Climate Change Valuation Adjustment (CCVA) using parameterized climate change impacts
CClimate Change Valuation Adjustment (CCVA)using parameterized climate change impacts
Chris Kenyon ∗ , Mourad Berrahoui † Abstract
We introduce Climate Change Valuation Adjustment to capture cli-mate change impacts on XVA that are currently invisible assuming typicalmarket practice. To discuss such impacts on XVA from changes to instan-taneous hazard rates we introduce a flexible and expressive parameteriza-tions to capture the path of this impact to climate change endpoints, andtransition effects. Finally we provide quantification of examples of typicalinterest where there is risk of economic stress from sea level change upto 2101, and from transformations of business models. We find that evenwith the slowest possible uniform approach to a climate change impact in2101 there can still be significant XVA impacts on interest rate swaps of 20years or more maturity. Transformation effects on XVA are strongly de-pendent on timing and duration of business model transformation. Using aparameterized approach enables discussion with stakeholders of economicimpacts on XVA, whatever the details behind the climate impact. ∗ Contact: [email protected]. This paper is a personal view and does notrepresent the views of MUFG Securities EMEA plc (“MUSE”). This paper is not advice.Certain information contained in this presentation has been obtained or derived from thirdparty sources and such information is believed to be correct and reliable but has not beenindependently verified. Furthermore the information may not be current due to, among otherthings, changes in the financial markets or economic environment. No obligation is acceptedto update any such information contained in this presentation. MUSE shall not be liable inany manner whatsoever for any consequences or loss (including but not limited to any direct,indirect or consequential loss, loss of profits and damages) arising from any reliance on orusage of this presentation and accepts no legal responsibility to any party who directly orindirectly receives this material. † Contacts: [email protected]. The views expressed in this presenta-tion are the personal views of the author and do not necessarily reflect the views or policiesof current or previous employers. Not guaranteed fit for any purpose. Use at your own risk. a r X i v : . [ q -f i n . P R ] F e b ontents Climate change risk comprises physical, transition, and liability risks to assets,companies and sovereign entities (Bank of England 2019; European CentralBank 2020). Credit valuation adjustment (CVA) quantifies expected loss oncounterparty default (Green 2015; BCBS 2021), and the costs of funding arecaptured in funding valuation adjustment (FVA), together XVA. However, CVAand FVA are based on extrapolation of credit default swap (CDS) spreads whichare typically traded only up to 10 year maturity, see Table 1, and inclusion ofbond trading where available.We introduce Climate Change Valuation Adjustment (CCVA) to capturethe difference in expected loss and funding between usual credit informationextrapolation and the parameterized inclusion of economic stress from climatechange endpoints and transition effects. The parameterization we introduceflexibly captures both climate endpoints, and transition effects. We show that Market implied counterparty default probability is inferred from spreads oftraded credit default swaps (CDS), augmented by bonds where available. How-ever, few CDS are traded beyond 5 years and almost none beyond 10 years.Many counterparties, e.g. project finance, have no CDS and so are priced andhedged primarily from CDS proxies. For these cases CDS indices are partic-ularly important. Table 1 shows volumes for CDS indices from a Swaps DataRepository . CDS indices are more traded than single name but not definedbeyond 10 years: we see 98% of trading volume is for maturities up to 5 years.Given the lack of data, market practice is to use some form of extrapolationbeyond 10 years. Ratings may inform bond prices and proxy CDS curves, butcorporate ratings typically have a three to five year look ahead (Fitch 2020). Since CCVA is based on model predictions rather than tradable instrumentsit is a P -measure quantity. Standard CVA may be thought of as a Q measurequantity. However, because of the lack of hedging beyond 5 to 10 years it is amix between replication-based pricing and a measure represented by the CDSextrapolation. We shall label this measure given by market practice of CDSextrapolation Ξ (Xi for eXtrapolation). umulative percentage by indexon DTCC 2021-01-21 to 2021-02-19 1 2 3 4 5 6 7 8 9 10 Credit:Index:CDX:CDXEmergingMarkets 0% 0% 0% 7% 100%Credit:Index:CDX:CDXHY 0% 1% 2% 5% 100%Credit:Index:CDX:CDXIG 0% 1% 3% 9% 98% 98% 98% 98% 99% 100%Credit:Index:iTraxx:iTraxxAsiaExJapan 0% 0% 0% 9% 100%Credit:Index:iTraxx:iTraxxAustralia 0% 0% 0% 20% 100%Credit:Index:iTraxx:iTraxxEurope 1% 3% 7% 10% 98% 98% 98% 99% 99% 100%Credit:Index:iTraxx:iTraxxJapan 0% 0% 0% 0% 100%
Grand Total 0.5% 1.8% 3.9% 8.5% 98.5% 98.6% 98.8% 98.8% 99.0% 100.0%CDS maturity rounded to neared year
Table 1: Cumulative CDS transaction volume for indices referring to corporates on DTCCover a recent 30-day period, 2021-01-19 to 2021-02-20. DTCC is a US Swaps Data Repositoryso sees mostly US transaction. CDS indices are more traded than single-name CDS.To discuss, precisely, the origin of Climate Change Valuation Adjustment, inSection 2.4 we introduce appropriate probability spaces and measures to capturemarket practice and inclusion of possible climate change endpoints.
