Client engineering of XVA in crisis and normality: Restructuring, Mandatory Breaks and Resets
CClient engineering of XVA in crisis and normality:Restructuring, Mandatory Breaks and Resets
Chris Kenyon ∗
27 September 2020Version 1.10
Abstract
Crises challenge client XVA management when continuous collater-alization is not possible because a derivative locks in the client creditlevel and the provider’s funding level, on the trade date, for the life ofthe trade. We price XVA reduction strategies from the client point ofview comparing multiple trade strategies using Mandatory Breaks or Re-structuring, to modifications of a single trade using a Reset. We analyzeprevious crises and recovery of CDS to inform our numerical examples.In our numerical examples Resets can be twice as effective as MandatoryBreak/Restructuring if there is no credit recovery. When recovery is atleast 1/3 of the credit shock then Mandatory Break/Restructuring can bemore effective.
Crises challenge client XVA management when continuous collateralization isnot possible because a derivative locks in the client credit level and the provider’sfunding level, on the trade date, for the life of the trade. We price XVA reductionstrategies from the client point of view comparing multiple trade strategies usingMandatory Breaks, Restructuring, to modifications of a single trade using aReset. Multiple trade strategies are inefficient when there is no credit changebecause later trades have XVA priced in without including the probability ofclient survival, because only surviving clients will enter into continuation trades.Pricing from the client point of view is necessary because continuation tradesin multiple trade strategies are invisible to the provider by definition. This ∗ 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. Cer-tain information contained in this presentation has been obtained or derived from third partysources and such information is believed to be correct and reliable but has not been inde-pendently 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. a r X i v : . [ q -f i n . P R ] S e p eans that pricing must use risk-neutral measures, and real-world-conditionalrisk neutral measures. We analyze previous crises and recovery to inform ournumerical examples on CDS shock sizes, and how long it takes a firm’s CDS torecover by how much.We price from the client perspective so P measures are important. All P measures are subjective as they depend on user-chosen criteria, e.g. the cali-bration, or back-testing setup. Our approach is to provide a mix of P -measureinformation, and scenarios to allow clients to assess risks of alternatives, not tocollapse this information within an expectation. This is because clients do nothedge own-credit and provider-funding, so we do not want to pre-judge whichscenario is most important to clients. This also avoids the anchoring effect ofgiving a single number since clients are not hedgers, unlike banks..For credit shocks and recovery we analyze a comprehensive CDS database(2002 – 20020) and give the historical P measure of shock recovery against timefrom shock for different shock sizes, see Table 1. This analysis defines the rangeof credit recovery and timing we use in results Tables 2 and 3. A vaccine forSARS-CoV-2 may be months (Krammer 2020) away, and recovery from previ-ous economic shocks generally took six months to 2–3 years. In the numericalexamples we consider CVA on an interest rate swap (IRS). The P -conditional Q measure is less important than might be expected because continuation tradesare done at-the-money (ATM) so changes in rates levels are largely factored out.We address changes in rates volatility by scenario analysis in Table 4.Pricing of derivatives from the client point of view seems to be absent in theliterature, probably because clients are assumed to be price takers. However,as we demonstrate, clients can chose which prices (instruments) they take andwhen, to achieve their objectives. This moves their price taking decisions intothe realm of multi-stage stochastic optimization (Birge and Louveaux 2011) forportfolios. However, we are interested in a simpler setup. Design of hedgingstrategies for clients is a typical service provided by banks and informed byjoint assessment of scenarios and risks. Derivative pricing taking into accountnon-financial institution actions is typical to capture prepayment in MortgageBacked Securities (Sirignano, Sadhwani, and Giesecke 2016). Similar consider-ations apply for pricing revolving credit facilities, but the published literatureis almost non-existent.The contributions of this paper are firstly to price XVA from the client pointof view which enables comparison of multiple trade and single trade XVA reduc-tion strategies. We provide a precise characterization of the required probabilityspaces, and conditional probability spaces. Secondly, we compare: restructur-ing; Mandatory Breaks; and Resets. Thirdly we provide a quantification of CDSshocks and recoveries from history to inform choices of strategies and timing.Finally we give numerical examples to quantify trade-offs of different strategies.XVA reduction strategies must be priced from the client point of view and thisis almost unique in the XVA literature. We first give definitions and contract examples using Mandatory Break/Restructuringand Reset, then the probability framework. We price from a client shareholdervalue point of view, not from a firm value point of view. That is, we assume2he client has no interest in events after their own default.
