Completing CVA and Liquidity: Firm-Level Positions and Collateralized Trades
CCompleting CVA and Liquidity:Firm-Level Positions and Collateralized Trades ∗ Chris Kenyon †
16 September 2010, Version 1.01
Abstract
Bilateral CVA as currently implement has the counterintuitive ef-fect of profiting from one’s own widening CDS spreads, i.e. increasedrisk of default, in practice . The unified picture of CVA and liquidityintroduced by Morini & Prampolini 2010 has contributed to under-standing this. However, there are two significant omissions for prac-tical implementation that come from the same source, i.e. positionsnot booked in usual position-keeping systems. The first omission isfirm-level positions that change value upon firm default. An exampleis Goodwill which is a line item on balance sheets and typically writtendown to zero on default. Another example would be firm Equity. Thesecond omission relates to collateralized positions. When these posi-tions are out of the money in future, which has a positive probability,they will require funding that cannot be secured using the position it-self. These contingent future funding positions are usually not bookedin any position-keeping system. We show here how to include thesetwo types of positions and thus help to complete the unified picture ofCVA and liquidity.For a particular large complex financial institution that profited$2.5B from spread widening we show that including Goodwill wouldhave resulted in a $4B loss under conservative assumptions. Whilst wecannot make a similar assessment for its collateralized derivative port-folio we calculate both the funding costs and the CVA from own defaultfor a range of swaps and find that CVA was a positive contribution inthe examples. ∗ The views expressed are those of the author only, no other representationshould be attributed.
The author wishes to aknowledge useful discussions with Roland Stamm and ShaneHughes. † Affiliation, [email protected] a r X i v : . [ q -f i n . P R ] S e p ompleting CVA and Liquidity Version 1.0 Recently bilateral counterparty valuation adjustment (CVA) [BPP09, BM05,BC10] has been introduced by a number of large complex financial institu-tions (LCFIs) leading to positive pnl effects at the firm level with increasingprobability of self-default. Additionally, [MP10, Pit10] have highlighted thesignificance of funding costs for asset pricing by including the effect of fund-ing, aka liquidity, costs into the pricing of individual assets. Here we pointout that for correct calculation of bilateral CVA additional trades mustbe included that are not booked in any system. We use two examples tomake our point concrete: costs of self-default; and funding costs of unfundedcollateralized trades. At least the second of the examples may appear para-doxical but we demonstrate that in both cases trades that are not bookedare significant. This contribution goes some way to resolving the paradoxof benefiting from your own default and completing the unified picture ofCVA and liquidity.At the firm level we consider Goodwill as an example of an asset thatis usually valued at zero after default. Whilst experts in Corporate Financewill be aware that the valuation of Goodwill is highly subjective [RW10],it is a line item on corporate balance sheets and reported regularly. Otherexamples of such firm-level assets also exist, e.g. Equity. This is also a lineitem on balance sheets and the majority of this is written down on default.Since bilateral CVA has been used to profit from spread widening on bookedtrades at the firm level, the debate on which corporate balance sheet itemsshould also be included in bilateral CVA is somewhat overdue. This papermakes a quantitative start on the debate.When a collateralized trade is out of the money collateral (often cash)must be posted, and hence funded. We quantify these funding costs for aswap in isolation. The implications at the firm level derive from netting andthe overall funding position — but without a knowledge of future fundingrequirements and costs the picture is incomplete. Collateralized trades havebeen considered in CVA calculations [Gre10] — but not in combination withtheir future contingent funding requirements. In as much as future fundingis required then these funding trades contribute to bilateral CVA. If netfunding requirements oscillated daily about zero then it would make senseto fund daily. However, banks typically do require significant short-termfunding as the crisis has made clear (this does not separate asset fundingform derivative funding). From a theoretical point of view, random walkstypically spend long periods away from their origin which would also implythe accumulation of net funding positions. Again, in as much as funding issignificant this will be funded at longer terms — precisely to avoid market A simple random walk on a d -dimensional lattice is recurrent only for d = 1 , Standard disclaimers apply.