To be able to discuss and compare paths of economic stress to climate endpointswe introduce a sigmoid parameterization of the instantaneous hazard rate evolu-tion S (1 has peak , ( t start , h start ); m, w ; u, ( t end , h end )), Section 4 gives details. Thisparameterization is expressive enough to cover different paths of economic stressbuildup, see Section 4.3. The parameterization flexibly connects the longesttraded CDS maturity and level, with the climate change endpoint, by allowingspecification of the mid point m of the stress and the width w of the stressbuildup. If we specify that instead of ending at a high hazard level the curve re-turns to the original level, i.e. 1 has peak is true, then the same parameterizationmodels transient transition effects.In this way we capture approach to default and transition with a single setof parameters. These parameters can be specified for each counterparty of abank for example by by internal risk management, or a regulatory body forall banks, to define climate change scenarios independent of the details of thedriving mechanisms. We pick one subset of climate effects defined by endpoints to demonstrate howClimate Change Valuation Adjustment can be calculated and provide a sce-nario analysis to gage the range of possible impacts on example interest ratesswaps with maturities from 10 to 50 years. The climate effects subset we pickis where it is reasonable to expect project finance or sovereign or sub-sovereignto have significant changes in default probability because of sea level change.By sea level change we include frequency of storm effects, and consider thatinfrastructure may be below ground level. For example tunnel entrances for aport city could be below sea level regularly at the climate end point in 30 to40 years. Although sea level rise puts the entity below sea level this does notmean the entity will be flooded (Estrada, Botzen, and Tol 2017). Mitigatingactions can be taken, but these create economic stress. CCVA captures thisadditional economic stress beyond market implied from constant CDS extrap-olation. Although some aspects of climate change may be contained within arating assigned to a project, because the CDS only go out 10 years this eithermisses later effects, or creates a distorted picture by moving risk beyond 10years to within 10 years.We pick a second subset of climate effects where there are transition stresses.That is, the corporate experiences a limited duration of economic stress duringa transformation of it’s business model. In this case we quantify XVA impactsw.r.t. the mid point of the stress and the width of the stress. As mentionedabove this is the same parameterization as the sigmoid curve, but specifyingthat hazard rates return to normal, rather than ending high.
We will define the CCVA as climate related expected loss and funding thatis not already captured by the usual market implied CVA and FVA. ThusCCVA captures the difference between a combined market implied and physicalmeasure expected loss considering the economic impact of climate change, versusa typical bank market implied expected loss from constant CDS extrapolationof hazard rates. In order to make this definition precise we must first describeand define the concepts and probability spaces involved. Before this we recallsome aspects of reduced form default modeling and the three lines of defensemodel typically used within banks for curve marking as well as aspects of theCDS market.
