Predicting a distribution of implied volatilities for option pricing

► Predicted option price ranges by the proposed method take always positive values. ► For the deep OTM or ITM, the CI predicted by the proposed method is tight. ► Near ATM the CI predicted by the proposed method is broad. In this paper, we propose a method that predicts a distribution of the implied volatility functions and that provides confidence intervals for the option prices from it. The proposed method, based on a Bayesian approach, employs a Bayesian kernel machine, so-called Gaussian process regression. To verify the performance of the proposed method, we conducted simulations on some model-generated option prices data and real option market data. The simulation results show that the proposed method performs well with practically meaningful option ranges as well as overcomes the problem of containing negative prices in their predicted confidence intervals by the previous works.