A probabilistic approach for denoising option prices

This paper aims to directly denoise option price while adhering to the no-arbitrage conditions. To achieve our goal, we propose the Gaussian Process (GP) method that entails training the GP on noisy data of option prices as a linear function of the pair of maturity and strike. Utilizing the GP approach not only allows for removing noises on the option price surface by verifying the noarbitrage conditions but also is a probabilistic approach that allows quantifying the uncertainty on the quantity of interest by constructing con dence bands around the estimate. The GP further permits forecasting out-of-the-sample prices without needing to compute the risk-neutral density of the option price surface. To investigate the e ciency of GP in removing the noise from option prices, we tested it on a simulated dataset. The overall MSE between the computed Black-Scholes prices and the GP denoised is 0.10, and between the Black-Scholes prices and the noisy prices is 2.21-a 95.33% noise removal. The curves of the graphs for the denoised prices are all convex and non-increasing in strikes, upholding the no-arbitrage conditions. To our best knowledge, the challenge of directly denoising option prices has led to little interest in this area, and our work is the rst to undertake this task.