CVA
Market Implied does not incorporate climate related risk where this has effectbeyond 5 or 10 years because of how CVA
Market Implied is calculated. CVA
Market Implied is based on CDS data. CDS data is market-based up to 5 or 10 years and thentypically extrapolated flat judging by data from CDS runs (i.e. strips of trade-able CDS quotes) and CDS data providers. Note that CDS data providerstypically provide extrapolated CDS values using their own internal model be-yond 10 years when they have insufficient contributors, obviously this is nottradable data. We capture the climate change difference of CVA
Climate Change above market CDS with flat extrapolation using CD.CVA, and the similar effecton FVA by CD.FVA defined below in Sections 2.4 and 3.CVA
Market Implied is priced using a market-implied methodology but it is nothedged in practice beyond 10 years judging from trade repository data, e.g.from DTCC . Thus banks face climate change, and other, risks on derivativesover 10 years because banks do not hedge these risks in the CDS market in asmuch as trade repositories are reflective of trading.Regulations require that derivative transactions are recorded and this databe publicly available in many jurisdictions, in the US this was a consequence ofDodd-Frank (Congress 2010). We model default and probability of default using a reduced form approach,rather than a structural approach. We use a reduced form approach because itis the standard in the front office and because it is more suitable for pricing,hedging, and risk management (Jarrow 2011). We briefly describe the twoapproaches below: reduced form
Default is modeled using an exogenous process, usually someform of marked point process. structural
The balance sheet of the entity is modeled and default occurs whenliabilities exceed assets.Reduced form models can be directly calibrated from, and hedged by, marketobserved Credit Default Swaps where they exist.
Most banks have a three lines of defense system for curve marking where thecurves affect PnL or risk. This is part of the market-implied pricing methodol-ogy. Thus there are strong controls around curves used for pricing which lockin market assumptions and practice. • Traders, the first line of defense, are responsible for CDS curve markingfor PnL of all positions. They have the responsibility for observing themarket and the setting the curve at the place where they believe they cantrade. • Product control, the second line of defense, are responsible for validatingthat the traders’ marks reflect where traders can trade. This involvesmarket surveillance and may include requiring traders to trade to verifythat they can trade at the prices where they mark their curves. Productcontrol are also typically responsible for holding reserves against othercosts such as bid-ask spread, price impact, etc. If product control aremarking price related items then there will be another second line groupthat validates these marks. • Internal audit are responsible for monitoring the processes whereby tradersmark the curves and product control and other validation groups validatesthese marks.Accounting rules like IFRS 13 (IASB 2016) require banks to price derivativesas other market participants would price them. This is largely based on the ideaof exit prices, i.e. what would another bank pay in a non-forced situation forthe product? 6 .4 Market-implied measure and physical measures
Market data may define a unique market implied measure, but physical measuresare always subjective as they derive from a choice of calibration. The results ofthese calibrations may have to pass regulatory requirements but regulations aresubjectively decided by committees.We want to be able to price CVA and FVA as banks normally price them andto price CCVA. For normal bank pricing we introduce the probability space: X = (Ω , F , P )on a set of events Ω( t ) with a filtration F ( t ) and corresponding probabilitymeasures P ( t ). The equivalent probability space with a risk-neutral measure,given that the last traded CDS maturity is T , is Y Q Ξ ( T ) = (Ω , F , [ Q ; T ; Ξ])on events Ω ≤ T = Ω( t ) s.t. t ≤ T with filtration F ≤ T = F ( t ) s.t. t ≤ T and riskneutral measure Q on F T . Note that the risk neutral measure only exists for t ≤ T . We introduce the measure Ξ for t > T on events Ω >T = Ω( t ) s.t. t > T with filtration F >T = F ( t ) s.t. t > T . Ξ is defined as a measure in which non-credit items can be hedged but credit items cannot be hedged but are pricedassuming that CDS’s are extrapolated flat. We assume independence of creditand non-credit events for simplicity.Note that Ξ is not P , even for t > T . Ξ can be thought of as an extrapolationof Q following the rule that CDS quotes are extrapolated flat, or according toa Bank’s internal methodology.To capture what may actually happen we introduce the probability spacecombining the risk neutral measure before T and the physical measure after T : Y QP ( T ) = (Ω , F , [ Q ; T ; P ])Obviously a bank can roll CDS hedges, but the roll takes place in the conditionalrisk neutral Q ω,C measure (Kenyon 2020). There