A Probabilistic Approach for Denoising Option Prices

Abstract

This paper aims to directly denoise option price while adhering to the no–arbitrageconditions. To achieve our goal, we propose the Gaussian Process (GP) method thatentails training the GP on noisy data of option prices as a linear function of the pairof maturity and strike. Utilizing the GP approach not only allows for removing noiseson the option price surface by verifying the no–arbitrage conditions but also is a proba-bilistic approach that allows quantifying the uncertainty on the quantity of interest byconstructing confidence bands around the estimate. The GP further permits forecastingout-of-the-sample prices without needing to compute the risk-neutral density of the op-tion price surface. To investigate the efficiency of GP in removing the noise from optionprices, we tested it on a simulated dataset. The overall MSE between the computedBlack–Scholes prices and the GP denoised is 0.10, and between the Black–Scholes pricesand the noisy prices is 2.21 - a 95.33% noise removal. The curves of the graphs for thedenoised prices are all convex and non–increasing in strikes, upholding the no–arbitrageconditions. To our best knowledge, the challenge of directly denoising option prices hasled to little interest in this area, and our work is the first to undertake this task