Volatility Model Pricing and Calibration with Neural Networks using Bayesian Optimisation

Goosen, Jenna

Volatility Model Pricing and Calibration with Neural Networks using Bayesian Optimisation

Master Thesis

2022

Abstract

Stochastic Alpha, Beta, Rho (SABR) and Heston Volatility models have been used in the financial industry due to their ability to price options as a function of time to maturity and moneyness. Implied volatilities for these models are accurately estimated using a numerical integration approach, Monte Carlo approach, series expansion approximation or using a two factor finite difference approach. However, these volatility calculations are computationally expensive. Therefore, this dissertation explores the use of deep artificial neural networks to calibrate volatility models by deploying computational resources to train a model (offline) and then utilise the pre-trained model to competitively price options (online). Deep neural networks in this paper are trained using an indirect and a direct method. The first step of the indirect method utilises a deep artificial neural network to approximate the pricing function (output) using the parameters as inputs. The second step of the indirect method implements a least squares optimisation algorithm to calibrate the parameters. The direct method, on the other hand, uses a deep artificial neural network to calibrate the model parameters using the implied volatility surface as input. Bayesian Optimisation algorithms are implemented to select models with the lowest loss metric for SABR and Heston volatility models. The best performing models are tested and compared for accuracy, speed and robustness for pricing and calibration. This dissertation finds that deep artificial neural networks using Bayesian Optimisation for the indirect and direct methods are able to efficiently and accurately price and calibrate the SABR and Heston Model. In addition, the results show that the implementation of the indirect and direct method, when there is no closed form approximation readily available, is advantageous from both a time and accuracy perspective for pricing and calibration.