Eugene Grigoriev
The applications of machine learning in quant finance seem endless, and they include such feats as the ability to predict future stock variance, to calibrate local volatility models, and more! In this article, Eugene Grigoriev, Quant Strategist at the Macquarie Group, explores how Gaussian processes could shape the future of this industry.
Machine learning (ML) is becoming a common tool in solving problems in finance, with scientists looking to extract and analyse enormous amounts of data to optimise the trading flow, design signals, and provide robust risk analysis. Recent advancements[1] introducing efficient and practical inference methods for Gaussian processes (GP) make the approach popular amongst practitioners due to its ability to capture uncertainty through probabilistic distribution with a non-parametric model. In this article, I share my view on a few examples how Gaussian processes and machine learning will undoubtedly shape the future of time-series forecasting.
One outstanding example of the use of Gaussian processes for financial time-series is the application of GPs to predict the future stock variance[2]. Traditional approaches for volatility modelling often contain restrictive assumptions e.g. linear relationship for the process of volatility evolution from past to current or symmetric influence of positive/negative returns on volatility. The paper is showcasing the application of Gaussian State-Space Model framework to financial data to introduce the non-parametric Gaussian Process Volatility Model (GP-VOL). Instead of restricting the functional relationship with a specific parametric form, the model places a Bayesian prior distribution on all possible functions and calibrates it with the available training data to obtain an analytical approximation of posterior distribution for the latent variable. This allows the model to eliminate assumptions about linear dependency between current and past volatility and account for asymmetric effects of positive and negative returns on volatility. In conclusion, the authors provide an experiment, comparing the GP-VOL against the industry-standard approaches such as GARCH, EGARCH and GJR-GARCH, showing the improved predictive performance of the new model. The practicality of this research is further bolstered by introducing a fast sampling algorithm to perform Bayesian inference.
Another practical application of Gaussian processes is designing the probabilistic framework based on the non-parametric Gaussian process model to calibrate[3] the local volatility model, widely used in derivatives pricing. The proposed calibration approach presents two important features of the Bayesian inference process. First, it is possible to provide an intuitive way of encoding the prior beliefs about local volatility function, such as smoothness properties, in the clean non-parametric functional model. Secondly, the model, albeit flexible, is not prone to overfitting as the number of parameters adapts along with complexity of the model itself given new available data. The proposed approach for volatility surface generation was tested on the time-series data with S&P 500 options prices, where the model would produce credible volatility surfaces, satisfying the smoothness conditions. The experiment then shows how the implied volatilities and call prices extracted from the calibrated volatility surface would compare to the market data. The results for both calibration and prediction are encouraging, given the focus of this paper was just to demonstrate the applicability of the framework for learning the local volatility model calibration.
As many reports suggest, further extensions to Gaussian processes are used to solve the problems of global optimisation, unsupervised learning and others. Lack of diverse and valuable “big data” in financial industry poses a great challenge for deep learning family of ML methods, making way for a Swiss Army knife of data science toolkit – Gaussian processes. In the industry, we build on these ideas to design machine learning aided strategies using the GP framework to provide accurate pricing, enhance risk analysis and hedging decisions.
James Hensman, Nicolo Fusi, Neil D. Lawrence, Gaussian Processes for Big Data, 2013
Yue Wu, Jose Miguel Hernandez Lobato, Zoubin Ghahramani, Gaussian Process Volatility Model, 2014
Martin Tegner, Stephen Roberts, A Probabilistic Approach to Nonparametric Local Volatility, 2019