Podcast: Julien Guyon on volatility modelling and World Cup draws

In the past couple of years, quantitative research has been increasingly focused on modelling volatility. “Volatility is the single most important factor driving the asset price dynamics, and the most important factor in derivatives pricing and hedging,” says Julien Guyon, professor of applied mathematics at the École des Ponts ParisTech.

Guyon is one of the most prolific and influential contributors in the field, and our guest in the latest edition of Quantcast. His latest work – a collaboration with former colleague Mehdi El Amrani, a quantitative researcher at Bloomberg – looks at the term structure of the skew of an option, or the slope of its volatility smile, and whether it follows a power law. The skew gives a measure of how much more expensive an out-of-the-money put option is compared with one that is at-the-money (ATM). The skew can be loosely interpreted as a measure of fear in the market – hence its importance.

Their paper has two objectives, Guyon says: “The first goal is to check if the term structure of the ATM skew really follows a power law, not just on a particular calibration date, but consistently over time. And so we looked at two years of historical data. We also wanted to pay close attention to short maturities and see whether the market is really indicating or not some blow-up or no blow-up at zero maturity.”

They find that the ATM skew indeed follows a power law for options with maturities of one month to three years, but that it behaves differently for those with shorter maturities. Rough volatility models with two parameters capture it well for long maturities – but, for shorter maturities, a third parameter is needed capture the market behaviour. In one of the new suggested models, third parameter has the effect of shifting the modelled curve to the left, and thereby removing the explosive values that would be reached when maturity approached zero.

Guyon goes on to discuss the joint calibration of S&P and VIX options. This is another topic of great importance because although the options’ underlying assets are tightly connected, option volatilities tend to display different patterns, and modelling them consistently presents serious challenges. Nevertheless, numerous quants have dedicated their efforts to solving the problem, and important progress has been made.

The third area of volatility modelling that Guyon is working on is path-dependent volatility, a natural family of models, as he describes it, because "they simply but accurately capture the feedback of past returns on volatility", produce “rich spot-vol dynamics using a single Brownian motion” and “hence they combine the benefits of local volatility and stochastic volatility models”. He believes the potential applications of this modelling approach are promising and that it could help to resolve the S&P-VIX calibration problem. Fellow quants seem to be looking closely at Guyon’s work – his paper on the subject is his most popular in terms of the number downloads, and some traders have been using it to price their derivatives positions.

Extra time

But it’s not all about volatility modelling. Guyon likes to apply his knowledge of statistics and probability theory to other disciplines.

A passionate football fan, in 2014, he took an interest in the system used by the game’s global governing body, FIFA, to draw the groups for the men’s World Cup finals in Brazil. He found that its system to ensure geographical constraints – so that no two teams from the same continent, except Europe, could play in the same group – led to unbalanced allocations. He sent a proposal for an alternative system to representatives of FIFA, which was published in The New York Times. When the 2018 men’s World Cup took place in Russia, the draw system had been updated.

Index

00:00 Introduction, volatility skew and power law

03:35 Paper that verifies whether power law holds

07:35 Link between power law and rough volatility

10:50 Study’s conclusion

18:00 Alternative parametrisations

21:30 Joint calibration of S&P and VIX options

29:15 Path-dependent volatility

36:30 Careers as bank quant, Bloomberg quant and academic

40:45 How to draw groups for football tournaments properly

54:00 Legacy of Black-Scholes

To hear the full interview, listen in the player above, or download. Future podcasts in our Quantcast series will be uploaded to Risk.net. You can also visit the main page here to access all tracks, or go to the iTunes store or Google Podcasts to listen and subscribe. Now also available on Spotify.