CVA is typically calculated for trades and assets in position-keeping systems.However, significant assets and liabilities are not booked on these systems.This means that CVA is incomplete with respect to firm-level assets andliabilities. To illustrate the need for completeness, i.e. including assets thatare not in the position-keeping systems, we consider Goodwill. Goodwill is acontroversial and subjective topic in the corporate finance world. However,in as much as it is a line item on a balance sheet it is a concrete asset.Goodwill is listed on financial reports that must be kept up to date by thefirms that report it. On default of the firm Goodwill is usually reduced tozero — indeed this can happen even on near default when customers loseconfidence in a firm, or when the firm’s brand value is lost.Goodwill is not the only firm-level asset we could consider, for example afirm’s Equity is usually damaged by default as well. We work with Goodwillas our example because it fits with what we want to consider: it is a firm-levelasset (and a line item on a firm’s balance sheet); it is not booked in position-keeping systems; and it is usually valueless on firm default. However, wenote that other firm-level assets, such as Equity, should be included in anyfirm-level reporting.Typically bilateral effects at the trade level are added up and presented asfirm-level effects, leading to the phenomenon of benefitting from one’s owndefault. For consistency, if bilateral CVA is used in firm-level accountingthen it should also be applied to firm-level assets, for example Goodwill,going-concern value etc. The basic idea of bilateral CVA is to continuevaluation past the default event. This event has implications beyond just thetrades booked in position keeping systems. We can include these unbookedassets within bilateral CVA to help complete the PnL picture. We showthat including these firm-level assets in the firm-level picture significantly
Standard disclaimers apply. > A net $2.5 billion positive CVA on derivative positions, ex-cluding monolines, mainly due to the widening of XXX’s CDSspreads. We note from the LCFI annual reports from 2008 and 2009 that Goodwillwas $27B at the end of 2008 and $26B at the end of the first quarter 2009.There was no mention of negative CVA on Goodwill. Between the end of2008 and the end of Q1 2009 the LCFI’s 5 year CDS spread moved fromroughly 196bps to roughly 667bps, at the same time the LCFI’s 20 year CDSspread moved from roughly 374bps and 532bps.The fair value of Goodwill must be updated by companies from time totime according to accounting standards , rather than amortized over time.Depending on the model of future value of Goodwill a wide range of outcomesare possible. We provide a range of alternatives since there is no consensusw.r.t. CVA as we are introducing this concept (applying CVA to Goodwill)in the present paper. This illustrates the uncertainties with moving CVA tothe level of the firm. We consider the following models for the developmentof Goodwill value. AMORTIZING the updated value of Goodwill does, in fact, decreaselinearly over some fixed horizon.
CONSTANT the Goodwill has a constant value. Thus a Goodwill valueobserved today as $10M will remain $10M perpetually until default.This is the limit of AMORTIZING with an infinite horizon.
STOCK
Goodwill has a constant expected discounted risk neutral value.This effectively models Goodwill like a stock, i.e. the risk neutralfuture value of the Goodwill is the same as its present value (i.e. it isa martingale). US GAAP FAS 142, IFRS 3. N.B. the author gives no guarantees regarding thepresent interpretation: consult an appropriate professional for financial, accounting orlegal questions.
Standard disclaimers apply. GW ( t, T ) = E t (cid:20)(cid:90) s = Ts = t G ( s ) df ( t, s ) λ ( s ) e − (cid:82) u = su = t λ ( u ) du ds | F t (cid:21) where: T horizon for Goodwill CVA calculation, G ( s ) Goodwill value at time s , λ ( s ) hazard rate, df ( t, s ) discount factor from t to s ,Considering the LCFI example it appears that the LCFI do not modelfuture Goodwill value as STOCK because in this case the CVA adjustmentwould be 100%, i.e. $27 ∼ $26B or on both sets of accounts. If the LCFIpicked AMORTIZING then we must also decide the amortization maturity.We observe from Figure 1 that the Goodwill changed between 2008YE and2009Q1 by 20% to 25% depending on the effective amortization maturitychosen. In dollars this is 25% of ∼ $26B between 2008YE and 2009Q1. Thiswould have changed the sign for the CVA: the CVA goes from a benefit of+ $2.5B to a CVA loss of about $4B Note that there is a significant CVA for the Goodwill in all future Good-will models — the higher the future Goodwill the bigger its CVA.