is a probability space X ω,C conditioned on events ω up to T in which the client C did not default. Q ω,C isthe equivalent risk neutral probability measure from T , within the conditionalprobability space Y ω,C . Q ω,C is not equivalent to P ( t ) s.t. t > T because thephysical measure includes events where C has defaulted and Q ω,C does not.We define CCVA relative to the usual bank calculation of CVA and FVAnot the actual hedging cost requiring repeated purchases of CDS at later dates.Repeated CDS purchases are needed due to the lack of longer-dated liquid CDSwhen the counterparty portfolio is longer than the liquid CDS. The two priceswill not be the same when the CDS curve is not flat assuming same-as-nowfutures (i.e. the CDS curve in the future looks like the one today). Now we have appropriate probability spaces and measures, we can define valua-tion adjustments based on market practice, based on including climate change,and then CCVA as the difference between these.We define CVA and FVA including the measure involved, based on (Burgardand Kjaer 2013) and then specialize these with to define CCVA.7 efinition 1 (CVA and FVA under probability space Y (Ω , F , Γ)) . CVA Y (Ω , F , Γ) = E Γ (cid:34)(cid:90) u = Tu =0 L GD ( u ) λ ( u ) e (cid:82) s = us = t − λ ( s ) ds D r F ( u )Π + ( u ) du (cid:35) (1)FVA Y (Ω , F , Γ) = E Γ (cid:34)(cid:90) u = Tu =0 s F ( t ) e (cid:82) s = us = t − λ ( u ) ds D r F ( u )Π( u ) du (cid:35) (2)The usual market implied CVA and FVA based on market practice are: Definition 2 (Market implied CVA and FVA, CVA MI and FVA MI ) . CVA MI = CVA Market Implied = CVA Y Q Ξ = CVA Y (Ω , F , [ Q ; T ;Ξ]) (3)FVA MI = FVA Market Implied = FVA Y Q Ξ = FVA Y (Ω , F , [ Q ; T ;Ξ]) (4)CVA and FVA including climate change are defined similarly based on proba-bility space used. Definition 3 (CVA and FVA including climate change, CVA CC and FVA CC ) . CVA CC = CVA Climate Change = CVA Y QP = CVA Y (Ω , F , [ Q ; T ; P ]) (5)FVA CC = FVA Climate Change = FVA Y QP = FVA Y (Ω , F , [ Q ; T ; P ]) (6)Now we can define CD.CVA and CD.FVA as the difference between the ver-sions including climate change and market implied (i.e. flat CDS extrapolation).The sum of the differences is the CCVA. Definition 4 (Climate Change Valuation Adjustment, CCVA, and climatechange differences in valuation adjustments for credit and funding) . CCVA = CD.CVA + CD.FVA (7)CD.CVA = CVA
Climate Change − CVA
Market Implied = CVA Y QP − CVA Y Q Ξ (8)CD.FVA = FVA Climate Change − FVA
Market Implied = FVA Y QP − FVA Y Q Ξ (9)These definitions capture what is not in the market implied valuation ad-justments. If market practice changes so that climate change is included then,e.g. CVA Climate Change = CVA
Market Implied , and the differences will be zero.Here we highlight was is not currently included. Below we estimate the size ofCCVA for a particular subset of entities where the calculation may be easiest.Note that CCVA will be less than zero for cases where climate change hasbeneficial effects for the entity concerned.
We introduce a sigmoid parameterization of how instantaneous hazard rates ap-proach a stressed climate change endpoint, i.e. maximum instantaneous hazardrate. With a very slight adjustment we can use exactly the same parame-terization for transition stresses where there is transient increase in economicstress before returning to normal. The parameter 1 has peak is True for transitionstresses and False for approach to a stressed endpoint. This parameterization8nables discussion of how climate change affects counterparty default and cal-culation of CCVA.The idea is that a 5 year CDS is available and fixes a constant Q measureinstantaneous hazard rate for the first 5 years, since this is the most liquidinstrument. Following this Q -measure section there is a sigmoid approach todefault for the P measure instantaneous hazard rate. We pick a sigmoid as thisis common in nature to describe approach to a limit and can express a widevariety of approach to default, see Section 4.3. The sigmoid parameterization is shown in figure 1 with parameters described inTable 2. The resulting curve is S (1 has peak , ( t start , h start ); m, w ; u, ( t end , h end )).Note that if the slope of the last section is greater than the slope of the midsection, then h mid end is reduced so there is a straight line between ( t mid start , h mid start )and ( t end , h end ). This is because it is physically reasonable to have a jump ininstantaneous hazard rates in the transition from the Q section to the P sec-tion, but there is no particular justification for such a jump at the end of the P section. The Q section is that covered by traded CDS, i.e. t = 0 to t = t start .The P section is the rest, i.e. the sigmoid. u (h start – h end ) w m(t start , h start ) (t end , h end )u (h start – h end ) (t mid end , h mid end )(t mid start , h mid start ) Figure 1: Sigmoid parameterization for the approach of instantaneous hazardrates to default, S (1 has peak , ( t start , h start ); m, w ; u, ( t end , h end )), with 1 has peak False. See Table 2 for details.