Definition 2.1.
Mandatory Break • A Mandatory Break is a legal agreement to end a derivative on the datespecified, at the current market price, and is part of the termsheet. • The market price is defined as the price of the derivative ignoring defaultrisk and funding costs.Reset has the same effect as a Mandatory Break post-trade providing XVArebates are available. In Mandatory Break and Reset the original contract stopsand a new contract is entered for the remaining life of the original trade. Sincethe new contract is only required by a surviving client the default probabilityresets as shown in Figure 1 MIDDLE, RIGHT. The other key difference with aReset is that the credit and funding levels are also reset to whatever the currentlevels are at the time of the start of the new contract. The profiles for Resetand Mandatory Break after 3 years are slightly different because the Reset isin the Q -measure and the Mandatory Break continuation exposure is in the P -conditional- Q -measure where we have picked the same-as-now future P measure.Section 2.3 provides a rigorous setup. Definition 2.2.
Reset • A Reset is a legal agreement to change some aspect of the trade on thedate specified such that the NPV becomes zero, and payment of the NPVdifference at the current market price, and is part of the termsheet. • The market price is defined as the price of the derivative ignoring defaultrisk and funding costs.A multiple trade strategy occurs with Mandatory Break, because thereis a second trade after the Mandatory Break. This second trade we call the continuation trade . This is also true for restructuring.Figure 1 shows the exposure and default probability profiles of the vanillatrade (TOP), then the effects of a Mandatory Break/Restructuring (MIDDLE)and Reset (BOTTOM).
Client valuation of trades with Resets is the same as that of the provider, thereare no uncertainties in the price of CVA and FVA.Client valuation of trades with Mandatory Break/Restructuring includes thecontinuation trade after the Mandatory Break. The continuation trade couldbe with a different provider to the original trade, and must be estimated by theclient. The market will also have moved by the Mandatory Break date so theclient also needs to estimate this effect. With a crisis the client aims to put theMandatory Break after the crisis so as not to lock in the crisis-level credit andfunding risks for any longer than necessary.3 .0 2.5 5.0 7.5 10.0Years0.020.010.000.010.02
Bank viewEPE, ENE and EV
Bank viewDefault probability
MB: Client viewEPE, ENE and EV
MB: Client viewDefault probabilityNo change in CDS
Reset: Bank viewEPE, ENE and EV
Reset: Bank viewDefault probability
Figure 1: TOP/LEFT: EPE, EV, and ENE profiles for 10y ATM EUR IRS with unit notional as of 2020-05-29.TOP/RIGHT: default probability curve. The curve gives the probability of default for the next 6m. MID/LEFT:EPE, EV, and ENE profiles for same trade with a Mandatory Break after 3y and the profiles for the new 7yATM IRS continuation trade assumed by the client that the bank uses from 3y to 10y. MID/RIGHT: defaultprobability curve used by the bank from t to 3y, and the default probability curve assumed by the client thatthe bank uses from 3y to 10y. BOTTOM/LEFT: EPE, EV, and ENE profiles for same trade with a Reset after3y. BOTTOM/RIGHT: default probability curve used by the bank from t to trade maturity.4hen clients use Restructuring, they wait and observe the market beforeacting. Choosing to potentially restructure later needs to be included in theoriginal assessment of XVA to compare strategies. We assume equivalence withMandatory Break here for simplicity, i.e. there is 100% rebate available ondemand for XVA.Thus clients view XVA from a future conditional measure perspective forMandatory Break/Restructuring, because they do not hedge their own defaultand they do not hedge their derivative provider’s funding cost and they assumetheir own survival. This requires the following probability development. To handle client valuation in the P measure conditional on their survival weintroduce the probability space X = (Ω , F , P )on a set of events Ω with a filtration F ( t ) and corresponding probability mea-sures P ( t ). The equivalent probability space with a risk-neutral measure is Y = (Ω , F , Q ) P ( t ) are the physical measures from the point of view of t . Given a MandatoryBreak date t m and a set of events (path) up to t m , ω ∈ F ( t m ), we define setsof conditional probability spaces from X as X ω = { (Ω ω , F ω , P ω ) | ω ∈ F ( t m ) } (1) X ω,C = { (Ω ω,C , F ω,C , P ω,C ) | ω ∈ F ( t m ) and τ C > t m } (2) τ C is the default time of the counterparty.