The hedging of derivatives, which manages the risk of certain financial contracts, is one of
the most successful areas of applying mathematical finance. Any model employed for this
task simplifies reality, in order to make the complexity of financial markets tractable. In
particular, models in current use allow to divide any asset into arbitrary small pieces. This
leads to theoretical trading strategies that cannot be implemented in practice. In this
project, the inherent integrality of actual trading portfolios will be analyzed from various
perspectives. We will investigate the hedge error that results from hedging derivatives with
integral, instead of real-valued, strategies. For large amounts of identical options, as are
commonly sold by investment banks, scaling effects will reduce this error, but so far there
is no research on this. Furthermore, we will study the trading volume resulting from
hedging. By classical approaches, which use stochastic processes of infinite variation, this
problem cannot be answered. Finally, we will study options on commodity futures. Here,
the underlyings granularity can be significant, such as multiples of 1000 barrels of crude
oil. Again, we will analyze how many options are needed to make the effect of integer
constraints manageable.