Optimizing the Number of Time-steps Used in Option Pricing

Abstract: Calculating the price of an option commonly uses numerical methods and can becomputationally heavy. In general, longer computations result in a more precisresult. As such, improving existing models or creating new models have been thefocus in the research field. More recently the focus has instead shifted towardcreating neural networks that can predict the price of a given option directly.This thesis instead studied how the number of time-steps parameter can beoptimized, with regard to precision of the resulting price, and then predict theoptimal number of time-steps for other options. The number of time-stepsparameter determines the computation time of one of the most common models inoption pricing, the Cox-Ross-Rubinstein model (CRR). Two different methodsfor determining the optimal number of time-steps were created and tested. Bothmodels use neural networks to learn the relationship between the input variablesand the output. The first method tried to predict the optimal number oftime-steps directly. The other method instead tried to predict the parameters ofan envelope around the oscillations of the option pricing method. It wasdiscovered that the second method improved the performance of the neuralnetworks tasked with predicting the optimal number of time-steps. It was furtherdiscovered that even though the best neural network that was found significantlyoutperformed the benchmark method, there was no significant difference incalculation times, most likely because the range of log moneyness and pricesthat were used. It was also noted that the neural network tended tounderestimate the parameter and that might not be a desirable property of asystem in charge of estimating a price in the financial sector.