Podcast: Lyudmil Zyapkov on the relativity of volatility

It was surely only a matter of time before someone applied the principles of Einstein’s general theory of relativity to options trading.

Lyudmil Zyapkov, a senior quantitative analyst at Bank of America, has done just that.

His research shows how gamma effects in options markets can warp the perception of time in volatility models, in much the same way gravity distorts space-time. 

Zyapkov’s innovative stochastic volatility model, which he calls the Gamma Clock, introduces two correlated bivariate gamma processes to measure the relationship between an underlying asset and its volatility jumps. The results reveal how the perception of forward volatility can be distorted by prevailing market conditions.   

“The clock at which the Brownian motion ticks is not the simple time,” says Zyapkov. “It’s a gamma transformed time.”

In this episode of Quantcast, Zyapkov explains that the model is intended to be calibrated daily to the level of forward volatility. Time dilates when the calibrated correlation is higher than a pre-determined break-even correlation, and contracts when it is lower. This can be thought of as the gamma clock slowing down or speeding up, respectively.

“The faster the markets move, and the more correlating underlying and volatilities become, the greater the time dilation.”

Zyapkov’s latest paper, published in Risk.net last month, builds on an initial version of the model he published in 2019 by incorporating a fractional Brownian model (FBM). The long-term memory of the FBM allows the model to respond better to recent price movements, as well as trends over time, and more effectively capture volatility clustering in markets.

The fractional feature of the new model is particularly relevant for short expiry options.

“We have observed that the fractional feature fades away or completely dissipates,” says Zyapkov. “This disappears for ultra long-expiry options like 20 years or 30 years expiry. So the new model, in a sense, unifies the short expiry with the long expiry by factoring in the fractional feature.”

The latest version therefore remains effective for long-expiry options, while the new path-dependent feature allows it to be more sensitive to the skew slope, making it more effective for short expiries.

Zyapkov has tested the model for FX options, but he says it could be easily adapted to equities and even commodities. His research, though, is still in the early stages. His next step is to implement a full Monte Carlo simulation, which – given the complexity of gamma subordinated FBM – will take some time to develop and execute. Even so, Zyapkov is confident the model, by its nature, will be both effective and fast for pricing and calibration purposes.

Index

00:00 Introduction

05:54 The Gamma Clock explained

09:56 Relativity of time in financial markets

11:57 FBM and rough volatility

15:51 Modelling short and long expiries

17:15 Applicability and implementation

24:22 Model relativity and the laws of nature

27:11 Future research

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 Spotify, Amazon Music or the iTunes store to listen and subscribe.