UBS’s Iabichino holds a mirror to bank funding risks

Framing FVA as an optimal control problem affords an alternative to proxy hedging

In an influential 2011 paper, Christoph Burgard and Mats Kjaer showed how a bank can hedge its funding risk by dynamically shorting its own bonds. As this is technically unfeasible, most banks construct a proxy hedge by shorting a basket of debt issued by their peers.

This approach never sat well with Stefano Iabichino, a quant structurer in the cross-asset quantitative investment strategies team at UBS. Hedging by proxy neglects the idiosyncratic nature of bank balance sheets, he notes. The other problem with the conventional frameworks for hedging funding risk is that they tend to generate a loss whenever the banking system suffers a shock. Funding valuation adjustment (FVA), a sophisticated measure of funding cost, is one such example.

This is why some banks prefer not to hedge their funding risks at all – which doesn’t sit well with Iabichino either. He argues the simpler solution is for banks to mirror their funding rate and then apply it to all client trades.

The advantage of this approach, Iabichino says, is that it is “focused on determining the optimal funding policy by minimising the volatility of net interest income (NII), driven by the stochastic nature of a bank’s debt costs”.

The research was inspired by a nagging sense that the financial industry had failed to address the root cause of major bank failures over the past two decades. “Despite intense efforts to mitigate funding risk in the aftermath of the financial crisis, it is almost ironic how the failures of Lehman Brothers, Silicon Valley Bank and First Republic share a strikingly familiar cause: the manifestation of funding risk, as each of these banks suffered massive NII losses leading up to their collapse,” Iabichino says.

Read the paper

Funding arbitrages and optimal funding policy 

Stochastic control can be used to manage a bank’s net asset income

The failures, he argues, ultimately stemmed from a mismatch between sticky receivables’ funding premia and rapidly changing payable spreads.

Iabichino frames this as an optimal control problem, which relates to the evolution of dynamic systems under uncertainty. This allows him to deal with real-world limitations – such as the impossibility of a bank shorting its own debt – and the stochastic nature of funding risk, which is the result of multiple factors including maturity mismatches and changes in a bank’s creditworthiness. 

The novel approach has drawn enthusiasts within the quant community. “Stochastic optimal control has been applied in a few areas in finance, but not in funding transfer policy, so it’s a welcome innovation,” says Ben Burnett, who heads a team of derivatives valuation adjustment (XVA) quants at Barclays.

Once the stochastic control problem is defined, Iabichino uses the Bellman equation to calculate the funding rate. “When we derive the Bellman equation for our stochastic optimal control problem, we can determine both the optimal fund spread the bank should apply to a client and its optimal leverage ratio,” he says.

The output is simply the amount a bank should charge its clients for their marginal contribution to its funding costs.

The downside of this approach is that the calculation – and the amount charged to clients – needs to be updated frequently to neutralise a bank’s funding risk. Iabichino refers to the variability in the funding costs passed on to clients as “elastic rates”.

Burnett at Barclays says that might be a hard sell for clients.

“The application of new technique like this is likely to face challenges because people have to get their head around it,” he says. “In my view the question on its applicability is not so much about the modelling side of it, but rather on the concept of elastic rates and whether clients can be persuaded to accept the bank’s funding risk.”

Iabichino proposes a solution to this potential problem. “If clients are reluctant to bear the bank’s funding volatility, they could enter a fixed-for-floating swap to hedge elastic rate fluctuations,” he says. This hedge would need to be structured ad hoc, but the overall cost would not exceed the FVA charges that clients currently pay for standard swaps, he adds. The swap would return the funding risk to the bank, but at that point Iabichino says it can be sold to market participants with the appetite for that kind of exposure.

Even with that extra step, Burnett thinks Iabichino’s approach is worth pursuing. “There is value to it because it shows the optimal case and one can benchmark against it,” he says.