“Adjustment Disorders” post crisis

Credit Value Adjustment (CVA) is a challenge and itself is a complicated topic to handle. While money managers concern themselves with what moves an instrument value and the cost of financing the position, CVA traders have to care much more, seemingly assuming the dual roles of a middle office responsible for counterparty credit risk “monitoring” (not talking about the predefined PFE limits, but the risk-neutral pricing of exposures they have with clients before we monitor if the “risk-adjusted exposure” exceeds risk appetite) and of a front office responsible for pricing a market-risk capital charge on all trades that “internal” trading desk will be quoting to its external clients. Yes, a profitable positions puts the CVA trader in a bad light, accused of overcharging its internal trading desk quotes when its rightful duties is to hedge its counterparty risk upfront into bid-ask quotes.
The role of CVA

role of cva desk.png


That said, CVA provides the reserve the bank needs to save itself when either one of its large counterparty runs off before footing the bill. Unlike CCP that resolves the bill after a member gone concern, CVA ensures the bill is paid upfront by its client. Basel III regulatory framework and IFRS13 accounting standards emphasis the need for CVA post GFC, given that 2/3 of defaults during GFC were caused by MTM. Upfront charges is hence legal and mandatory before business and it has become the duty of clients themselves to protect their credit ratings and solidify their balance sheet away from vulnerabilities deemed as likely candidates for penalty. Why this “adjustment disorder” to anyone and push of self responsibility to clients? 2008 GFC taught a painful lesson to many unsuspecting victims who believed that “too-big-to-fails” are as they sound – infallible, guaranteed AAA credit ratings, here for good. Not really. House prices fell, MBS downgraded, CDS on MBS activated, insurers’ ratings dropped, collateral agreements kicked in, bailout needed to contain default. This “adjustment disorder” is not forgotten till today as we see that the ratio of risk-neutral PD over real-world (historical) PD for AAA ratings is much higher than that for non-investment grade (BB+ and lower).
Everything about adjustment is relative, not necessarily there’s a 2-way reciprocation of collaterisation/margin funding terms

lifetime cost of OTC derivative.png
Lifetime cost of an OTC derivative.

CVA desk care about its clients credit position benchmark to theirs, their internal cost of capital and funding (after netting and offsetting segregated/IA/initial margin, remaining exposure will be offset against expected collateral balance. If non-cash collateral, there needs to be a margin-period-of-risk of at least ten days, accounting for colVA and possible disputes. For collateral received, there’s a collateral rate receiver has to pay to the giver. How much are they receiving for holding someone’s collateral that’s eligible for rehypothecation i.e. if you rehypothecate and post someone’s collateral, you are in fact repo-ing out and have to pay for the cash you indirectly borrowed or capital freed up, irregardless if there’s a need for the cash), after knowing the aforementioned, transfer pricing of insurance cost to clients upfront, and upon becoming counterparties to one another, hedging the risk that the client defaults on its outstanding exposure to the bank. Banks being always ready to deal with eligible clients, means they would enjoy the benefit of owning many collaterals from its clients along with the negotiated CSA (1-way against or favoring or 2-way) specifying the collateral terms. That said, CVA desk ought to optimise its collateral inventories by choosing the collateral to post in line with pricing the “cheapest-to-deliver” collateral.
Hedging of counterparty risk isn’t easy

As much as money managers reinvent micro, macro and alternative data as proxies as leading indicators to gain an edge, they are of no use to CVA desk if they are not marketable. Marketability means accessible, tradeable and liquid or cost-efficient. Market tradeables are single-named CDS, basket CDS, asset swap spreads, bonds or loans prices or some proxy mapping. Banks wouldn’t turn down clients because their risk profiles are not hedgeable.

Below is the set of decisions hedgers ask:

  1. If there’s a “liquid” CDS, use it directly as the credit spread = [ 1-Recovery Rate from collateral held, guarantees from parent, legals like first in line seniority) * ProbDefault[t] i.e. term structure shape determines PD over time ]
  2. Otherwise, is there another liquid benchmark (e.g. corporate bond)? If Yes, use derived credit spread with basis adjustment.
  3. Otherwise, is there a single name proxy? Is yes, use proxy possibly with some credit-spread adjustment.
  4. Otherwise, map to generic proxy.
cva mapping curve
Example decision tree in order to map a given counterparty credit spread.

Using grid style categorisation by its (rating, region, sector) relative to the bank’s unique risk profile to these categories, generic externally priced risk-neutral curves can be constructed. First, define the pool of single-name tradeable CDS satisfying a minimum liquidity threshold. Then, bucket these categories by the categories. Then, exclude outliers in each bucket and impute missing points using interpolation. Finally, construct the curve with the relevant points average weighted on the relative liquidity of each point. Third-party curve providers e.g. Markit sector curves uses these categories with cross-sectional multiplicative factor regression approach rather than credit spread mapping.