Ω ω are all possible events, conditional on the set of events ω up to t m . F ω is the filtration F conditional on the set of events ω up to t m . P ω ( t ) are the probability measures P ( t ) for t ≥ t m , conditional on the set ofevents ω up to t m .Hence X ω is the set of all future probability spaces at t m , indexed by thestate of the world ω up to t m , and X ω,C is the set of all future probability spaceswhere the client survived up to and including t m . This modifies (Ω ω , F ω , P ω )to (Ω ω,C , F ω,C , P ω,C ) by adding the additional conditioning.Figure 2 illustrates the probability spaces X and X ω = ω a for a specific ω a .The vertical State axis indicates the multi-dimensional state of the world. Linesindicate which states are reachable from each other. We have chosen a recom-bining tree because it makes it easier to display F and F ω a . In the contextof the Figure, X ω,C consists of those conditional probability spaces where theclient does not default on the possible paths ω up to t m . So, for example, itmay be that only some of the points at t m exist in ∪ ω { Ω ω,C } considering all ω in F up to t m .Now for the probability spaces in X ω , or X ω,C , we can create sets of equiv-alent risk-neutral probability spaces Y ω , or Y ω,C , i.e. Y ω = { (Ω ω , F ω , Q ω ) | ω ∈ F ( t m ) } (3) Y ω,C = { (Ω ω,C , F ω,C , Q ω,C ) | ω ∈ F ( t m ) and τ C > t m } (4)5 imeState TimeState t m Figure 2: Illustration of unconditional (LEFT), and conditional (RIGHT) prob-ability spaces. LEFT: X = (Ω , F , P ), where Ω = dots, F =lines. RIGHT, X ω a = (Ω ω a , F ω a , P ω a ) for a specific ω a in F up to t m where ω a =red path;Ω ω a =green dots because only these are reachable from ω a ; F ω a =green lines, asthese are the only futures reachable from ω a . In X ω a ,C , Ω ω a ,C will be the emptyset if the client C defaulted along the path ω a , otherwise Ω ω a ,C = Ω ω a .These Y ω and Y ω,C are equivalent to X ω and X ω,C because they see the sameevents, same filtrations, but have different measures, and agree on sets of mea-sure zero (Shreve 2004) Definition 1.6.3. For example Q ω,C are found by cali-brating to the future P ω,C measure observables at t m for each ω ∈ F ( t m ) and τ C >t m . t Here we give the normal pricing, i.e. without Mandatory Break or Reset. Thiscovers pricing with Reset as this contract is priced in its entirety at t .Derivative providers price XVA as the risk-neutral expected loss of a deriva-tive, or portfolio, from counterparty default and the funding cost whilst thetrade is alive. We assume independence of exposure and default for simplicity.Following (Burgard and Kjaer 2014), the XVA at inception is:CVA( t ; t , T ) = L GD (cid:90) u = Tu = t λ ( u ) e (cid:82) s = us = t − λ ( s ) ds E Q (cid:2) D r F ( u )Π + ( u ) (cid:3) du (5)FVA( t ; t , T ) = (cid:90) u = Tu = t s F ( t ) e (cid:82) s = us = t − λ ( u ) ds E Q [ D r F ( u )Π( u )] du (6)CVA( t ; t , T ) means that the CVA is calculated at t for exposure from t to T and similarly for FVA. We make the definitionXVA Q ( t ; t , T ) := CVA( t ; t , T ) + FVA( t ; t , T ) (7)where we include the measure that the XVA used for clarity. Also: λ ( t ) = counterparty hazard rate.