Putting the H in XVAs

Dealers make various adjustments to the fair value of derivatives contracts to account for the credit risk, funding costs and capital requirements associated with these transactions. But, somehow, the cost of hedging has so far escaped the attention of XVA desks.

While it is standard practice to set aside ad hoc reserves to cover the cost of hedging, a formal mathematical formula for calculating these has been lacking. “Banks typically take transaction costs into account, but normally using just a heuristic approach,” says an XVA quant at a global bank.

This gap may now be filled. Ben Burnett, a director in the XVA quant team at Barclays Bank, proposes a hedging valuation adjustment (HVA) in his paper – HVA, fact and friction.

“The point of introducing the HVA is to try and improve the incentives for people to take into account these expected future costs upfront and promote a more sustainable business,” says Burnett.

To that end, the methodology needs to be easy enough to incorporate into existing frameworks without requiring fundamental changes in pricing models.

Burnett obtains the HVA by including transaction costs in the value of the derivatives book that is being hedged. The costs depend on the values of gamma in the portfolio and its variations, as well as the volatility of the assets. It is ultimately calculated by separating the risk neutral value from the adjustment value. “The approach is very much of the kind of standard XVA approaches, where we look at the cost as an adjustment to the original value,” he explains.

A similar technique can be used to calculate HVA for a portfolio that is not hedged. That is useful in case a bank wants to estimate the hedging costs over the life of the portfolio, without hedging the exposure itself.

Burnett’s approach is flexible enough to handle a variety of hedging strategies. One of the inputs sets the threshold of the portfolio delta beyond which re-hedging is triggered. The lower the value of that threshold, the more frequent – and costly – the re-hedging. 

The point of introducing the HVA is to try and improve the incentives for people to take into account these expected future costs upfront and promote a more sustainable business

Ben Burnett, Barclays Bank

“Nobody, as far as I’m aware, has so far designed a model for transaction and hedging costs and built a valuation adjustment on them. It is innovative, although at the same time it uses arguments similar to those used for other valuation adjustments,” says the XVA quant at the global bank.

That’s surprising, given transaction costs have always played a big role in the P&L. So why now?

Burnett says last year’s market meltdown focused greater attention on hedging costs. 

“It’s been exacerbated by the Covid crisis,” he says. “Whenever spreads blow out or there’s a drop in market liquidity, hedging gets much more expensive.”

Recent experience may also encourage adoption of HVA. 

“Two factors might contribute to that,” says Yi Tang, head quant for XVA and structured solutions trading at Wells Fargo, “the industry awareness of this approach, and a market event that makes a rigorous calculation of hedging costs a priority.”

Tang spoke with Risk.net in a personal capacity and his view may not necessarily reflect those of Wells Fargo.

For now, HVA is a standalone measure. For it to be implemented, it’s crucial to incorporate it in a general XVA framework, where the interaction with the other valuation adjustments is modelled consistently. Burnett and his colleague Ieuan Williams have been working on incorporating it into a general XVA framework where it can be modelled consistently with other valuation adjustments. The pair also explored several sources of HVA and found that its size is comparable to that of the other valuation adjustments. A paper detailing their findings will soon be published in Risk.net’s Cutting Edge section.