Note that only direct tradeables, despite poor liquidity, are eligible for full capital relief. Generic or single-name proxies of better liquidity providing only partial CVA (spread) variation hedge and no hedge against default is seen by regulators as inappropriate tools and hedgers receives partial or no regulatory capital relief. Given that not all counterparties are publicly listed, its expected that the use of proxy spreads would be prevalent. In Dec 2017, the European Banking Authority (EBA) estimates that proxy spreads are applied for 77% of counterparties.
Not all clients need CVA charges

The handful of black sheeps are typically clients with any OTC derivatives that are long dated, of poor quality and under- or uncollateralised. CSA includes terms such as thresholds and minimum amount to reduce frequency of collateral postings and calls. Collateral agreed to be rehypothecated should not be recalled so soon that its repo-ing out cannot buy enough time for the cash to earn its term premium, at least, if collateral poster is paying risk-free OIS without term premium. Wide minimum amounts reduces chances of rehypothecated collaterals being called back or substituted with alternatives but increases the likelihood of undercollaterised outstanding exposures. High thresholds given to highly rated clients is analogous to extending an undrawn credit line that’s costless with unsecured funding costs (FVA) and no collaterisation, ignoring the independent amount (aka initial margin) posted at the origin.
Funding Value Adjustment (FVA) relationship with CVA

Relationship between BCVA (CVA and DVA) and FVA (FCA and FBA). The dotted lines represent thresholds in the collateral agreement for each party.

Most of the time, CVA desk hedge trades are collaterised. So if that trade with client is under- or uncollaterised, funding benefit is incurred if client’s position is ITM – as would CVA desk hedging position (same as client’s) be ITM – resulting in receiving of collateral and OIS payments from the collaterised leg with the hedge trade while not requiring to post any collateral on the client’s trade.

The origin of funding costs and benefits. A bank trades with a client with no collateral arrangement and hedges with collateralised transactions.

Assuming allowing the reuse of collateral, funding costs arise from the uncollateralised (+) MTM of a portfolio i.e. unrealised profit yet to receive and therefore has to be funded. By contrast, the uncollateralised (-) MTM creates a funding benefit i.e. unrealised loss that have not pay and therefore is extra fund.

If collaterised, funding cost arise if funding exposure is (+) i.e. MTM > collateral posted, vice versa for funding benefit.

collaterised FVA.png

Defining the funding spread to use in the FVA formula is difficult

Derivatives, due to their dynamic nature and the funding approach of banks, are not term-funded. Traditionally, the funding has been generally considered to be short-term, but regulation (e.g. LCR and NSFR) is pushing banks to rely less on short-term funding. Overall, this means that a party defining their appropriate funding curve represents a difficult and subjective problem.

The first is that funding costs represent credit risk and yet credit risk has already been priced in via CVA. The second is that the funding cost applied to a derivative transaction should be the incremental one and not the average funding cost of the party in question. Indeed, this is why many assets have no funding costs, since they can be effectively self funded via repo.

When buying poor-quality assets, lenders should be charged a higher funding rate than for high-quality assets: the quality of the derivative should drive the asset’s funding cost. But the quality of a derivative portfolio is already priced in with the CVA. Furthermore, FVA creates a problem for accountants, since a party’s own cost of funding does not represent the correct component to be included in an exit price.

Differing funding rates together with the CDS–bond basis with respect to the OIS rate (Note: Bond-CDS basis is negative, though not necessarily true always)

FVA debate resolved

One important idea is that only the funding liquidity risk premium should be priced into FVA. This is the result of Morini and Prampolini (2010), who state that this liquidity spread (or equivalently the CDS–bond basis) contributes as a net funding cost to the value of a transaction.

If the CDS spread is assumed to be a “pure credit spread” reflecting only default risk, then the liquidity component of the credit spread equals the negative of the CDS–bond basis. This is often known as liquidity value adjustment (LVA), which might be defined to account for “liquidity related costs not already accounted for by the CVA”.

Role of FVA in the risk premium add on

Factors that drive the CDS–bond basis aka FVA

  • CDSs have significant wrong-way risk (e.g. One european bank acting as issuer of CDS for another european bank such that insurer ability to insure weakens when the covered company defaults) which tends to make the basis negative.
  • CDS are unfunded/uncollateralised so funding at levels above LIBOR tends to make the basis positive.
  • Bonds that can be borrowed for short lending are typically sourced from a liquid and short-dated repo market. They usually trade special as they are highly demanded and widely eligible across legal legislation hence making the basis positive.
  • Credit events are vulnerable to divergence from CDS legal documentation, despite improvements by ISDA in standardisation.
    • Technical credit events may cause CDS protection to pay out on an event that is not considered a default by bondholders, which tend to make the basis positive i.e. bond value appreciates
    • Alternatively, a credit event may not kick in even if bondholders take credit losses, which tends to make the basis negative i.e. bond yield rise further
  • The “Cheapest-to-deliver” option in a CDS contract may have some additional values in certain circumstances, such as restructuring credit events. This would tend to make the basis positive.
  • A delivery squeeze involves a shortage of CDS deliverable debt and would tend to make the basis negative i.e. strong demand for bonds.
  • Fixed-rate bonds can trade significantly above or below par because of changes in interest rates. CDS protection is essentially indexed to the par value of a bond and bonds trading above (below) par will tend to make the basis negative (positive). The use of fixed coupon CDS reduces this effect.
  • In the event of default, a bond typically does not pay accrued interest for any coupons owed, whereas a CDS does require protection buyers to pay the accrued premium up to the credit event. This cause the basis to be negative.

