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Mean Reversion of Rates and Prices in the South African Market

Abstract Value at Risk (VaR) has become a widely accepted concept and has been hailed by both financial institutions and regulators. Many methods use instrument volatilities to estimate VaR. There are several procedures to calculate volatility and many use the simple standard deviation of a set of returns. Whilst this method is not wildly inaccurate under stable market conditions, it makes several assumptions about returns which are invalid during periods of high market activity, rendering the estimation of VaR inaccurate at times its value is most needed. In this paper we examine the assumption that the price (or rate) series is an entirely random process. One of the implications of this assumption is that price changes are independent of previous changes. In practice, price series tend to revert to their long run means and the omission or inclusion of this fact alters the calculated volatility and hence the VaR.