The estimation of daily volatility using high frequency data in the South African equity market

Abstract

Financial market volatility is central to the theory and practice of asset pricing, option pricing, asset allocation, portfolio selection, portfolio rebalancing and hedging strategies as well as various risk management applications. Most textbooks assume volatility to be constant; however in practice this is a very dangerous assumption to make and has lead to a research program regarding the distributional and dynamic properties of financial markets. Given that financial markets display high speeds of adjustment, studies based upon daily observations may fail to capture information contained in intraday or high frequency market movements and until relatively recently the use of daily or equally spaced data was considered the highest meaningful sampling frequency for financial market data. Recently the volatility modelling literature took a significant step forward. Andersen et al. (2001) proposed a new approach called 'realized' volatility that exploits the information in high frequency returns. Basically, the approach is to estimate daily volatility by taking the square root of the sum of the squared intraday returns which are sampled at very short intervals. We discuss several theoretical measures for volatility of which quadratic variation (QV), integrated variance (IV) and conditional variance (CV) are the most popular. Realized variance is a consistent estimator for QV and can approximate IV and CV under various conditions. GARCH models are only concerned with estimating CV.