Π + = positive exposure of position w.r.t. counterparty. r F ( t ) := s F ( t ) + r ( t ) = Bank funding cost, and separation into fundingspread and riskless rate.Since trades end on their Mandatory Break dates, XVA is calculated up tothe Mandatory Break date of the derivatives with Mandatory Breaks, and to6he full term with Resets, where T is the date of the last payment. To continuethe trade after a Mandatory Break the client must enter a new trade and payXVA on this continuation trade. t > t To price Mandatory Breaks from the client point of view we need to price thetrade and XVA after the Mandatory Break/Restructuring as well as the tradeand XVA before the Mandatory Break/Restructuring.Clients do not hedge their own default probability nor the funding cost ofthe provider so they value XVA in the real world, i.e. the P -measure. Clientswill only enter into a trade after a Mandatory Break if they survive so we needto consider this.A key factor in Mandatory Break valuation is the setup of the continuationtrade after the Mandatory Break. Typically this will be at the money (ATM),not at the previous level. The settlement at the Mandatory Break date providesthe hedge against changes in riskless value from changes in market level. Thisis the functional hedge aspect of the trade in action.Assuming a single trade, without a Mandatory Break the XVA, here CVAand FVA, cost to a client is just Equation 7:XVA Client ( t ; t , T ) = XVA Q ( t ; t , T ) (8)The Reset case is covered by the above when the exposures within Equations 5and 6 are from the resetting trade.With a Mandatory Break at t m the client cost is the sum of the XVA on thetrade with the mandatory break, and the later continuation trade to originaltrade maturityXVA MBClient ( t , ω ; t , T ) = XVA Q ( t ; t , t m ) + XVA Q ω,C ( t m ; t m , T ) (9)XVA MBClient ( t , t m ; t , T ) is a random variable because it depends on the futurestate of the world via the events up to t m , i.e. ω , and the client survival upto t m within Q ω,C . As we saw above, Q ω,C is a future risk-neutral measuredependent on earlier P measures.The client cannot hedge XVA Q ω,C ( t m ; t m , T ) at t with the street at a pricethe client will accept because the client considers that the observed CDS curvedoes not reflect the client’s recovery post-crisis. Also, counterparties may bereluctant to trade CDS referring to the client with the client. In short, theclient’s view is that supply and demand for their CDS does not reflect futurecredit risk levels, but includes additional premia. Another way of saying this isthat the client does not calibrate the drift of their P measures to the currentobserved CDS curve.Below we look at examples of how the Mandatory Break changes the totalXVA cost to the client, MB( t m , ω ), as a function of the Mandatory Break date t m and the assumptions on recovery, i.e. P ω,C MB( t m , ω ) := XVA Client ( t ; t , T ) − XVA
MBClient ( t , ω ; t , T ) (10)= XVA Q ( t ; t , T ) − (cid:16) XVA Q ( t ; t , t m ) + XVA Q ω,C ( t m ; t m , T ) (cid:17) (11)7e characterize classes of ω by the change in credit spread of the client at t m relative to t .We now look at historical CDS shocks and recovery to inform the numericalexamples. Here we analyze CDS shocks and their recovery. The CDS universe used is pre-selected for a minimal level of liquidity, starts in May 2002 and ends May 2020.The main indicator we use is the maximum of the 1Y and 5Y CDS spreads toallow for CDS curve and liquidity changes under stress.We want to detect shocks that are significant to firms and recoveries thatare usable for hedging purposes, so data is prepared as follows to reduce effectsof noise, insufficient data, and missing data. • Only consider names from three regions, Asia, Europe, and North Amer-ica, because these have the largest number of active names ( >
500 each). • Remove any name that has less than 2.1 years’ data. 2.1 as a cutoff isderived from the window of 1 year for detecting shocks and the 1 yearno-detect period after a shock detection. Gaps are permitted and linearlyinterpolated. We use a window size of one year so if there is less than twoyear’s data the name will not provide a useful contribution. • Apply a 21-point median filter. This takes the median across a month sothat the results are not affected by daily noise.Data preparation reduces the initial dataset from 10.1m observations to 6.6mand the total number of names from 5.4k to 3.4k. Very roughly half of the namesare active on any given date. Obviously the results may be biased towards liquidnames so this caveat should be