CVA related concepts: |
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A Credit valuation adjustment (CVA), [lower-alpha 1] in financial mathematics, is an "adjustment" to a derivative's price, as charged by a bank to a counterparty to compensate it for taking on the credit risk of that counterparty during the life of the transaction. CVA is one of a family of related valuation adjustments, collectively xVA; for further context here see Financial economics § Derivative pricing. "CVA" can refer more generally to several related concepts, as delineated aside. The most common transactions attracting CVA involve interest rate derivatives, foreign exchange derivatives, and combinations thereof. CVA has a specific capital charge under Basel III, and may also result in earnings volatility under IFRS 13, and is therefore managed by a specialized desk.
In financial mathematics one defines CVA as the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty's default. In other words, CVA is the market value of counterparty credit risk. This price adjustment will depend on counterparty credit spreads as well as on the market risk factors that drive derivatives' values and, therefore, exposure. It is typically calculated under a simulation framework. [4] [5] (Which can become computationally intensive; see [lower-alpha 2] .)
Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation can be written as
where is the maturity of the longest transaction in the portfolio, is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity , is the loss given default, is the time of default, is the exposure at time , and is the risk neutral probability of counterparty default between times and . [7] These probabilities can be obtained from the term structure of credit default swap (CDS) spreads.
Assuming independence between exposure and counterparty's credit quality greatly simplifies the analysis. Under this assumption this simplifies to
where is the risk-neutral discounted expected exposure (EE):
The full calculation of CVA, as above, is via a Monte-Carlo simulation on all risk factors; this is computationally demanding. There exists a simple approximation for CVA. This consists in buying default protection, typically a Credit Default Swap, netted for each counterparty. [8] The CDS price may then be used to back out the CVA charge.
The CVA charge may be seen as an accounting adjustment made to reserve a portion of profits on uncollateralized financial derivatives. These reserved profits can be viewed as the net present value of the credit risk embedded in the transaction. As outlined, under IFRS 13 changes in counterparty risk will result in earnings volatility; see XVA § Accounting impact and next section.
In the course of trading and investing, Tier 1 investment banks generate counterparty EPE and ENE (expected positive/negative exposure). Whereas historically, this exposure was a concern of both the Front Office trading desk and Middle Office finance teams, increasingly CVA pricing and hedging is under the "ownership" of a centralized CVA desk. [9]
In particular, this desk addresses volatility in earnings due to the IFRS 13 accounting standard requiring that CVA be considered in mark-to-market accounting. The hedging here focuses on addressing changes to the counterparty's credit worthiness, offsetting potential future exposure at a given quantile. Further, since under Basel III, banks are required to hold specific regulatory capital on the net CVA-risk, the CVA desk is responsible also for managing (minimizing) the capital requirements under Basel.
Value at risk (VaR) is a measure of the risk of loss of investment/Capital. It estimates how much a set of investments might lose, given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses.
In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs).
Credit risk is the possibility of losing a lender holds due to a risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased collection costs. The loss may be complete or partial. In an efficient market, higher levels of credit risk will be associated with higher borrowing costs. Because of this, measures of borrowing costs such as yield spreads can be used to infer credit risk levels based on assessments by market participants.
A swaption is an option granting its owner the right but not the obligation to enter into an underlying swap. Although options can be traded on a variety of swaps, the term "swaption" typically refers to options on interest rate swaps.
In finance, a swap is an agreement between two counterparties to exchange financial instruments, cashflows, or payments for a certain time. The instruments can be almost anything but most swaps involve cash based on a notional principal amount.
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Financial modeling is the task of building an abstract representation of a real world financial situation. This is a mathematical model designed to represent the performance of a financial asset or portfolio of a business, project, or any other investment.
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: Mathematical finance § Derivatives pricing: the Q world for discussion of the mathematics; Financial engineering for the implementation; as well as Financial modeling § Quantitative finance generally.
The following outline is provided as an overview of and topical guide to finance:
The term Advanced IRB or A-IRB is an abbreviation of advanced internal ratings-based approach, and it refers to a set of credit risk measurement techniques proposed under Basel II capital adequacy rules for banking institutions.
Loss given default or LGD is the share of an asset that is lost if a borrower defaults.
Exposure at default or (EAD) is a parameter used in the calculation of economic capital or regulatory capital under Basel II for a banking institution. It can be defined as the gross exposure under a facility upon default of an obligor.
Collateral has been used for hundreds of years to provide security against the possibility of payment default by the opposing party in a trade. Collateral management began in the 1980s, with Bankers Trust and Salomon Brothers taking collateral against credit exposure. There were no legal standards, and most calculations were performed manually on spreadsheets. Collateralisation of derivatives exposures became widespread in the early 1990s. Standardisation began in 1994 via the first ISDA documentation.
Damiano Brigo is a mathematician known for research in mathematical finance, filtering theory, stochastic analysis with differential geometry, probability theory and statistics, authoring more than 130 research publications and three monographs. From 2012 he serves as full professor with a chair in mathematical finance at the Department of Mathematics of Imperial College London, where he headed the Mathematical Finance group in 2012–2019. He is also a well known quantitative finance researcher, manager and advisor in the industry. His research has been cited and published also in mainstream industry publications, including Risk Magazine, where he has been the most cited author in the twenty years 1998–2017. He is often requested as a plenary or invited speaker both at academic and industry international events. Brigo's research has also been used in court as support for legal proceedings.
Expected loss is the sum of the values of all possible losses, each multiplied by the probability of that loss occurring.
Basel III is the third Basel Accord, a framework that sets international standards for bank capital adequacy, stress testing, and liquidity requirements. Augmenting and superseding parts of the Basel II standards, it was developed in response to the deficiencies in financial regulation revealed by the financial crisis of 2007–08. It is intended to strengthen bank capital requirements by increasing minimum capital requirements, holdings of high quality liquid assets, and decreasing bank leverage.
Under the Basel II guidelines, banks are allowed to use their own estimated risk parameters for the purpose of calculating regulatory capital. This is known as the internal ratings-based (IRB) approach to capital requirements for credit risk. Only banks meeting certain minimum conditions, disclosure requirements and approval from their national supervisor are allowed to use this approach in estimating capital for various exposures.
An X-Value Adjustment is an umbrella term referring to a number of different “valuation adjustments” that banks must make when assessing the value of derivative contracts that they have entered into. The purpose of these is twofold: primarily to hedge for possible losses due to other parties' failures to pay amounts due on the derivative contracts; but also to determine the amount of capital required under the bank capital adequacy rules. XVA has led to the creation of specialized desks in many banking institutions to manage XVA exposures.
In finance, a zero coupon swap (ZCS) is an interest rate derivative (IRD). In particular it is a linear IRD, that in its specification is very similar to the much more widely traded interest rate swap (IRS).
The standardized approach for counterparty credit risk (SA-CCR) is the capital requirement framework under Basel III addressing counterparty risk for derivative trades. It was published by the Basel Committee in March 2014. See Basel III: Finalising post-crisis reforms.