Calibrating the Hurst Parameter for Rough Volatility Models with Application in the South African Market

Pettit, Paul

Calibrating the Hurst Parameter for Rough Volatility Models with Application in the South African Market

Master Thesis

2022

Abstract

It is known that accurate and efficient calibration of any fractional stochastic volatility model is important for trading and risk management purposes. Under the rough Heston model proposed by El Euch et al. (2019), the Hurst parameter governs the roughness of the volatility process. This dissertation explores the different calibration methods used to obtain an estimate for the Hurst parameter, under the scope of the rough Heston model. Three different calibration methods are presented, namely, a Brute Force minimisation procedure, a Neural Network calibration and a Linear Regression procedure. European option prices are simulated from the rough Heston model using the characteristic function pricing approach as in El Euch and Rosenbaum (2019) and numerical techniques, such as the fractional Adams method which are implemented in MATLAB. These simulated prices are then used to test and compare the three proposed calibration methods in terms of accuracy and efficiency. Thereafter, additional experiments are conducted on South African market data from traded options and the fitted models are compared across the calibration methods used. The results of our numerical experiments are used to justify the nature of rough volatility in the South African options market and recommendations are made on the appropriateness of each calibration scheme in practice. Overall, we find that the performance measured by accuracy on our simulated data of the Neural Network method is similar to the Brute Force minimisation method, whereas the Linear Regression method, is the least accurate. When calibrating on the market data, the results of the fitted models show that both the Neural Network and Brute Force method resembles the market behaviour. All three methods were shown to be suitable in estimating the Hurst parameter and suggesting rough volatility in this South African market.

Keywords

Mathematical Finance

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