included in making any use of the results in thispaper.We define a shock in historical CDS as: • A shock for an individual company is an increase of CDS spread over apast window of at least a given size, where this shock occurs at least onewindow period after any previous shock. – The window period chosen is one year. – We look at shocks sized 250bps, 500bps, and 1000bps. Shock size ismeasured asshock size := CDS(t) − quantile(10% , { CDS( u ) : t − ≤ u < t } )(12) • A crisis for the market is when the percentage of CDS names undergoingshocks is at least a given percentage of active CDS names. • Recovery is the change in CDS spread at fixed horizons after a shock foran individual company. – Change in CDS spread at 6m, 1y, 2y, 3y, 4y, and 5y horizons aftereach shock. 8 P e r c e n t o f a c t i v e C D S w i t h s h o c k Crisis periods from CDS responsesover last one year
Figure 3: Percent of active names with shocks over the last year. Differentcolors correspond to different shock sizes: 250bps = green, 500bps = black, and1000bps = red. Crisis periods are shown by lowered levels of the blue curve.Small variations of this definition have no effect on results. – CDS spread change at each horizon is defined as the change to themedian CDS level at ±
5% of the horizon. This is to model clientshaving some flexibility on exactly when to transact any re-hedge, i.e.considering horizon h with a shock date of t :CDS spread change :=quantile(50% , { CDS( u ) : t + 0 . × h ≤ u < t + 1 . × h } ) − CDS(t) (13)The blue line in Figure 3 shows the definition of market crises used: 6% ofactive names with at least a 250bps shock in the last one year. This definitionwas chosen to highlight the periods with elevated percentages of CDS withshocks. Small variations of this definition have little effect on results.
We first describe historical recovery from shocks and then give effects of alter-native XVA management strategies.
Table 1 gives the quantiles of distribution of changes in CDS spreads as definedin Equation 13 for horizons of { } in crisis periods. Wecan observe that • Looking at the median rows (0.50s) by two years most of the initial shockis recovered. For the largest shock, 1000bps, 80% of the recovery is afterone year. 9hock 0.5y 1.0y 2.0y 3.0y 4.0y 5.0y n250.0 horizon (years) at 2y0.05 -920 -1230 -1490 -1345 -1500 -1617 16860.25 -171 -251 -316 -331 -337 -347 16860.50 -28 -160 -205 -176 -212 -233 16860.75 171 62 -91 -81 -93 -152 16860.95 1331 1728 417 380 437 175 1686shock 0.5y 1.0y 2.0y 3.0y 4.0y 5.0y n500.0 horizon (years) at 2y0.05 -1370 -2293 -2433 -2277 -2462 -2769 8980.25 -342 -515 -613 -637 -691 -710 8980.50 -64 -350 -453 -438 -493 -534 8980.75 352 -9 -262 -266 -307 -416 8980.95 3140 2951 741 475 487 132 898shock 0.5y 1.0y 2.0y 3.0y 4.0y 5.0y n1000.0 horizon (years) at 2y0.05 -1546 -2750 -3361 -2943 -3317 -3026 4690.25 -715 -1042 -1241 -1199 -1280 -1378 4690.50 -237 -812 -953 -915 -999 -1096 4690.75 773 -89 -714 -658 -797 -936 4690.95 6557 5194 822 334 792 -221 469Table 1: Quantiles of distribution of changes in CDS spreads from shocks forhorizons of { } in crisis periods. All shocks and changesare in bps. The number of shocks in the last column (n) for the 2y horizon. Thefirst column gives the quantile of the distribution of the change in CDS spread.We display { } quantiles.10 At least 5% of the time there is no recovery. Things get worse. •
25% of the time there is mild recovery until five years when most of theshock is recovered. For the largest shock, even in the 25th percentile 70%of the recovery is present by two years.There appears to be survivor bias in this analysis since we only observeCDSs that do not default. However, from a Mandatory Break point of viewthis is correct because in the case of default the client is not concerned abouttrade renewal. That is, we only want to consider cases where the client survives.There is no bias from the Mandatory Break use and design perspective.We now have a quantification of both recovery and risk or degree of recoveryfrom historical CDS shocks. Now we need to add the CVA quantification w.r.t.Mandatory Break and to bring the two parts together.
