The Implied Volatility Surface (IVS) represents the variation of implied volatility across different strike prices and maturities for options on the same underlying asset. It provides a three-dimensional view where implied volatility is plotted against strike price (moneyness) and time to expiration, capturing market sentiment about expected future volatility. Unlike the assumption of constant volatility in the Black-Scholes model, the IVS typically shows patterns such as the “volatility smile” or “smirk,” where implied volatility tends to increase as options move further in- or out-of-the-money, and it may also vary over different expiration dates.
Reference [1] examines five methods for forecasting the Implied Volatility Surface of short-dated options. Specifically, it applies Ordinary Least Squares (OLS) as the first approach, followed by an autoregressive model of order one (AR(1)). Additionally, three machine learning techniques are used: the Elastic Net (ENet) method, the Random Forest (RF) method, and an artificial neural network (NN) method. These methods are applied to forecast the level, slope, and curvature of the IVS. The author pointed out,
The main goal of this research was to find out how machine learning methods perform in forecasting the characteristics of the implied volatility surface for weekly options on the S&P 500. We used three different machine learning methods and two non-learning-based methods, where we found that the non-learning-based methods perform comparatively well with the machine learning methods. On the other hand, there is one model that consistently outperforms all other models, which is the Random Forest model. An unexpected result which is found in this paper is that the Neural Network models do not manage to make accurate forecasts for the slope and curvature characteristic. Conversely, the Neural Network model does make relatively accurate forecasts for the level characteristic. The linear ML method Elastic Net is consistently outperformed by the non-linear ML method Random Forest, as well as the Neural Network model for the level characteristic.
In summary, among the five methods studied, the Random Forest model performs the best.
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References
[1] Tim van de Noort, Forecasting the Characteristics of the Implied Volatility Surface for Weekly Options: How do Machine Learning Methods Perform? Erasmus University, 2024
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