Pricing American Options Through Model-Guided Machine Learning Incorporating Asset Characteristics and Market Environments

Abstract

In the face of volatile financial markets, a sufficiently accurate estimation and prediction of stock option prices is crucial for researchers, traders, and investors. Since the development of the influential Black-Scholes model in 1973, many parametric option pricing models have been proposed to better capture the implied volatility surface, which is skewed across the moneyness-maturity space and changes dynamically over time. However, weaknesses in these models still incur significant pricing errors when they are applied to real world data. With the rapid development of modern machine learning techniques, in particular deep neural networks, and their success in various areas of science and engineering, it is realized that their universal approximation power and their capability of nonparametrically modeling complicated nonlinear relationships have great potential to further improve the prediction accuracy in volatile financial markets. In addition to pure neural networks, it is also expected that a parametrically-guided machine learning approach can achieve both improved accuracy and enhanced interpretability. In a recent work [Almeida et al., 2022], feedforward neural networks are employed to further correct the residual errors of various parametric attempts to model the implied volatility curve of European-style S&P 500 index options. In this thesis, we make further explorations by applying a similar methodology on American-style equity options. In particular, we use parametric models, purely nonparametric neural networks, and parametrically-guided neural networks to investigate individual stock components of the S&P 100 in order to determine the level of prediction errors they incur and how readily they accept neural network correction. We also conduct a cross-sectional analysis of the errors generated from all the company stocks and perform regressions to find relationships between prediction errors and various covariates that reflect the state of the market and characteristics of the company, including P/E ratio, market beta, average volume traded, and average share price, in order to determine the market conditions and company types that generate the best modeling results. We find that as in previous literature, nonparametric correction from neural networks generally results in substantial gains; however, such gains vary dramatically across sectors. We also confirm that correcting a better specified parametric model usually leads to additional improvements in performance; however, such improvements are mostly marginal, and the final effect of the model-guided nonparametric approach depends on many factors involving the complicated interaction between the parametric model and the neural network. We also find that company characteristics play an important role in determining correction performance. Most notably, options from defensive sectors that remain stable during volatile market conditions are more resistant to accurate modeling and error correction than those from cyclical and sensitive sectors that are more responsive to market trends. Through our cross-sectional regression, we found that among the regressors we investigated, market beta and average share price are the most influential upon error levels, both having statistically significant negative correlations with implied volatility modeling errors. These discoveries are useful for determining market conditions and company characteristics that are conducive to low modeling error and finding improved techniques for options less receptive to error correction. More broadly, our methodology can be applied to scenarios in a wide diversity of fields that involve the prediction of high volatility data.