Collateralized positions are unbooked to the degree that their future fund-ing requirements are not captured in position-keeping systems. Consider astandard swap contract, at inception its NPV is zero. On trade date ATMswaps require no funding. CVA applied to uncollateralized swaps recognizes Using Markit data (with the CDS spread increase for the Y20 point) we observed tworegimes for the CVA change result: maturity of less than 17 years; maturity of greater than17 years. Twenty years corresponds roughly to the point at which the survival probabilityof the LCFI was 20% for both dates. If we consider a conservative effective amortizationmaturity of less than 17 years then the change in their CDS curve would indicate thatthe CVA adjustment would have changed by 25% ∼
30% of ∼ $26B between 2008YE and2009Q1. This would have changed the CVA from a benefit of $2.5B to a loss of ∼ $4B.That is, substantially the same result with Markit data as with Bloomberg data. Standard disclaimers apply. P e r ce n t CVA for Goodwill, and change
Figure 1: CVA for Goodwill for a particular LCFI versus its effective ma-turity in years assuming linear amortization in practice (not by regulation)asof 2008YE (lowest full line), asof 2009Q1 (middle full line). The shadedarea represents the change from 2008YE to 2009Q1. The dashed line givesthe change in CVA for Goodwill from 2008YE to 2009Q1. This change isroughly 20% to 25%. The top, constant, line shows the CVA for Goodwillat any date assuming that the discounted Goodwill value is a martingale inthe risk neutral measure.that at later times they may be in the money and thus they require a coun-terparty adjustment. For collateralized swaps, the swap NPV itself requiresno counter-party adjustment (assuming no gap risk, and that collateral callsare made daily, and ignoring one-day moves). In reality, disputes and otherdelays create a period of several days in which the called-on value of thederivative is at risk. [Gre10] assumes 10 days, so the usual VaR methodol-ogy applies. However, we concentrate here on the funding aspects.Now, when the swap is out of the money in the future this must befunded. CVA for collateralized products has been considered in the literature[Gre10] (Chapter 5) but not including funding, and funding is the criticalpoint here since the funding trades cannot (by definition) be collateralizedthemselves. Typically, banks do not book contingent funding trades forpotential future collateral requirements. Thus the funding must come fromunsecured funding as the standard swap in our example is not an asset thatcan be placed into repo. We can make a first estimate of this cost for astandard swap by modeling its future value on coupon dates, i.e. assumingthat the collateral calls are on those dates and ignoring market movements
Standard disclaimers apply.
We consider two banks, Y and Z. A fair vanilla fixed-for-floating swap hasvalue zero on trade date. At later dates it has non-zero value, and the priceof co-terminal swaptions for a strike equal to the fixed rate in the fair swapgive the risk neutral information on how the market sees the future value ofits remaining length asof today.When a swap is collateralized bank Y receives collateral, here assumedto be cash, when it is in the money. Bank Y posts collateral when it is outof the money (OTM). This cash must be funded unsecured w.r.t. the swapconsidered in isolation. The swap itself cannot be used as collateral whenOTM since it is OTM.
We can model the cost of the collateral postings by both banks at time zeroassuming funding trades at interval τ : K = S ,β (0)SWAP FUNDING (0) = α = β − τ (cid:88) α = τ A α,β (0) E α,β [ τ ( F τ ( T α ) − F OIS τ ( T α )) × ( S α,β ( T α ) − K ) + (cid:3) (1)where: A α,β ( t ) is the value of the Annuity associated with the swap S α,β , E α,β is the expectation relative to the Annuity measure. F τ ( T α ) is the tenor τ forward rate at T α (N.B. in Annuity measure) F OIS ( T α ) is the tenor τ forward rate based on the overnight index at T α (N.B. in Annuity measure) S α,β ( T α ) fair swap rate at T α . Standard disclaimers apply. F τ ( T α ). It might be argued that a bankcan fund overnight and so only pay OIS for funding. Firstly this is onlytrue if the funding is secured. Secondly, no bank willingly gets its fundingovernight because then the slightest operational or market disruption wouldproduce immediate issues. It is normal to roll capital market funding atsome tenor (e.g. 3 months or 6 months) for the vast majority of the amount.Funding trades will be done every day, just not for a tenor of one day. Someminor day-to-day changes will be done using overnight, but only a very smallproportion of the total.We approximate Equation 1 as (ignoring for the moment the change ofmeasure for the forward rate):SWAP FUNDING ≈ α = β − τ (cid:88) α = τ τ A α,β (0) E α,β [( F τ ( T α ) − F OIS τ ( T α ))] (2) × E α,β (cid:2) ( S α,β ( T α ) − K ) + (cid:3) ≈ α = β − τ (cid:88) α = τ τ A α,β (0) E α,β [ F OO τ ( T α , T α ))] (3) × E α,β (cid:2) ( S α,β ( T α ) − K ) + (cid:3) ≈ α = β − τ (cid:88) α = τ τ A α,β (0) F OO τ (0 , T α ) (4) × E α,β (cid:2) ( S α,β ( T α ) − K ) + (cid:3) where: F OO τ ( U, V ) is the funding cost for tenor τ over overnight at time V asseen from time U .The main element to the approximation in Equation 2 is the covari-ance between the funding cost F τ ( T α ) − F OIS τ ( T α ), actually funding overovernight F OO , and the positive part of the difference in future swap prices() + . Whilst the covariance between forward and swap rates will generalbe significant for short swaps the covariance between the forward rates andthe positive difference will be much lower (because the negative part of thedifference will detract from any correlation). A secondary element to theapproximation in Equation 3 is the use, by implication, of a zero correlationbetween the funding over overnight and the forward rate. In as much asthe included forward OIS and forward CDS rates are not correlated with Standard disclaimers apply.
