The volatility paradigm that’s stirring up options pricing

‘Rough volatility’ models promise better pricing and hedging of options. But will they catch on?

There are whispers of a revolution in options pricing. But like many revolutions, it might take a few years to unfold.

A recent approach to volatility modelling dubbed “rough volatility” is gaining momentum across the quant community. At least nine firms – including US and European banks, market-makers and hedge funds – are known to be experimenting with models based on the technique, or plan to put them into production.

Rough volatility models are more accurate than their established cousins, proponents say. They could allow market-makers to narrow the spread they offer on Vix futures and options by 15–20%, according to estimates from Societe Generale.

“You can make a business out of it,” says Philippe Dumont, the bank’s head of quantitative volatility trading.

An arbitrage strategy exploiting the difference in spreads between rough volatility and traditional models was able to boost profits by a fifth in tests at Shanghai Luoshu Investment Company, a high-frequency multi-strategy quant fund.

Natixis backtested a theoretical rough-volatility trade that arbitraged pricing discrepancies across 15 options markets, delta-hedging to neutralise risk. The strategy recorded a Sharpe ratio above two.

Rough volatility models work by providing a more direct way of pricing and hedging options. Determining the implied volatility of an underlying asset is a key part of options pricing. Existing models, such as Black-Scholes and SABR, require users to run numerous volatility calculations for each tenor of an option. These outputs are then stitched together to form an implied volatility surface – a 3D map of volatility at different strikes and expiries for the option.

Rough volatility models spit out the whole surface in one go, without the need to recalibrate for each tenor.

“With rough volatility you may use one model to generate plausible volatility smiles for multiple expiries,” says Mark Greenwood, a quant trader formerly at Merian Global and NatWest Markets.

At the core of the new approach is the use of the so-called Hurst parameter, which captures the memory effects in markets. In essence, the model captures how far the path of past volatility affects the likely path of future volatility.

As banks, market-makers and buy-siders often run models up to several times an hour, depending on the markets they trade, the time savings of rough volatility models are a part of their appeal.

Jim Gatheral, one of the architects of the method alongside Matthieu Rosenbaum, jokes that rough volatility makes options pricing as easy as cranking the handle on a sausage machine. “You stick in high-frequency data at one end and the fair price of options comes out at the other,” he told listeners to a Risk.net webinar in February. Gatheral and Rosenbaum won Risk.net’s award for Quants of the Year this year for their work.

Of course, it’s not quite as simple as that. Widespread acceptance of the models would require financial markets to unlearn a whole credo of volatility modelling and embrace what Gatheral describes as a “new paradigm”. Banks and investors may decide that existing models, for all their shortcomings, are adequate.

“Simpler models can do the job,” says one pessimist.

Another says: “As a piece of maths, it’s very nice. But it’s an answer to a problem the industry has largely solved.”

Implementing the models will be expensive. The process of calibration is complex and time-consuming. So, while rough volatility models promise better pricing and hedging of options, getting them to the start line is a daunting task.

Under the (volatility) surface

The origins of rough volatility are in a 2014 paper by Gatheral, Rosenbaum and Thibault Jaisson. The practical applications of the concept have picked up pace in the past couple of years.

At Natixis, certain desks are running rough volatility models as “challenger models” in some markets, according to Adil Reghai, head of quantitative research. Two more banks are doing the same but preferred to remain anonymous. SG hopes to use the models in market-making and pricing exotics. Jump Trading uses rough volatility already, but is cagey about exactly how.

In market-making, once calibrated, the models can be run quickly enough to generate volatility surfaces for thousands of underlyings across equities, foreign exchange and other asset classes, including in illiquid markets, quants say.

And because the models are more accurate, they can help firms price with confidence when markets are jumpy, which is also when spreads widen and most of the money in making markets gets made.

Reghai draws an analogy with the work of scientists Johannes Kepler and, later, Isaac Newton. Kepler observed the ellipsoid shape of planetary orbits but would take a year to confirm his observations. Building on this work, Newton was able to calculate the same movements theoretically long before the full orbit had elapsed.

In exotics, rough volatility models can do a better job of pricing payoffs that are path-dependent, such as barrier options or American options or autocallables.

