated spread (e.g., a

spread on a particular bond, or a 6-year CDS spread for some obligor) on to other risk factors.

3.4 Turning on CreditGrades

CreditGrades are related to calculated spreads, in that the CreditGrades model is one of the ways in which

the calculated spread might be derived. This applies to both bond and CDS spreads. CreditGrades spreads

require special treatment because they could be viewed as having either spread risk (spread shifts causing a

shift in the CreditGrades spread) or equity risk (equity shifts causing a shift in the CreditGrades spread). We

need to be very clear about how different risk factor shifts impact CreditGrades spreads in the application.

To begin with, if users shift calculated spreads but do not shift equities in a Generalized Stress Test, then

we will treat spreads calculated using CreditGrades like any other calculated spreads, and will shift them

according to the discussion in Section 3.3. (If a user shifts spread risk factors but not equities, our calculation

has no connection to CreditGrades at all, and fixed income instruments modeled via CreditGrades will be

left alone.)

Next, a user who shifts equities but not spreads will be offered a choice (via a checkbox) of whether or not

to apply equity shifts to CreditGrades spreads. If the user chooses to pass equity shifts on to CreditGrades

spreads, then all instruments priced using the CreditGrades model will be repriced based on the new equity

price. If a user does not choose to pass equity shifts on to CreditGrades spreads, then all instruments priced

with CreditGrades should be left alone.

Finally, we need to consider the case when the user shifts both spreads and equities. Because we are

shifting equities, we again need to offer the user a choice of whether to pass equity shifts on to instruments

priced using CreditGrades. If the user says no, there is no issue. If we are shifting spread risk factors,

then instruments priced using CreditGrades are not affected at all. If we are shifting calculated spreads,

we continue to apply the spread shift outlined in Section 3.3. In other words, the treatment for credit-

related instruments is exactly the same as it was without any equity shift. In particular, if some spreads are

calculated using the CreditGrades model, the calculation of the initial spread (before the spread shift) should

be calculated based on the original equity price (before the equity shift).

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Now suppose that the user is shifting both spreads and equities, and wants to pass equity shifts on to Cred-

itGrades spreads. If the spread shift is applied to spread risk factors, it is clear what we should do. A

credit-related instrument might be priced using either spread risk factors or CreditGrades (or neither), but

never both. Thus, for instruments priced using CreditGrades, we use the new equity price to reprice the

instrument based on the CreditGrades model.

However, if the spread shift is applied to calculated spreads, it may not be immediately clear what we should

do if the user wants to pass equity shifts on to CreditGrades spreads. Should we reprice the instrument by

shifting the CreditGrades spread according to the spread shift, or by shifting the equity and rerunning the

CreditGrades model? To answer this, we observe that if we choose to apply the spread shift, the behavior

would be exactly the same as if the user hadn’t chosen to pass equity shocks on to CreditGrades instruments.

Thus, the better choice in this case is to have the equity shift override the spread shift, and to reprice the

instruments directly through the CreditGrades model, using the new equity price.

Finally, it is probably worth mentioning in this section that the option to pass equity shifts on to CreditGrades

spreads should apply to historical and user-defined stress tests as well. If the user asks to pass on equity

shocks to CreditGrades spreads in stress testing, we implement this exactly as above (reprice the instruments

using the CreditGrades model, taking the new equity price as an input). Note that for these stress tests,

passing an equity shock to CreditGrades spreads is the only way to change the price of an instrument priced

using CreditGrades, because the stress tests are defined through risk factors only, and there is no available

option to shift calculated spreads directly.

3.5 Risk Type Drilldown

We should also include spread risk in the risk type drilldown for stress test statistics. This should separate

out the spread component from the current IR risk component in the drilldown. The spread component of the

risk should be calculated by applying any spread shift (either to spread risk factors or to calculated spreads),

but not the interest rate shift. The interest rate component will be calculated by applying the interest rate

shift but not the spread shift. Note that if we are shifting both interest rates and spread risk factors, then we

apply two shifts to risky yield curves to calculate the total stress test PV or PV delta, and one shift for each

of the interest rate and spread drilldowns.

References

[1] RiskMetrics Research Department, Generalized pvbp extension and generalized stress tests, Research

Technical Note.

[2] , Generic bond, Research Technical Note.

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