CVA (0) =
LGD α = β − τ (cid:88) α = τ (Survive( T α ) − Survive( T α + α )) (5) × A α,β (0) E α,β (cid:2) ( S α,β ( T α , ATM) − K ) + (cid:3) where: LGD is the loss given default of the LCFI;Survive(S) is the survival probability to time S .The logic is that the funding is only taken on providing the bank survivesto the start of a funding period, and the funding is only not paid back ifdefault occurs before the funding is rolled.Note that there is no CVA for counterparty default — the collateraltakes care of this (up to gap risk and overnight moves, see [Gre10] for moredetails). We need a funding cost to calculate CVA for collateralized trades whichare funded from the capital markets when OTM (i.e. posting collateral sohaving to raise it). Since our example LCFI above explicitly referenced CDSspreads we need to distinguish the non-CDS component of funding costs. Wedo this very simply by assuming (for both spot and forward):funding spread over overnight = credit spread + scarcity spread (6)In the commodity literature a scarcity spread is also referred to as a con-venience yield. When negative it is typically referred to as a storage cost(or yield). In general it can be positive or negative although it is usuallypositive. We assume that the scarcity spread is a market-wide phenomenonwhereas the credit spread is specific to a particular institution. Thus we canestimate the market-wide scarcity spread directly as the difference between
Standard disclaimers apply. (cid:144) (cid:144) (cid:144) (cid:144) p e r ce n t
6m Deposit (cid:45)
6m Eonia (cid:72)
BLUE (cid:76) quotes,and median bank CDS 6m (cid:72) median of 5 (cid:144) (cid:144)
15 best banks (cid:76)
Figure 3: Components to funding costs. Vertical line is on the date ofLehman default. Upper thick line is 6 month Deposit rate minus 6 monthEonia. Lower thin lines are the medians of the CDS spreads of the best5/10/15 A-rated banks with Euro-quoted CDS spreads. (N.B. the 6 monthEuribor rate is very close to the 6 month Deposit rate).the left hand side of Equation 6 and an appropriate credit spread. We as-sume that the appropriate credit spread is the average CDS spread of a setof good banks, e.g. the banks that make up the Eonia/Euribor committee.For this paper we use the median spread of the best 10 banks in theEurozone with at least an A rating to calculate the market-wide (spot)scarcity cost, see Figure 3. By ”best banks” we also mean that they had CDSspreads of less than 50bps pre-crisis in January 2008. Note that in Figure 3the scarcity cost jumps from about 50bps pre-Lehman to about 150bps justpost-Lehman. The next phase of market development is the central banksadding liquidity, so reducing the scarcity spread, and the increase in banks’cds spreads peaking around May of 2009. At this point, and at the end of2009 Q1 the scarcity spread is actually negative 50bps.It might appear from Figure 3 that there was an arbitrage opportunityaround May 2009 when banks’ cds spreads were higher than funding costs.However, this is not the case because a short position is very different to along position in terms, precisely, of funding costs. Thus it is legitimate forthe CDS curve to be above Euribor - Deposit.For forward funding costs we use exactly Equation 6 now applied to theforward credit spreads and forward funding spreads. The equation for the
Standard disclaimers apply. (cid:45) p e r ce n t Convenience Yield (cid:61) (cid:72)
Euribor (cid:45)
Eonia (cid:76) (cid:45)
CDS
