High frequency data are often used to construct proxies for the daily volatility in discrete time volatility models. We introduce a calculus for such proxies, making it possible to compare and optimize them. The two distinguishing features of the approach are (1) a simple continuous time extension of discrete time volatility models and (2) an abstract definition of volatility proxy. The theory is applied to eighteen years worth of S&P 500 index data. It is used to construct a proxy that outperforms realized volatility. Paper available at: http://staff.science.uva.nl/~marvisse/