An Empirical Stochastic Volatility Model for Bitcoin Price Range Forecasting

Abstract

By applying a Heston-like stochastic volatility model to an empirical returns-based drift-diffusion model, we show by extensive backtesting that we can improve Bitcoin price forecast accuracy for investment horizons of 7, 30, 45, and 60 days. In particular, we can improve median forecasts and also extreme tail forecasts simultaneously by applying a nonlinear parameter optimization procedure to find stochvol model parameters and by targeting the optimization to fit to historical data. The stochastic volatility model as solved provides additional backtest accuracy versus the baseline empirical drift-diffusion model, and forecasts from a tuned stochvol model are notably different than an associated baseline model, especially at the more extreme percentiles. Since contemporary daily returns on DOGE coin were noted to be mostly orthogonal to other high market cap crypto currencies, the model was tested and tuned on a 1 day forecast DOGE coin backtest, with positive results.