The sigmoid parameterization for a transition effect where economic stress re-turns to normal is shown in Figure 2. Parameters described in Table 2, exceptthat 1 has peak is now True. The resulting curve is S (1 has peak , ( t start , h start ); m, w ; u, ( t end , h end )). Figure 2 also defines the parameters9 arameter Example value Description has peak False m
40 years time to mid-impact w
20 years width of middle section( t start , h start ) (5, 0.0170) coordinates of end of Q measure sectionand start of P measure section that ap-proaches default( t end , h end ) (80, 0.2000) coordinates of end of impact u
10% fraction of impact ( h end − h start ) for ini-tial increase, and final approach to h end Table 2: Sigmoid parameterization for the approach of instantaneous hazardrates to default, S (1 has peak , ( t start , h start ); m, w ; u, ( t end , h end )). Note that ifthe slope of the last section is greater than the slope of the mid section, then t mid end is reduced so there is a straight line between ( t mid end ) , h mid start ) and( t end , h end ). See Figure 1 for graphical view using the example parameters. u (h start – h end ) w m(t start , h start ) (t end , h end )(t mid end , h mid end )(t mid start , h mid start )(t mid mid , h mid mid ) Figure 2: Sigmoid parameterization for modeling of transition stress uses thesame parameters, S (1 has peak , ( t start , h start ); m, w ; u, ( t end , h end )), but now with1 has peak True. See Table 2 and Section 4.2 for details. Now h end = h start , h mid end = h mid start and t mid mid = m = ( t mid start + t mid end ) / .3 Expressivity Figure 3: Examples of sigmoid parameterization expressivity. Subfigure titles,e.g. ”Slowest”, refer to the build up of economic stress expressed as instanta-neous hazard rates. See text for details.Different parameter settings of S (1 has peak , ( t start , h start ); m, w ; u, ( t end , h end ))give different ways that instantaneous hazard rates can approach default when1 has peak is False. I.e. S (1 has peak , ( t start , h start ); m, w ; u, ( t end , h end )) parameter-izes the link between physical and economic climate change effects for the entityunder consideration.The range of possibilities displayed in Figure 3 is described below. Slowest
Set: m = ( t end + t start ) / w = w max = ( t end − t start ) /
2, with u = 0.Economic stress increases continuously at slowest possible continuous rate. Slowest with jump
Set: m = ( t end + t start ) / w = w max = ( t end − t start ) /
2, with u >
0. There is a jump in economic stress on changingfrom Q measure to P measure and then economic stress increases contin-uously at slowest possible continuous rate. Early
Set w < w max and m < ( t end + t start ) / u ≥
0. Economic stressbuilds up earlier and then reaches a limit that can be close to default.
Late
Set w < w max and m > ( t end + t start ) / u ≥
0. Economic stressbuilds up later and then reaches a limit that can be close to default.When 1 has peak is True m moves the mid point of the stress in time, and w changes the duration of the transition stress.11 Numerical Examples
We consider climate change end point test cases using the sigmoid parame-terization of approach to default of instantaneous hazard rates. The first setof cases we quantify are those where the entity has reasonable expectation ofdefault from continually increasing economic stress caused by rising sea level.Examples of such entities include low-lying coastal cities, and associated specialpurpose vehicles (SPVs) used for essential infrastructure, such as roads, bridges,tunnels, housing, etc.The second set of cases we consider are transition risks where the economicstress of the transition occurs from 20 to 70 years in the future and has aduration of 1 to 10 years. We do not need to consider transition stresses within10 years because we assume that CDS are traded to 10 years and that the Bankcan fully hedge XVA up to 10 years.
