Quantitative Stock Market Modeling Using Multivariate Geometric Random Walk

We propose a new stock market model based on multivariate geometric random walk without imposing any parametric assumptions (such as Gaussianity) or structural assumptions (such as ellipticity) on log-increments and establish connection with continuous-time Geometric Brownian Motion (GBM). Our approach can be applied to simultaneous modeling of a variety of stocks traded at multiple stock exchanges and can adequately account for heavy tails and other distributional departures from Gaussianity. Both calibration and forecasting steps assume a nonparametric innovation process. Model calibration involves multivariate imputation to account for partially overlapping trading hours, while simulation and forecasting is performed using resampling from imputed observations. Our model is applied to a wide selection of stocks traded at NYSE and LSE. Analyzing three months’ worth of closing stock price data collected from 324 stocks sampled every minute, respective forecast regions are constructed and successfully backtested on a one-month horizon of historical data. Based on a benchmarking study, our model was shown to outperform standard GBM as well as geometric random walk models with Student’s t-like and Laplace log-increments at forecasting future value of a custom portfolio comprised of US and UK stocks.