We now look at XVA management strategies informing the range of our analysisby the timescale of shock recovery, i.e. 1-5 years, in the previous section andthe sizes of the observed shocks and recoveries, i.e. 250 to 1000bps.We consider an example 10 year EUR IRS as of 2020-05-29, where the clientreceives the floating rate. This is typical in that it provides the client withprotection from increases in interest rates, and EUR is currently at historicallylow levels, although rates can go down as well as up beyond previous levels.When pricing forward XVA we assume that the current interest curve andvolatility is the same at the Mandatory Break point. This assumption is oftencalled same-as-now as opposed to risk-neutral where, for example, we wouldmove up the yield curve. We also consider changes in volatility at the MandatoryBreak point below. We compare with using a Reset which is priced at t socannot benefit from later changes of client credit risk but as mentioned abovehas the advantage of using conditional survival probability for the part of thetrade after the reset (and all times in fact). Table 2 shows the XVA reduction as a percentage of XVA charge without aReset for Reset points at 1y to 5y and CDS shocks of 500bps and 1000bps.Note that the CDS level is locked in for the whole life of the trade. In thisexample the change in exposure from the different reset dates roughly balancesthe different default probabilities. There is a 20% to 25% reduction in XVA forReset points at 1 to 5 years. This reduction has little dependence on the CDSlevel.Since the trade has a Reset there is no dependence on the P measure, orlater realized CDS levels or realized interest rate volatility levels. We assume that the continuation trade is ATM. Table 3 shows the reduction inXVA compared to a trade without a Mandatory Break, or post-trade restruc-turing. We assume that the restructuring rebate pays 100% of the XVA andis available. The continuation trade is at the future CDS level of the client, so11DS level 1 2 3 4 5IRS maturity dVol shock reached reset point (years)10 0.0 500.0 600.0 19.9 24.9 24.2 20.7 16.01000.0 1100.0 21.8 24.8 22.1 17.5 12.5Table 2: XVA reduction as a percentage of XVA charge without a Reset forReset points at 1y to 5y and CDS shocks of 500bps and 1000bps. Note that theCDS level is locked in for the whole life of the trade. dVol of zero means thatthere is no change to the interest rate volatility.CDS level 1 2 3 4 5maturity dVol shock reached CDS change mandatory break point (years)10 0.0 500.0 600.0 -250.0 -4.4 2.0 4.9 5.9 5.70.0 12.6 15.9 15.7 13.8 11.1125.0 23.5 24.5 22.2 18.5 14.2250.0 36.4 34.5 29.7 23.8 17.6500.0 69.4 59.4 47.7 36.0 25.41000.0 1100.0 -500.0 -2.9 -3.1 -4.0 -4.2 -3.70.0 7.6 6.5 4.2 2.5 1.4250.0 16.7 14.2 10.4 7.2 4.8500.0 29.4 24.5 18.5 13.2 8.81000.0 71.8 57.0 42.3 29.7 19.5Table 3: XVA reduction as a percentage of XVA charge without a MandatoryBreak for Mandatory Break points at 1y to 5y and CDS shocks of 500bps and1000bps. We also consider CDS change at the time of entering into the continu-ation trade. Interest rate volatility and yield curve same-as- t for continuationtrade. Negative reductions indicate increases.we include a range of possibilities, including improvement and worsening. Evenwith significantly worse CDS levels there is little increase in total XVA, lessthan 5%. For as-is CDS levels the Mandatory Break is roughly half as effectiveas a Reset. This is because the surviving client at the Mandatory Break datepays XVA without the benefit of the conditional survival probability: defaultingclients simply have no need of the continuation trade.When the CDS level improves after the initial shock the reduction in XVAcan be two to three times the reduction from a Reset. For a 500bps shock,starting from 100bps, the break-even w.r.t. a Reset is roughly an improvementof 1/4 of the shock. For a 1000bps shock the break-even is roughly 1/3 ofthe shock. The XVA reduction pattern is almost always better with a shorterMandatory Break date, provided the CDS level has improved.Table 4 shows XVA reduction as a percentage of XVA charge without aMandatory Break for Mandatory Break points at 2y for CDS shocks of 500bpsand 1000bps. We also consider CDS change at the time of entering into thecontinuation trade. Interest rate volatility differences covered are -10bps to+10bps, whilst the yield curve is same-as- t for continuation trade. We observethat there is significant interplay between the volatility effect and the CDS12Vol -10.0 0.0 10.0maturity