We quantify effects on at the money (ATM) USD interest rate swaps (IRS)using the setup below: • first context: IRS associated with an entity with reasonable expectationof default from rising sea level. Examples of such entities include low-lying coastal cities, and associated special purpose vehicles (SPVs) usedfor essential infrastructure. • second context: IRS associated with an entity that transforms its busi-ness model in response to climate change and so has transient elevatedeconomic stress from the transition. • uncollateralized trade. This is typical for infrastructure projects via SPVs. • climate change end points considered: 30 to 80 years (to 2101) • maximum instantaneous hazard rate at climate change endpoint: 2500basis points (bps). This roughly corresponds to a forward CDS level of20%. It is rare to observe entities with CDS above 20% for extendedperiods. • recovery rate on CDS, 40%. This may appear strange if the climate changeendpoint results in negative relative sea level effects. However, as wedemonstrate below, economic stress (probability of default) will probablyresult in earlier default and at these earlier default times there may stillbe significant positive recovery. • IRS length: 20 to 50 years. Thirty years may be a reasonable maximumfor SPVs, we include longer maturities in case these are associated withsovereign or sub-sovereign entities. • Funding spread is 100bps, flat • We assume traded CDS out to 10 years, flat, at 100 bps.12aturity CDS(linear hazard) (bps) survival(linear hazard) survival(flat hazard)0.5 100.0 99.17 99.171.0 100.0 98.35 98.352.0 100.0 96.72 96.723.0 100.0 95.12 95.124.0 100.0 93.55 93.555.0 100.0 92.00 92.007.0 100.0 88.99 88.9910.0 100.0 84.65 84.6515.0 114.0 74.64 77.8820.0 138.0 60.55 71.6530.0 180.0 31.04 60.6540.0 203.0 11.40 51.3450.0 212.0 3.00 43.4660.0 214.0 0.57 36.7970.0 215.0 0.08 31.1480.0 215.0 0.01 26.36Table 3: CDS rates implied from slowest uniform approach of instantaneous hazard rate to climate changeendpoint in 80 years, starting from CDS of 100 bps up to 10 years. shown in Figure 4. The flat CDSextrapolation is 100bps for all times. Survival probabilities are to the maturity in the first column.
Here we consider CCVA for the slowest possible approach to a default instanta-neous hazard rate that is reached by 2050 to 2100. We first consider the mostbenign example where the climate change endpoint is reached in 80 years, andthen a range of endpoint dates.
Figure 4 shows an example of slowest uniform approach of instantaneous hazardrate to climate change endpoint in 80 years starting from CDS of 100bps up to10 years, and the derived average hazard rates, and survival probabilities. Thederived CDS rates are shown in Table 3. Note that we have ignored IMM datesas these have little effect on results.We see from Figure 4 and Table 3 that even in one of the most benign exam-ples we can create, i.e. start from 100 bps up to 10Y, approach climate changeendpoint in 80Y, there are significant consequences for survival probabilities at20Y and by 50Y the survival probability has almost reached zero. In as muchas there are earlier economic consequences adapting to distant (80Y) futureclimate endpoints can have significant earlier effects.Although the CDS spreads only double at 40Y to 80Y, this is deceptive. Thereason that the CDS spreads do not increase further is that both the fee andprotection legs effectively cease to exist around 50Y, so further quotes carry noinformation. 13
10 20 30 40 50 60 70 80 years r a t e Hazard and CDS instantaneous hazard rate: interpolation to endpointimplied zero hazard rate from aboveCDS from interpolation to endpointCDS from flat hazard 0 10 20 30 40 50 60 70 80 years p r o b a b ili t y Survival probability interpolation to endpointflat extrapolation
Figure 4: Slowest uniform approach of instantaneous hazard rate to climate change endpoint in 80 years,starting from CDS of 100bps up to 10 years on LEFT above, and derived zero (average) hazard rate. OnRIGHT the derived survival probabilities.
Here we give the XVA changes considering climate change endpoints at 30 to80 years against IRS of 20 to 50 year maturities. Here the instantaneous hazardrates increase at the slowest uniform rate, i.e. a straight line from the end ofthe traded CDS at 10 years to the climate change endpoint. Hazard rates arekept constant once reaching the maximum level of 2500bps.We observe in Table 4 that there are significant effects on the CVA for allIRS, even as short as 20 years given a climate change endpoint in 2101 (i.e. 80years from 2021), of an increase of 23%. The decrease in FVA, because fundingcosts are paid for less time partly mitigates this increase, and the overall effectsis roughly a 10% increase in CVA+FVA, i.e. CCVA is roughly 10% of the valueignoring climate change. This is the most benign case.With increasing IRS length and shorter time to climate change endpoint theoverall effect is still always an increase in XVA, of up to 70% for long IRS andshortest time to endpoint, i.e. 2051.
