Guest post by Nandita Jhajharia and Lev Borodovsky
In banking, particularly recently, one often hears the term “Credit Value Adjustment” or CVA. Is it a new fashion trend in the world of finance world is it there more to it? Why are traders, quants, and risk officers at large institutions feverishly trying to deal with this topic all of a sudden? It turns out that the increased focus on counterparty risk after the financial crisis as well as the new Basel requirements for bank capitalization (see document) have added urgency to the CVA implementation by international banks, forcing them to focus on the topic.
What is CVA? Those researching CVA for the first time may find it a daunting task simply because a great deal of technical literature has been written on this concept - see this for example. According to Wikipedia, CVA is defined as “the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of counterparty’s default. In other words, CVA is the market value of counterparty credit risk.” This assessment of credit exposure is determined by the bilateral nature of transactions and fluctuations in asset prices. Other factors contributing to CVA valuation include market volatility and correlations across markets as well as legal settings and collateral agreements.
Imagine that you bought two long-dated over-the-counter call options on IBM. One was from JPM and the other from Joe's 1st National Bank - the same amount, strike, maturity, etc. Imagine that both options are in-the-money and your handy Black Scholes calculator says they are each worth $100 (premium value). But the Black Scholes model knows nothing about who you bought these from and what the likelihood is that you will get your money upon exercising the options. So if you try to sell them prior to exercise, the one that will be paid out by Joe's 1st National Bank will sell at a discount to the one from JPM because of the different counterparty risk. That price differential between the "riskless" counterparty and the "risky" one - when applied to a single position or a whole portfolio - is the CVA.
Indeed those who were facing Lehman as a counterparty in 2008 were asking themselves why they weren't differentiating among the dealers when pricing their swap contracts. It was time to start doing so.
The CVA measure is different from the concept of standard Credit Risk because it combines the uncertainty of exposure with the bilateral nature of exposure. It measures the risk that the counterparty to a financial contract will default prior to its expiration and will not make the specified payments. At the same time the amount of those specified payments may have increased due to market movements.
Different types of financial contracts will have different potential future exposure (see definition) profiles (due to different sensitivity to markets). Consider an interest rate swap for example. The longer the swap the more tame rates have to move and the more exposure one has to the counterparty. But as time goes on, the amount of exposure declines as the swap approaches maturity (shorter swap would have lower exposure to the market). That's why the maximum potential future exposure for a swap is about a third of its term.
On the other hand a currency swap that exchanges principal (one currency for another) at maturity will have its potential future exposure grow with time. Unlike a rate swap, the market risk on a currency swap does not diminish with time.
This potential future exposure is then combined with the probability of default of the specific counterparty over time in order to determine the CVA. That process is usually performed via a Monte Carlo simulation, particularly in situations when the counterparty credit quality is correlated with the specific market exposure in a contract. For example if you execute a long-dated gold swap with a mining firm, the potential future exposure of the swap cannot be analyzed separately from the credit quality of the mining firm.
It becomes particularly important to use simulations when a bank has multiple contracts in different markets with a single counterparty. This requires a calculation that simulates multiple markets that are correlated with each other. This makes such analysis quite challenging technically, particularly when one has hundreds of counterparties with contracts across multiple markets. There are 3 components of calculating the distribution of counterparty level credit exposure.
- Scenario Generation – future market scenarios are simulated for a fixed set of simulation dates using evolution models of risk factors
- Instrument valuation (revaluation under varying market conditions)
- Portfolio aggregation
- calculating the mark to market of the derivative contract (MTM without CVA),
- adjusting the discount rates by incorporating the credit spread (counterparty`s credit spread if the derivative is an asset or processing organization`s credit spread if the derivative is a liability),
- calculating the mark to market applying the new discount rates.
- The difference between the two mark to markets (one that includes the probability of default and one that does not) is the CVA.
CVA is the premium charged on a specific derivatives contract or a portfolio of contracts that takes into account both the volatility of the contract(s) as well as the probability of the counterparty’s default. Major banks view the implementation of this measurement as one of their top strategic priorities. In the next discussion on CVA we plan to have an overview of the Basel regulation that is adding urgency to CVA implementation at banks as well as special cases that make this implementation particularly challenging.
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