shock reached split CDS change volatility change (bps)10 500.0 600.0 2 -250.0 18.8 2.0 -14.80.0 29.3 15.9 2.4125.0 35.9 24.5 13.1250.0 43.5 34.5 25.6500.0 62.4 59.4 56.51000.0 1100.0 2 -500.0 13.5 -3.1 -19.70.0 20.8 6.5 -7.8250.0 26.7 14.2 1.6500.0 34.6 24.5 14.51000.0 59.2 57.0 54.8Table 4: XVA reduction as a percentage of XVA charge without a MandatoryBreak for Mandatory Break points at 2y for CDS shocks of 500bps and 1000bps.We also consider CDS change at the time of entering into the continuationtrade. Interest rate volatility differences covered are -10bps to +10bps, whilstthe yield curve is same-as- t for continuation trade. Negative reductions indicateincreases.change effect as we would expect as both are important in XVA. As the CDSrecovery increases there is less relative effect of change in volatility. Here we have considered client XVA management using either Mandatory Breaks/Restructuring or Resets as tools adapted for recovery from crises and normaltimes respectively, and the cross-over between them. Restructuring are similarin XVA effects to Mandatory Breaks but can be done on any date if the provideragrees and if an XVA rebate is given. The issue when CDS levels are high isthat a derivative locks in the client credit risk level and the provider’s fundinglevel on the trade date, for the life of the trade.Analysis of historical crises defined by CDS shocks 2002–2020 shows thatrecovery is largely complete two years after the initial shock considering themedian CVA recovery. For 500bps shocks the 75% of the names recover by atleast half by two years, with 5% showing continuing deterioration.We found that if the CDS level does not recover, or if there was no shock inthe first place, then a Reset for a 10y IRS is roughly twice as effective in reducingXVA as a Mandatory Break. If the CDS level improves for the client by even1/3 of the shock to the CDS level, then a Mandatory Break or restructuring isat least as good as a Reset, and can be several times better. Analysis of CDSshock recovery from historical crises indicates that this level of recovery occursin at least 75% of cases.Pricing from the client point of view answers whether a Mandatory Breakand then a continuation contract is a true break, i.e. two separate contracts,or just a single contract in practice. For both parties the riskless price of thecontinuation trade after a Mandatory Break is different seen from the originalstart date compared to the continuation from a Reset, because it is a Q -in- P Q measure price. We provided a precise definition of therelevant probability spaces and measures. Also the client faces higher XVA witha Mandatory Break than with a single contract containing a Reset. These differ-ences are invisible when pricing from the usual bank point of view because thenonly the contract up to the Mandatory Break is priced. However the client hasto compare using a Reset in a single trade, or a Mandatory Break/Restructuringwith two sequential trades.Hedge accounting is highly relevant and will be covered elsewhere in detail(Kenyon and Kenyon 2020). A key aspect is that Accounting can follow the“entitys risk management objective and strategy for undertaking the hedge” sois not limited to contracts that exist at some particular time, e.g. at originaltrade inception. This objective and strategy requires “formal documentation”by the entity, see (IFRS 2018), Section 6.4.1.b and must meet hedge effectivenesstests in Section B6.4.1 including effects of credit risk in Section B6.4.7.This paper is almost unique in taking the client’s perspective in XVA val-uation using a real-world perspective, rather than considering valuation fromthe provider’s side in the risk-neutral perspective. However, consideration ofMandatory Break makes this a requirement as the provider is indifferent (allrisk is hedged) whereas the client is exposed to changes in their own credit riskand the providers funding risk. Since we are currently in the Covid-19 crisis asdefined by CDS shocks we have considered Mandatory Break valuation from thispoint of view, i.e. within a crisis from the historical CDS analysis. During nor-mal times, or for clients unaffected by XVA, with no significant changes in CDSlevel a Reset can be twice as effective as a Mandatory Break or restructuring. The author would like to gratefully acknowledge discussions with Kohei Ueda,Hayato Iida, Robert Wendt, Susumu Higaki, Muneyoshi Horiguchi, RichardKenyon. and Dott. Donatella Barisani.
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