Here we assume that the impact on the instantaneous hazard rate is aroundthe mid point of the time to the climate change endpoint. We also assume thatthere is a 5% build-up, and approach to maximum instantaneous hazard rate,i.e. u = 0 . u = 5%, i.e. there is a build-up, there is also a jump in instantaneous hazardrate at the switch from Q to P for the slowest increase.14hange in CVA %IRS length (years) 20 30 40 50width (years)20 71.0 141.0 140.0 130.030 51.0 113.0 117.0 113.040 39.0 93.0 100.0 100.050 32.0 80.0 88.0 90.060 27.0 69.0 78.0 81.070 23.0 61.0 70.0 74.0change in FVA %IRS length (years) 20 30 40 50width (years)20 -4.0 -18.0 -19.0 -21.030 -3.0 -13.0 -15.0 -16.040 -2.0 -11.0 -12.0 -14.050 -2.0 -9.0 -10.0 -12.060 -1.0 -8.0 -9.0 -10.070 -1.0 -7.0 -8.0 -9.0change in XVA %IRS length (years) 20 30 40 50width (years)20 37.0 67.0 73.0 73.030 26.0 54.0 62.0 64.040 20.0 45.0 53.0 57.050 17.0 39.0 47.0 51.060 14.0 34.0 42.0 47.070 12.0 30.0 38.0 43.0Table 4: Slowest uniform increase in hazard rate results. Changes in CVA (top),FVA (mid), and CVA+FVA (bottom), i.e. relative sizes of CD.CVA, CD.FVA,and CCVA compared to flat CDS extrapolation. Notice that increased hazardrates is beneficial for FVA but not so for CVA. FVA and CVA are different sizesso the overall result is not a simple average.15hange in CVA %, 30Y IRSIRS length (years) 20 30 40 50width (years)1 2.0 8.0 10.0 16.010 3.0 9.0 11.0 18.020 3.0 10.0 14.0 24.030 4.0 13.0 19.0 31.040 6.0 19.0 29.0 40.050 8.0 32.0 44.0 53.060 18.0 54.0 64.0 69.070 42.0 82.0 88.0 89.0change in FVA %, 30Y IRSIRS length (years) 20 30 40 50width (years)1 -0.0 -1.0 -1.0 -1.010 -0.0 -1.0 -1.0 -1.020 -0.0 -1.0 -1.0 -2.030 -0.0 -1.0 -2.0 -2.040 -0.0 -2.0 -2.0 -3.050 -0.0 -3.0 -4.0 -5.060 -1.0 -6.0 -6.0 -8.070 -2.0 -10.0 -11.0 -13.0change in XVA %, 30Y IRSIRS length (years) 20 30 40 50width (years)1 1.0 4.0 5.0 9.010 1.0 4.0 6.0 11.020 2.0 5.0 8.0 14.030 2.0 6.0 11.0 18.040 3.0 9.0 16.0 24.050 4.0 16.0 24.0 31.060 9.0 26.0 34.0 40.070 22.0 39.0 46.0 50.0Table 5: Impact around mid point to 2101 for instantaneous hazard rate, and u = 0 .
05. Changes in CVA (top), FVA (mid), and CVA+FVA (bottom), i.e.relative sizes of CD.CVA, CD.FVA, and CCVA compared to flat CDS extrap-olation. Notice that increased hazard rates is slightly beneficial for FVA butnot so for CVA. FVA and CVA are different sizes so the overall result is not asimple average. 16
10 20 30 40 50 60 70 80 years h a z a r d slowest uniform years h a z a r d impact around mid Figure 5: Slowest uniform test case approaches of instantaneous hazard rate to climate change endpoint,starting from CDS of 100bps up to 10 years on LEFT above. On RIGHT test cases when the impact isaround the mid point from now to 2101. XVA impacts are given in Sections 5.2.2 and 5.3.
Table 6 shows the effect on XVA and survival probabilities within the transitionstress t mid start to t mid end , with u = 0 .
