Investigating Rough Volatility in Fractional Processes of Financial Time Series Models

Specialeforsvar: Peter Hjortskov Andersen

Titel: Investigating Rough Volatility in Fractional Processes of Financial Time Series Models

Abstract: This Master’s thesis investigates the modelling of volatility processes in financial time series. More specifically, we examine whether there is statistical evidence to conclude that volatility is rough, i.e., should be modelled by so-called rough processes with a roughness H < 1 2 . Through detailed numerical examples, we demonstrate that wellknown roughness estimators, which perform well on instantaneous volatility data, can systematically underestimate the true roughness of the underlying model when based on realized volatility data. Consequently, models with diffusive or smooth behaviour (i.e.,H ≥ 1
2 ) may also be compatible with observed roughness in empirical realized volatility data. We show that the distortion of the roughness estimates arises from estimation errors when approximating volatility by realized volatility. Additionally, we investigate the performance of the sequential scale estimator, which is designed to account for estimation errors. We find that the sequential scale estimator requires a large number of observations to be fully unaffected by proxy errors. Thus, it does not resolve the primary issue of distortion from proxy errors in our numerical examples, which are based on realistic sample sizes encountered in high-frequency financial data.

Vejleder: David Skovmand
Censor: Mads Stenbo Nielsen,  CBS