Rough volatility’s steampunk vision of future finance

Some of the trickiest puzzles in finance could be solved by blending old and new technologies

Rough vol
Image: Mark Long, NB Illustration

Rough volatility has generated a good amount of buzz in quant finance circles lately, which is somewhat surprising given its throwback origins. The models rely on a mid-20th century statistical measure called the Hurst parameter to capture the memory effect in markets. In an era of big data and machine learning, that makes them something of an anachronism. A quant at one large bank says, half jokingly, that his firm is “only interested in data-driven approaches”.

But dismissing rough volatility because of its old-school mechanics may be a mistake. The models are based on well-established, time-tested research. The Hurst parameter was originally developed by the British hydrologist Harold Hurst, who spent his career studying the Nile river. After noticing that fluctuations in the waterline were far from random – overflows were followed by heavier floods, and dry spells by worse droughts – he invented a way to measure the path dependence of time series. Hurst’s work led to the construction of the Aswan High Dam, the world’s largest embankment dam, and earned him the nickname “father of the Nile”.

The Hurst parameter has appeared in quant research over the years. Most recently, finance professors Jim Gatheral and Mathieu Rosenbaum in 2014 repurposed it to capture the tendency of past moves in finance to influence future ones. They coined the term “rough volatility” for models that use the parameter.

The models can generate a surface of implied volatilities for different option strikes in a single calculation. With existing volatility models, such as Black-Scholes and SABR, numerous calculations are required to estimate implied volatilities for each tenor of an option – a process that is both time consuming and error-prone. Rough volatility models do the job faster and, some argue, more accurately.

For financial firms, the benefits could be huge. Quants at Societe Generale estimate that bid/offer spreads for Vix futures and options would shrink by 15–20% if rough volatility models were widely adopted by market-makers. Some hedge funds are already developing arbitrage strategies to exploit the differences between rough volatility and traditional models.

Others, though, seem reluctant to make the shift. The models are still largely untested and require extensive calibration. They will be expensive to implement. And budgets have already been committed to more trendy machine learning projects that have the potential to deliver similar or even better results. But that attitude appears shortsighted.

A new study suggests rough volatility models are a useful complement to data-driven approaches, such as deep hedging. This is because machine learning models struggle most when markets exhibit the sort of memory effects that rough volatility captures. Blanka Horvath, an academic at Kings College and one of the authors of the study, says firms can use rough volatility to cross-check the output of black-box algorithms to ensure they are not going astray. This dynamic works in reverse, too – some quants are using machine learning to calibrate rough volatility models and check their outputs against Black-Scholes-generated volatilities.

Machine learning and artificial intelligence are revolutionary tools that will transform the financial markets in due time. But that does not mean quants should turn their back on the past. The financial models of the future could be built on the foundations of a 60-year-old dam.

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