CVA Calculation

CVA is a risk-neutral conditional expectation actualized losses. Risk neutral as it uses current market pricing (ProbDefault) which discounts for risk premium expectations, conditional as it assumes counterparty defaults at time t, actualised loss with positive expected exposure at time t, ceteris paribus.


Here, it considers the correlation between the bank exposure and the credit quality of the counterparty (+ = Wrong Way Risk i.e. exposure EE(t) and default risk PD(t) increase together). This meant measure introduces the joint distribution of market factors and the credit factors that drives the potential default of the counterparty.

CVA is not an addictive measure like VaR due to possible netting benefits at portfolio level from the new trade and the existing trades. This arise due to the netting and collateral agreements that prevail on some OTC transactions, and also due to the asymmetric nature of the credit exposure (OTM MTM => EE = 0 ). That said, the sequence of trade execution would optimise the subsequent CVA charge. A favorable sequence would avoid stacking of correlated trades back-to-back.

Therefore, the Desk has to compute CVA and credit Exposures on both trade and portfolio levels.

Full simulation-based pricing incorporates all aspects (netting, collateral and portfolio effects) can only be done accurately with simulation-based approaches that can run an entire group of transactions (typically at the counterparty level but potentially at the portfolio level). Practically, this requires a simulation engine that can generate all relevant market variables and compute values of the current transactions and the new transaction in all required scenarios through time. This requires very rapid processing power and/or use of significant data storage.

CVA Value per trade is a must have requirement for:

  • Better decision making at trade inception: ensure incremental CVA is positive to Global CVA
  • Allocation purposes after the deal is done : Global CVA is then decomposed as the sum of individual Marginal CVA

CVA Desk assignment could be sum up as follow:

  • At Pre deal level: Being able to deliver on demand to the Trading Desk an incremental CVA expressed as a spread
  • During the lifetime of the deal : integrating in real time executed trades in the global CVA process
  • At post trade level: Analyzing Global CVA and Marginal CVA per trade
  • Managing the CVA portfolio: Hedging the CVA variation (detecting Wrong Way Risk, convexity correlation), satisfying the legislation in terms of capital charge allocation.

Further adjustments to CVA could arise due to:

  • Warehousing good credit risk that would generate profits i.e. default is unlikely and upfront charge can used as rebates to subsidise subsequent trades
  • Favorable work-out process i.e. reputable legals, seniority in claims, clear recourse instructions
  • Expectations of more profitable or higher volume trades from the client, or early terminated trades such that CVA cost will not be realised
  • Capital relief if the counterparty risk is easy to hedge
  • Relaxation or tightening of regulations
  • Changes in rating or internal policy affecting cost of capital and funding

Predict and explain P&L changes in relation to xVA

This is a common requirement for CVA desks to understand the performance of their hedging and the source of any material unhedged moves. “P&L explain” aims to decompose the P&L changes into simple drivers that may be related to market movements that can be hedged or changes to contractual terms or data that cannot.

The following components to be included in a P&L explain for xVA:

  • Market risk:
    • time decay (theta)
    • deltas (e.g. rates differentials tom-next swap, FX forward curve convergence)
    • volatility (vega i.e. CVA are typically partial counterparty risk hedge and its volatility are covered by CVA capital charges)
    • credit spreads (i.e. generic curve mapping if direct CDS not tradeable)
    • cross-gamma correlation (convexity exposure due to confounding factor affecting 2 legs thought to be independent and hence vertical spread may not be an effective hedge after origin)
    • default events
    • funding and capital costs
  • Trading decisions:
    • new transactions (incremental CVA)
    • unwinds (marginal CVA, which is cheapest to unwind)
    • novations (e.g.. backloading risk, replacing bilateral contract with 1 counterparty with a contract with a CCP, bilateral to mulilaterial netting with correspondents, CCP to another CCP)
    • terminations
    • exercise decisions
  • Contractual terms and other changes:
    • changes to netting terms (definition of “hedging set” and what is eligible for netting, how much haircut or discounting of correlation with a floor if its only reliable as a partial hedge? Types of netting: close-out on default, master, cross-products, cross-affliate e.g. UBS-Lehman)
    • changes in collateral terms (CSA renegotiation e.g. quarterly regular restriking or termination to keep PFE add on small and free up capital)
    • rating changes (leading to a change in credit spread curve mapping?)
    • model changes or recalibration of semi-static parameters (e.g. mean reversion)


  • The xVA Challenge – Counterparty Credit Risk, Funding Collateral and Capital (Jon Gregory)
  • BCBS 424: Basel III: Finalising post-crisis reforms
  • Finaxium: Basle III and CVA measure impacts

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