Deep Calibration of Option Pricing Models

Dadah, Sahil

Deep Calibration of Option Pricing Models

Master Thesis

2022

Abstract

This dissertation investigates the calibration efficiency of short rate models using deep neural networks. The main focus is on the calibration of one-and-two factor Hull-White models to caplets and swaptions data, where the inputs are interest rate derivative prices or implied volatilities, and the outputs are the model parameters. A direct and indirect neural network calibration framework is adopted. The former method involves a direct inversion of the standard option pricing function using neural network. The indirect framework uses two consecutive steps; the first step estimates the option pricing function using a neural network. This is followed by applying the pre-trained model in a calibration procedure to fit the model parameters to a set of market observables. The neural networks are trained using simulated data and an optimum set of hyperparameters is obtained via the Bayesian optimization. The best set of hyperparameters is used to train the networks and tested on out-of-sample actual market yield curves data. It is shown that the direct method has substantial improvements in time with a sacrifice in accuracy (a mean relative error of 2.88%). On the other hand, using the indirect method, it is shown that the calibrated parameters reprice the set of options to a mean relative error of less than 0.1% (similar to numerical calibration), with a significant improvement in speed whose execution is twenty-six times faster compared to the conventional calibration procedures currently used.

Keywords

Mathematical Finance

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