Realised volatility estimators

Königkrämer, Sören

Realised volatility estimators

Master Thesis

2014

Publisher

University of Cape Town

Department

Division of Actuarial Science

Faculty

Faculty of Commerce

Abstract

This dissertation is an investigation into realised volatility (RV) estimators. Here, RV is defined as the sum-of-squared-returns (SSR) and is a proxy for integrated volatility (IV), which is unobservable. The study focuses on a subset of the universe of RV estimators. We examine three categories of estimators: historical, high-frequency (HF) and implied. The need to estimate RV is predominantly in the hedging of options and is not concerned with speculation or forecasting. The main research questions are; (1) what is the best RV estimator in a historical study of S&P 500 data? (2) What is the best RV estimator in a Monte Carlo simulation when delta hedging synthetic options? (3) Do our findings support the stylized fact of `Asymmetry in time scales' (Cont, 2001)? In the answering of these questions, further avenues of investigation are explored. Firstly, the VIX is used as the implied volatility. Secondly, the Monte Carlo simulation generates stock price paths with random components in the stock price and the volatility at each time point. The distribution of the input volatility is varied. The question of asymmetry in time scales is addressed by varying the term and frequency of historical data. The results of the historical and Monte Carlo simulation are compared. The SSR and two of the HF estimators perform best in both cases. Accuracy of estimators using long term data is shown to perform very poorly.

Description

Includes bibliographical references.

Keywords

Mathematical Finance

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