Research Post

CVA and the law of one price

CVA and the law of one price

22 December 2015

There is a well-known philosophy adage that states all idealism ends in tyranny. On reflection it seems the financial world is no exception – the idealism in this case being traditional economic and financial theory. Why?

Well, we all know how little economics has in common with formal science – the problem being that in the world of human behaviour very little can be considered truly predictable and therefore economic models are at best sketches of how we think things might work.

All too often, economic theories also take on their own life, becoming accepted as standard until a crisis results in assumptions being questioned and new – but equally limited – theories taking their place. Quantitative finance suffers similar difficulties, based as it is on formal statistical techniques and supported by an academic sector that benefits greatly from the success of theoretical finance as a field of study.

Although this problem is widely understood and recognised as a contributing cause of recent market crises, little is actually done about it aside from periodically adapting existing models in an attempt to make them more robust or conservative.

A combination of political expediency and business reality means that finance practitioners are often forced to shrug their shoulders and say “this is the best model I have” or “well that’s what the regulator asked for” rather than adopting more realistic but less tractable modelling approaches. Risk takers are well aware of this of course, and have traditionally responded by overlaying official risk and pricing models with their own directional views on hazard and opportunity.


The emerging wave of regulations is, however, challenging this model by demanding consistency between the models and data used by front, middle and back office and by pressing for symmetry of pricing between peers.

A particular problem is credit valuation adjustment (CVA). The general accounting principle regarding valuation is that my asset should equal your liability – that is, if I owe you I shouldn’t be able to claim my obligation has lower value to me as a liability than it has to you as an asset, other than some conservative allowance for the potential cost of disposing of the asset or liability. In other words, a clear symmetry should exist between us.

A related concept is the quantitative law of one-price, which asserts that a financial contract has an absolute value – regardless of who is holding it – and that any combination of contracts that exactly replicate its payout characteristics will have the same value. Again, a nice theory which when assumed leads to all kinds of convenient mathematical possibilities.


However, as we start considering CVA and the valuation of counterparty risk, things become complicated. In pricing credit risk, we are putting a financial value on the cost of insuring against a negative outcome in all possible future states of the world. The utility value of this insurance is very different to each party, depending on the outcome. Derivatives contracts are not truly fungible and transferable in the same way as say cash or physical goods and that there is not even an equal and opposite value or utility between two sides of the same contract.

When we trade together the fair value of the trade to me is dependent on the exact combination of this trade, your credit worthiness, my creditworthiness, all my other positions, collateral and funding arrangements, and all the regulatory and capital obligations that comprise my business. This value is subjective and will be different from the value you perceive from your side. At this point there isn’t an objective arbitrage-free price, but instead the start of a negotiation – and our relationship is not one of exchanging goods but becoming contractual partners. The price will presumably be somewhere between your fair value and mine. As they say, price is what you pay and value is what you get.

This is a much closer summary of how negotiations work elsewhere in the real world. There isn’t generally an expectation that economic utility will be equal and opposite for both parties. Instead, the objective of the seller is to convince the buyer of the rarity and desirability of the goods, while hiding their need to sell it. Likewise, the objective of the buyer is to hide their urgent need to buy while convincing the seller of how plentiful and commonplace the goods in question are. In most cases there isn’t a ‘real’ value at all, only the price at which a particular contract is struck between two parties at a given time.


This is unsettling as at first sight it undermines the concept of risk neutral pricing. A number of adjustments can be made to standard models to preserve fairness and impartiality of valuation, but the fact remains that market prices in these circumstances can no longer be relied upon as implying an ultimate fair price of risk.

The challenge for banks then is to convince customers, accountants and regulators that the terms ‘market price’ and ‘arbitrage-free’ are no longer solid concepts and that every complex transaction requires a unique individual perspective on risk and pricing.

This has implications in terms of quantitative modelling and validation but also internally in terms of price quotation, risk calculation and fair value accounting. As with all things XVA banks are faced with yet another level of complexity despite the strong need to reduce costs.

The answer in many cases is proving simple if unpalatable – shut down the most complex product offerings altogether and focus on a narrow range of generic products where individual risks can be easily priced in at the time of trade. This has been a growing trend and is likely to be a recurring theme over coming years.

Meanwhile for those banks and intermediaries capable of running high volumes of hypothetical scenarios, the ability to optimise client portfolios, balance sheets, clearing venues and funding choices will continue to provide significant competitive advantage.

Back to Articles