Figure 4: Cash scarcity spread as (6 month Deposit rate minus 6 monthEonia) − median CDS spread of best 10 A-rated banks with Euro-quotedCDS spreads. This is negative from end January 2009 through July 2009,note however that funding costs will still be positive.forward CDS rate R α,β (0) at time zero is: R α,β (0) = LGD (cid:82) u = T β u = T α df ( u ) d ( e − Γ( u ) ) (cid:80) i = βi = α +1 τ i e − Γ( T i ) as in [BM06] where: df ( s ) is the discount factor to time s ; e − Γ( s ) = Q ( κ > s ) the survival probability to time s ( κ is the defaulttime). For our example we consider swaps traded by the large complex financialinstitution (LCFI) mentioned above on 2008 year end and 2009 quarter 1.We need overnight and tenor-based curves for building forward rates. Sinceit is easier to obtain long (i.e. 20 year) maturities for both types of swaps inEuro-land we will switch our example from USD to EUR. This example isillustrative — we are not implying anything about an actual LCFI althoughwe take inspiration from that context.It might be argued that a LCFI can fund overnight and so will onlypay OIS/Eonia/Sonia for funding. Firstly this is only true if the funding issecured. Secondly, no bank willingly gets its funding overnight because thenthe slightest operational or market disruption would produce immediateissues. It is normal to roll capital market funding at some tenor (e.g. 3
Standard disclaimers apply. (cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:230)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224)(cid:224) (cid:72) years (cid:76) p e r ce n t LCFI Forward 6m Funding Spread (cid:61)
6m CDS (cid:43)
6m Scarcity
Figure 5: Forward funding rate for the LCFI at 2008YE and 2009Q1. As aconservative estimate of the funding costs for the LCFI we use the averagevalues which are 1.0% and 3.7% respectively for all maturities.months or 6 months) for the vast majority of the amount. Funding tradeswill be done every day, just not for a tenor of one day. Some minor day-to-day changes will be done using overnight, but only a very small proportionof the total.As a base case we consider a funding spread of zero (i.e. Euribor flat,rolled semi-annually) in Figure 7. The overnight rate for the cash collateral(Eonia), is received for cash posted to the counterparty. Thus we have netfunding costs of Euribor minus Eonia. We then consider the LCFI in ourprevious example and take its funding cost over overnight to be forward 6month scarcity spread (spot is +150bps 2008YE, then spot is -50bps 2009Q1)plus the its (forward) 6 month CDS spread as appropriate in Figure 8. Notethat we estimate the forward 6 month scarcity spread by using Equation 6for forward rates.Note that the funding costs for the two sides (whether long or short) ofthe swap will not be symmetric — this is easily understood by looking atPayer/Receiver swaption prices using as strike the ATM swap level (for theoriginal swap), see Figure 6.The resulting expected funding costs for the two counterparty banks arealso shown (or alternatively the same bank on either side of a fixed-for-floating). Note that these are not symmetric. This is as expected from thefact that the ATM swap rate varies and hence the swaption prices are notequal for payer and receiver.
Standard disclaimers apply.
Swaption PricesRelative to 10Y ATM Spot Swap
Figure 6: Payer and Receiver Swaption prices (lowest and humped lines).Swaptions are for the remaining length of the swap so although the strike(constant, from 10Y ATM spot swap) is not ATM for these swaps, theirvalue decreases in the end because the referenced swap length decreases.
Figure 7. For the vanilla ATM swaps considered, funding costs (assumingfunding at Euribor flat for both counterparties, rolled semi-annually andreceiving Eonia from posted collateral), were up to 20bps to 35bps (Payer /Receiver) for 20 year maturity. Note that the funding costs are asymmetric— hence we expect ATM swaps as market traded to actually be biased.Bilateral CVA applied to the funding required for the vanilla ATM swapsconsidered showed a considerable benefit of 150bps to 200bps depending onthe side. The CVA is much larger than the funding cost because on defaultthe whole notional of the funding has a CVA whereas the funding cost is thenotional times the difference of two forward rates. N.B. this CVA benefit isclearly due to the high probability of self default of the LCFI in question.
