  We develop a methodology for index tracking and risk exposure control using
financial derivatives. Under a continuous-time diffusion framework for price
evolution, we present a pathwise approach to construct dynamic portfolios of
derivatives in order to gain exposure to an index and/or market factors that
may be not directly tradable. Among our results, we establish a general
tracking condition that relates the portfolio drift to the desired exposure
coefficients under any given model. We also derive a slippage process that
reveals how the portfolio return deviates from the targeted return. In our
multi-factor setting, the portfolio's realized slippage depends not only on the
realized variance of the index, but also the realized covariance among the
index and factors. We implement our trading strategies under a number of
models, and compare the tracking strategies and performances when using
different derivatives, such as futures and options.
