Kazem Nouri - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran
Maryam Elahi - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan University

Many option pricing formulas have been developed to overcome the restrictive assumptionsof Black and Scholes models and to give more accurate prices. Most of the methods arefocused on a point prediction of option price.In this paper, we propose a method that predicts a distribution of the implied volatilityfunctions by applying a Gaussian process regression and estimating con dence intervals ofoption prices using the predicted volatility distributions. To verify the performance of theproposed method, we conducted simulations on some model-generated option prices dataand real option market data. The simulation results show that the proposed method per-forms well with practically meaningful option ranges as well as overcomes the problem ofcontaining negative prices in their predicted con dence intervals by the previous works.

Option pricing, Implied volatility, Gaussian processes, Confidence intervals