Figure 8. We now consider the same vanilla swaps but with funding costsfor the LCFI as calculated in Section 2.3.2. The major difference is thatthe funding costs themselves are much higher (as input to the scenario) at2008YE. In addition the increase in funding costs from 2008YE to 2009Q1is large, up to 300bps for a 20 year swap.The CVA on the funding costs is substantially the same with LCFI fund-ing costs as opposed to FLAT in the previous section. This is because theCVA is dominated by the LCFI default probability which is the same in
Standard disclaimers apply. F r ac ti ono f N o ti on a l Expected Funding Costs 2008YEPayer (cid:144)
Receiver (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) F r ac ti ono f N o ti on a l Change in Expected Funding CostsPayer (cid:144)
Receiver F r ac ti ono f N o ti on a l Expected CVA on Funding Costs 2008YEPayer (cid:144)
Receiver (cid:45) (cid:45) (cid:45) F r ac ti ono f N o ti on a l Change in Expected CVA on Funding CostsPayer (cid:144)
Receiver
Figure 7: Funding at
Libor flat . upper: Payer and Receiver Swap fundingcosts for spot ATM swaps of different lengths at 2008YE. right:
Changesin Payer and Receiver Swap funding costs for spot ATM swaps of differentlengths at between 2008YE and 200Q1. lower:
CVA due to self defaulton Payer and Receiver Swap funding costs for spot ATM swaps of differentlengths at 2008YE. right:
Changes in CVA due to self default on Payerand Receiver Swap funding costs for spot ATM swaps of different lengthsbetween 2008YE and 2009Q1.both funding scenarios. Since the CVA is substantially the same betweenthe scenarios it is no surprise that the change in CVA is also substantiallythe same with different funding costs.
For the example we see that the CVA on the collateralized swaps is substan-tial as a fraction of swap notional (up to 2% for 20 year swap) and that thischanges from 2008YE to 2009Q1 but that the sign of the change dependson whether the swap is fixed-for-floating or floating-for-fixed. The CVA isalmost independent of the funding costs but (as expected) dependent on thedefault probability.
Clearly collateralized positions are netted by counterparty according to CSA(collateral support agreements). The net posting requires funding and the
Standard disclaimers apply. F r ac ti ono f N o ti on a l Expected Funding Costs 2008YELCFI as Payer (cid:144)
Receiver F r ac ti ono f N o ti on a l Change in Expected Funding CostsLCFI as Payer (cid:144)
Receiver F r ac ti ono f N o ti on a l Expected CVA on Funding Costs 2008YELCFI as Payer (cid:144)
Receiver (cid:45) (cid:45) (cid:45) F r ac ti ono f N o ti on a l Change in Expected CVA on Funding CostsLCFI as Payer (cid:144)
Receiver
Figure 8: Funding at
LCFI level above Eonia , i.e. 1.0% for 2008YE and3.7% for 2009Q1. Note the altered vertical scales for the upper plots. upper:
Payer and Receiver Swap funding costs for spot ATM swaps of differentlengths at 2008YE. right:
Changes in Payer and Receiver Swap fundingcosts for spot ATM swaps of different lengths at between 2008YE and 200Q1. lower:
CVA due to self default on Payer and Receiver Swap funding costsfor spot ATM swaps of different lengths at 2008YE. right:
Changes in CVAdue to self default on Payer and Receiver Swap funding costs for spot ATMswaps of different lengths between 2008YE and 2009Q1.positions themselves cannot, as mentioned before, be used as security forthe funding. Thus some sort of unsecured funding must be paid. At thefirm level this is generally set internally and charged by funding desks toderivatives desks.
Bilateral CVA calculated using only the trades currently booked and thenreported at the firm level leads to intuitively strange effects — such asprofiting from one’s own default. What bilateral CVA does is valuation pastthe default event of the firm. We have a number of conclusions for CVA:1. If CVA calculation goes across the firm default event then firm-levelassets that are not booked must also be included for consistency. In theparticular example where a large complex financial institution profited
Standard disclaimers apply.
Standard disclaimers apply.
Appendix: Curves and Surfaces
USD Yield Curve 20081231 and 20090331
Figure 9: USD Yield curves, the upper curve is for the earlier date.
EUR Yield Curve 20081231 and 20090331
Figure 10: EUR Yield curves, the lower curve is for the earlier date.
Standard disclaimers apply.
Euribor (cid:144)
Eonia Basis20081231 and 20090331
Figure 11: Euribor/Eonia basis. The lower curve is for the earlier date.
EUR ATM Swaption Vol 2009Q1 Σ Figure 12: EUR ATM Swaption implied volatility 2009Q1 and data points,the earlier date is similar but a little higher.Yield curves, basis curves, and swaption volatilities. N.B. we used swap-tion smile volatilities as well as the ATM surface presented below.
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