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The fundamental theorem behind financial markets is that stock prices areintrinsically complex and stochastic. One of the complexities is the volatilityassociated with stock prices. Volatility is a tendency for prices to changeunexpectedly [1]. Price volatility is often detrimental to the returneconomics, and thus, investors should factor it in whenever making investmentdecisions, choices, and temporal or permanent moves. It is, therefore, crucialto make necessary and regular short and long-term stock price volatilityforecasts for the safety and economics of investors returns. These forecastsshould be accurate and not misleading. Different models and methods, such asARCH GARCH models, have been intuitively implemented to make such forecasts.However, such traditional means fail to capture the short-term volatilityforecasts effectively. This paper, therefore, investigates and implements acombination of numeric and probabilistic models for short-term volatility andreturn forecasting for high-frequency trades. The essence is that one-day-aheadvolatility forecasts were made with Gaussian Processes (GPs) applied to theoutputs of a Numerical market prediction (NMP) model. Firstly, the stock pricedata from NMP was corrected by a GP. Since it is not easy to set price limitsin a market due to its free nature and randomness, a Censored GP was used tomodel the relationship between the corrected stock prices and returns.Forecasting errors were evaluated using the implied and estimated data.

Short-term Volatility Estimation for High Frequency Trades using Gaussian processes (GPs)