Cutting Edge introduction: pricing the CVA doom loop

Pricing the CVA doom loop

In its half-year results, Deutsche Bank revealed it had lost €94 million as the result of a capital relief programme. The loss was from credit default swap (CDS) positions that can be used to mitigate Basel III’s charge for credit valuation adjustment (CVA)  volatility – which they did, and then some. The bank’s capital requirement halved from €28 billion to €14 billion.

Whether this was worth it is a matter of opinion, but it illustrates the different uses to which derivatives can be put in the world of Basel 2.5 and III – and when sources of demand change, prices adjust. Exactly how they adjust is the subject of Pricing CDSs’ capital relief, by Chris Kenyon and Andrew Green, quants at Lloyds Banking Group in London.

It is one of the first attempts to quantify a hotly debated feedback loop between capital requirements and prices (Risk November 2011, pages 16–20, and Risk March 2013, pages 14–18). “Markets have been pricing-in capital use all year. It’s a bit of a black art, but you can sort of reverse-engineer trades you go for but missed out on, and back out all the pieces. Once you’ve accounted for everything else it’s the only logical thing left,” says the head of CVA trading at a European bank.

The article’s approach is direct: capital relief is treated as another feature of the contract. In addition to the standard premium and protection legs, a fictional third capital-relief leg is included, and priced. It gives an extra term in the fair spread equation, bumping it up according to the firm’s instantaneous cost of capital, and the size of the saving. Standardised and internal model method (IMM) approaches to the CVA charge are considered, as well as the Basel 2.5 default risk charge that uses the Basel I-based current exposure method, and for which CDSs can also reduce capital requirements.

The effect can be sizeable, say the authors. By setting different credit ratings’ typical spread levels equal to their three-legged version of the traditional spread formula, the proportions of the spread that are for default protection and capital relief can be backed out.

Only 27% of an A-rated counterparty’s CDS spread is for default protection for a dealer without model approval, with the Basel 2.5 default risk and Basel III CVA charges eating up 42% and 31% respectively. The numbers are 38%, 36% and 26% respectively when an internal model is available. As the credit ratings worsen, two competing effects mean the three legs’ proportions of the spread change little. On the one hand, the default probability goes up, and so do capital requirements. But the expected lifetime of a trade with a similarly rated counterparty goes down, and partly cancels the extra value of mitigation. A CCC-rated counterparty’s spread is split roughly evenly between the three parts, and there is little difference between standardised and IMM banks.

This is, of course, an artificial example with fixed input spreads. In reality, a bank facing higher capital consumption from a trade will simply charge a higher spread, and one that stands to benefit from a reduction in the CVA charge may be prepared to pay more. For Lloyds Banking Group’s Kenyon, that is reminiscent of another controversial adjustment (Risk April 2013, pages 14–18). “In some ways, including the effects of capital in pricing is analogous to the funding valuation adjustment (FVA), because it can be a cost or a benefit. The portfolio effects mean working out whether a trade will reduce or increase capital is complicated. The details need to be worked through,” says Kenyon.

This has some uncomfortable consequences for market – and regulatory – practice, because CDSs are used to back out implied default probabilities (PDs). So, if there is more than one price, there is more than one PD. Though this is already the case once FVA is included, the idea that capital mitigation might be behind a trend that is muddying the very data on which it relies is unlikely to go down well.

“What it means is the end of a single market-implied default probability. The unknown amount of capital relief included in CDS prices means a range of possible default probabilities, all market implied. That is going to add a level of complexity to CDS interpretation, and market-implied default probability use, for everybody,” says Kenyon.

Also this month, Hedge backtesting for model validation, by Lee Jackson, a director in the strategic risk management team at Credit Suisse, looks at the most basic question one can ask of a model – whether it is losing money for the user. Jackson draws links with classic theory to find mathematical conditions that can be used to check whether a pricing model admits arbitrage. Conditions analogous to the Black-Scholes partial differential equation can be checked against a confidence level to determine bleed, and the model recalibrated on failure.

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