Don L. McLeish - Estimating parameters of financial time series using highs and lows

Observations on security prices, currency exchange rates interest rates and other financial time series usually include not only open and closing values over periods of time but also highs and lows for the same periods. This information on highs and lows is often disregarded, in part because the joint distributions are very complicated in fact most are unknown). However, these observations are highly informative about the volatily, the correlations among securities, how to hedge one using another, testing for a change in drift, and the valuation of certain options lookback, barrier, etc.) that depend on upper and lower barriers. We suggest some semi-parametric methods for using this information efficiently, illustrating the methods using the stock prices of the major Canadian Banks.