Some Simple Properties of High, Low, Open, Close: Simulating Financial Time Series and Tracking Volatility

Observations on security prices, currency exchange rates, interest rates,and other nancial time series usually include not only an open and close, but also a high and low price for the period. The information on high and low prices of considerable value, particularly for estimating volatility, and essential in the pricing of look-back and barrier options. For pricing more general derivatives, this information is useful to the extent that changes in volatility is an important ingredient in the price. This available information is used to estimate parameters , conduct tests, provide simple simulations, and generate plots sensitive to the volatility parameter.