Semi-parametric forecasts of the implied volatility surface using regression trees

Abstract

We present a new semi-parametric model for the prediction of implied volatility surfaces that can be estimated using machine learning algorithms. Given a reasonable starting model, a boosting algorithm based on regression trees sequentially minimizes generalized residuals computed as differences between observed and estimated implied volatilities. To overcome the poor predictive power of existing models, we include a grid in the region of interest, and implement a cross-validation strategy to find an optimal stopping value for the boosting procedure. Back testing the out-of-sample performance on a large data set of implied volatilities from S&P 500 options, we provide empirical evidence of the strong predictive power of our model.

Implied volatility surface predictability: The case of commodity markets

“…The primary intuition behind these models is that, instead of estimating a highly parameterized model, it is better to use non-or semi-parametric techniques with the amount of complexity controlled to avoid overfitting. However, of the studies cited above, only Audrino and Colangelo (2010) produce out-of-sample forecasts of the IVS in line with the aim of our paper. They utilize regression trees informed by a cross-validation strategy to produce forecasts of the surface, an approach that we also follow in our out-of-sample analysis.…”

“…This allows us to construct a forecasted IVS using these predicted coefficients. Finally, we employ the regression tree benchmark model from Audrino and Colangelo (2010). We now present each specification in more detail.…”

“…In Audrino and Colangelo (2010), the IV is regressed on a vector of predictors x pred through an unspecified function f m,τ such that…”

“…A third related methodology is that of machine learning and non-parametric techniques to model the IVSs, as in Cont and Da Fonseca (2002); Fengler et al (2003Fengler et al ( , 2007; Audrino and Colangelo (2010); Fengler and Hin (2015). The primary intuition behind these models is that, instead of estimating a highly parameterized model, it is better to use non-or semi-parametric techniques with the amount of complexity controlled to avoid overfitting.…”

Online adaptive machine learning based algorithm for implied volatility surface modeling

“…Based on an analysis of the Korea Composite Stock Price Index (KOSPI) 200 index options market, they find that their prediction yields option prices closer to theoretical values than generic algorithms. Audrino and Colangelo (2010) present a semi-parametric model by means of regression trees to forecast implied volatility and conduct an empirical study for S&P500 index options. Wang, Lin et al (2012) apply a neural network trained by backpropagation to forecast TXO (Taiwan Futures Exchange Option) prices under different volatility models using intraday data from 2008 to 2009.…”