“New autocall products have intricate forward dynamics that you may think you are hedging appropriately. But at some point the market pops and the P&L explained by your models’ exotic risk attribution does not reflect the market behaviour,” says Aitor Muguruza Gonzalez, head of modelling at Kaiju, a hedge fund that is exploring the use of the new models.

A model that matches those dynamics better allows a firm to hedge better, he says. “And that should be reflected in your P&L and your trades. Rough volatility is almost purpose-made for this. It catches these deeper level dynamics more accurately.”

Such a benefit might be especially timely for structured product dealers, who lost hundreds of millions of dollars in the product in 2020.

Traders like things they can intuitively link to economic drivers and to hedging portfolios. For rough volatility, traders cannot yet map in their heads what the model says and how to hedge it or use it to make a profit

Russell Barker, Morgan Stanley

For buy-siders that seek to arbitrage differences in option prices, the models promise to unlock fresh opportunities.

Employing a model with different paramaterisations for different tenors makes it hard for investors to know whether ridges or dips in the implied volatility surface represent true dislocations, or simply are a figment of the modelling. Variations on the surface translate to differences in option prices. With rough volatility models, buy-siders know for sure that a deviation in the surface reflects an inconsistency in pricing. “That’s not something you can do readily with many conventional models,” Greenwood says.

Buy-siders say rough volatility could help also with the short-term forecasts of volatilities and covariance matrices they employ in risk management and to size positions.

The likely volatility of markets or instruments in the near term is a key input, for example, when adjusting the leverage of multi-asset portfolios. The Hurst parameter can help estimate the diffusion of volatility by accounting for both short-term components of noise in the data – known as ‘innovations’ – and long-term memory effects in price changes, says Artur Sepp, head of research at Quantica Capital.

The roughness of volatility itself can act as a trading signal, says Bryan Wisk, chief investment officer at Asymmetric Return Capital, a New York hedge fund. Changes in volatility that become more synchronised point to an increased likelihood of big market moves and hence heightened tail risk, with implications for the pricing of options.

Tough sell

Rough volatility models appear to have a growing band of adherents, but persuading the wider market to adopt a new way of thinking will not be easy, Gatheral admits.

“I believe that rough volatility is the true model,” he says. Convincing others, though, is “a big process”.

Elegant models have failed to catch on before. Lévy process models developed in the 1990s, which sought also to model randomness in markets, drew much attention among academics but fell flat with practitioners. Jump models, which try to capture sudden moves in markets, make obvious sense, practitioners say. Few traders ever adopted them.

Forming the output from the models into practicable hedges is tricky. The hedges they produce depend not only on the state of the market – as with conventional models – but also on the path the market took to get there. That clouds a trader’s sense of why a model is suggesting a given course of action.

Traders ordinarily adjust what a model tells them to account for transaction costs, internal risk limits and gaps in market data. Without an instinct for what’s driving the outputs, the task becomes harder. Hedging using rough volatility models “seems straightforward”, SG’s Dumont says. “Actually, it’s not.”

Traders talk – and think – in terms of the SABR models that are standard across the industry today. The alpha, beta and rho parameters of SABR have become the “lingua franca” of options trading, Greenwood says. For example, traders know how the rho in SABR models affects the shape of the volatility smile and how to hedge it.

Understanding how to hedge a change in the Hurst parameter – a change in how much markets ‘remember’ the past – is a different proposition.

“Traders like things they can intuitively link to economic drivers and to hedging portfolios,” says Russell Barker, global head of macro data strategies at Morgan Stanley. “The more intuitive the model, the better the link between what the model says and how a firm hedges that risk. For rough volatility, traders cannot yet map in their heads what the model says and how to hedge it or use it to make a profit.”

At their heart, rough volatility models are simple: the most basic versions use only three parameters, one being the Hurst parameter. But this simplicity could be a hindrance rather than a help.

Options pricing models need to fit volatility surfaces to market prices at up to 50 different strikes at every expiry, often having to rely on incomplete market data. Rough volatility models capture the market well at a high level. But zoom in on all the individual points and the fit can be less accurate, quants say.

Rough volatility might produce a good fit 80% of the time, the head of quant research at the European bank estimates. But risk management of a trading book may require more like 98%.