05 and the peak hazard rate at 2500bps,for a 30 year IRS. We consider mid-transition from 15 years in the future to 75years in the future, and transition durations of 1 to 10 years. The counterpartyhas a traded CDS level of 100bps, and we imagine that the counterparty expe-riences economic stress from changing their business model to adapt to climatechange. We further assume that if they overcome the transition period thenthey have the same risk level as at the start, i.e. 100bps.We observe that there are significant impacts to XVA pricing if the transitionstress occurs up to the end of the IRS, i.e. within 30 years, but almost no effectthere after. Of course there is no effect from any transition actions up to 10years because the XVA risk is assumed fully hedged up to then.The lowest table in Table 6 provides the change in survival probability overthe transition period, whether this is 1, 5, or 10 years. This change in probabilityprovides another way to understand the impact of the transition timing andduration relative to the effects on XVA.17hange in CVA %time to mid 15.0 25.0 35.0 45.0 55.0 65.0 75.0width1 47.0 26.0 10.0 8.0 6.0 5.0 4.05 112.0 54.0 11.0 8.0 6.0 5.0 4.010 161.0 81.0 13.0 9.0 6.0 5.0 4.0change in FVA %time to mid 15.0 25.0 35.0 45.0 55.0 65.0 75.0width1 -7.0 -2.0 -1.0 -1.0 -1.0 -0.0 -0.05 -19.0 -4.0 -1.0 -1.0 -1.0 -1.0 -0.010 -29.0 -6.0 -1.0 -1.0 -1.0 -1.0 -0.0change in XVA %time to mid 15.0 25.0 35.0 45.0 55.0 65.0 75.0width1 22.0 13.0 5.0 4.0 3.0 2.0 2.05 52.0 27.0 6.0 4.0 3.0 2.0 2.010 73.0 41.0 6.0 4.0 3.0 3.0 2.0percent change in survival probabilitytime to mid 15.0 25.0 35.0 45.0 55.0 65.0 75.0width1 -9.0 -7.0 -5.0 -4.0 -3.0 -3.0 -2.05 -34.0 -27.0 -21.0 -16.0 -13.0 -10.0 -8.010 -51.0 -40.0 -31.0 -24.0 -19.0 -15.0 -12.0Table 6: Impact of transformation stress for 30 year IRS, depending on timing(mid point) and duration (width). Changes in CVA (top), FVA (mid-upper),and CVA+FVA (mid-lower), and change in default probability over the trans-formation period (1, 5, or 10 years), i.e. relative sizes of CD.CVA, CD.FVA,and CCVA compared to flat CDS extrapolation.18
Discussion
We introduce Climate Change Valuation Adjustment to capture currently in-visible economic impact on credit losses and funding from climate change inas much as this is different to market implied XVA using current CDS extrap-olation. We also provide a rigorous basis both in terms of probability spacesand measure, and in terms of contrast of potential climate change effects withmarket practice.In addition to mathematical formalism we introduce a sigmoid parameter-ization of the impact of climate change on instantaneous hazard rates. Thisprovides a way to discuss economic impacts in a uniform way, whatever thesource of modeling of the economic developments. This parameterization cancapture approach to a stressed endpoint, e.g. negative relative sea level, andalso transient transition stresses, e.g. from transformation of business model toadapt to climate change.Surprisingly, we find that even for climate change endpoints as far away as2101, if there is the slowest possible uniform increase of hazard rates then thereare significant credit impacts even on 20y IRS. We also see that the effect onFVA is opposite in sign to the effect of CVA, simply because increased defaultprobability means less time to pay funding costs. However, the overall effect isstill an increase of XVA.Transition effects, unsurprisingly, depend on when they occur and their dura-tion. Our modeling enables this to be captured with a few clearly interpretableparameters that can then form the basis of discussion with stakeholders, e.g.the risk department, or regulators.The contributions of this paper are: firstly the introduction of Climate ChangeValuation Adjustment to capture climate change impacts on XVA that are cur-rently invisible assuming typical market practice; secondly the introduction ofa flexible and expressive sigmoid parameterization to capture the path of in-stantaneous hazard rates to climate change endpoints and transition modeling;and thirdly a quantification of examples of typical interest where there is riskof economic stress from sea level change or business model transformation.
The authors would like to gratefully acknowledge discussions with Robert Wendt,Cathyrn Kelly, and Astrid Leuba.
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