The bald truth about collateral haircut modelling

HSBC’s Wujiang Lou says parametric modelling of haircuts has many advantages over historical value-at-risk

With the derivatives industry moving towards greater use of collateralisation – thanks to mandatory clearing, as well as compulsory margining for non-cleared derivatives – deciding what level of haircut to apply to an asset lodged as collateral is an increasingly critical question.

Haircuts – the discount applied to the value of a collateral asset for calculating margin or regulatory capital – are usually determined using historical price data to calculate a VAR loss for a given confidence level, typically 99%.

The trouble with this method is that it relies heavily on the availability of data, meaning the determination of the haircut becomes more art than science for assets where liquid data is not available.

“The problem is that the data is very non-uniform. For some assets, we have excellent data along an empirical time series, which is very clean. But some instruments are less liquid, and we don’t have as much data as we would like,” says one quant at a European bank.

Historical VAR’s reliance on past data makes it an inherently backward-looking measure; when market conditions change, haircuts can change significantly – as became evident during the financial crisis.

“If we use historical data from before summer 2007 to compute haircuts on AAA and AA US residential mortgage-backed bonds, we would find small haircuts – around maybe 5%. Whereas just after that, with the subprime crisis, we saw much higher losses even on AAA and AA securities,” says Mohamed Selmi, head of risk methodology at LCH in Paris.

In this month’s first technical, Haircutting non-cash collateral, Wujiang Lou, a director in global fixed-income trading at HSBC in New York, proposes an alternative model to fix these problems, by using parameters to calculate the haircuts.

Lou proposes a parametric model, or one that uses explanatory factors to determine the value of the asset, instead of a purely data-driven approach. The technique seeks to model asset prices based on a jump diffusion model, and introduces a credit risk measure to reflect the impact of credit ratings on haircuts. The model is then calibrated to the benchmark originally used to model the asset’s haircut under the historical approach – such as the S&P 500 for equities, for instance. One key difference is that illiquid assets will have very different haircuts in reality versus the index used to calibrate the model – so to reflect the specific characteristics of the collateral asset, adjustments can be applied to calculated parameters in the form of sensitivities.

This parametric model has volatility as a parameter, so we can take the vega or the derivative with respect to volatility. So if you find a particular bond or collateral is very volatile, you can do a little adjustment using the product of the vega times what you expect the volatility change to be

“This parametric model has volatility as a parameter, so we can take the vega or the derivative with respect to volatility. So if you find a particular bond or collateral is very volatile, you can do a little adjustment using the product of the vega times what you expect the volatility change to be. The calibration uses a relatively liquid index, but for illiquid bonds or individual bonds you apply the sensitivity adjustment to get you closer to the real world,” says Lou.

Credit rating characteristics can be further incorporated by tweaking the jump size of the asset value and the probability of the jump.

Both the Basel capital framework and the margin rules for non-cleared derivatives allow haircuts to be calculated using either a standardised approach or internal estimates. The regulatory approaches in existence and internal models used at banks mainly rely on data-driven estimation of haircuts, applying more intuitive considerations on individual assets where necessary.

Things are beginning to change, though. A handful of dealers are understood to have begun using parametric models when the collateral asset is illiquid or otherwise lacks reliable data, according to two people familiar with the matter.

Perhaps one of the biggest advantages of parametric models is that they have more explanatory power, as they are based on factors that explain behaviour.

“When we use a parametric model we can actually explain what is going on. When we use a completely data-driven or machine-learning type of approach, we have zero explanatory power. We can say our haircut is 5%, but why? Is it driven by volatility alone, or is it because we have a lot of volatility, but also strong mean reversion that suppresses diffusion? We don’t know, so we can’t explain,” says the quant at the first European bank.

Given the importance of collateralisation in today’s regulatory environment, it makes sense for both dealers and regulators to pay more attention to the age-old problem of insufficient data for haircut modelling. The use of parametric models helps in not only fixing the data problem, but also translating intuitive considerations such as the credit quality changes in the exposure or expectation of higher volatility into a model that can quantify those considerations.