To help improve the fit, many of the production models that practitioners use now either have more parameters or a non-parametric component. That gives quants more levers to pull to make the model match market quotes and reality.

Practitioners worry, too, about how the newer models might behave in unforeseen conditions. “Can the model blow up? Can it do strange things in the wings of the volatility surface? These questions haven’t been fully answered yet,” Barker says.

It’s for reasons of trust that modified versions of decades-old and inexact Black-Scholes models still get used in banks. They are proven and their limitations are well understood. “Traders know they are paying theta – time decay – to get long a certain amount of gamma – convexity. But they know if the market tanks or rallies they’ll make a lot of money,” the head of quant research says.

He compares it to the feeling of security a driver gets from an old, familiar car compared to a new, souped-up vehicle. “I’m not saying rough volatility is not robust. But we haven’t taken it out for a drive yet,” he says.

Compared to conventional alternatives, meanwhile, the new models take far longer to calibrate, and demand more powerful hardware to do so.

Quants have spent years developing methods to calibrate existing models more efficiently. Gatheral and Rosenbaum themselves are working on ways to do the same for rough volatility. But the methods are nascent.

The straightforward Monte Carlo approach of simulating future paths for the underlying asset, computing options prices and adjusting the model parameters to match the observed market quotes is too slow.

“A naive implementation will take you forever,” the quant research head says. The approach is unusable for firms that need to generate prices rapidly or across many products. Greenwood ran more than a million simulations to calibrate just a prototype model.

As for the wider operational task of upgrading a firm’s production system, that too is huge. It’s a “minimum one-year project, probably much more”, SG’s Dumont says.

To accommodate the shift, banks would have to change their options pricer, which feeds information to several other elements of the architecture for trading options.

Changing the pricer requires changing the market data put into it, Dumont says. The variables it produces go into the tools that traders use to make pricing and hedging decisions, so those tools also may have to be upgraded.

Adoption curve

Any new technology or theory will have doubters, and quants are working to win over the critics.

To build trust in the new models, quants at two banks are backtesting heavily the hedging strategies that the models help them create. The aim is to be sure the models won’t “blow up” in certain circumstances, the quant research head says. “Without the backtesting you can’t take that leap of faith.”

To calibrate the models faster, firms are turning to machine learning. By training algorithms using market simulations, the quants can map links between calibrations of the rough volatility model and Black-Scholes-generated smiles at various expiries.

Effectively the machine learns to identify calibrations that fit a range of templates for how markets might look. Firms might use those approximations as a starting point for calibration of the models in real markets.

The technique reduces to “a matter of seconds” the speed at which the task can be performed for all expiries on a single underlying, Greenwood says.

There is lots to do, though. How soon might rough volatility be more widely taken up? A few firms are optimistic about putting rough volatility models into production soon. Luoshu expects to be in live trading within nine months. One bank hopes to have models in production around the end of the year.

Others see evolution but on the more distant horizon. Greenwood says little may change in the next 12 months, but change is coming. “There’s always inertia. But five years from now things could be very different.”

Some foresee slow progress giving way to a possible rush to adoption. In time, rough volatility could influence market dynamics so that its use becomes necessary, thinks a quant in the model risk team at a US bank.

“Markets change depending on what models you have in the market and how people use them,” he says. Such effects occurred when Black-Scholes models first became used in the 1970s and 1980s.

Once a critical mass of acceptance has occurred, the rest of the market may have to fall into line fast. “You need to understand how other parties make prices if you trade against them. At some point, using rough volatility models might become table stakes.”

The bank head of quant research, who is “cautiously optimistic” about the outlook for rough volatility, thinks buy-siders may be quickest to use the new models. The computational burden matters less when pricing one or two trading opportunities rather than tens of thousands of positions.

Gatheral and Rosenbaum, themselves, report contact from three hedge funds asking about rough volatility in the past couple of months.

The sell side also may prove more adaptable than some are assuming.

“When traders first learnt about SABR, that wasn’t intuitive either,” the research head says. “After a while it becomes second nature. Trading is 100% results driven. If we prove rough volatility gives superior hedging performance in backtesting and it works when we try it out, traders are going to jump on it.”

Editing by Alex Krohn