  We propose a new method of measuring the third and fourth moments of return
distribution based on quadratic variation method when the return process is
assumed to have zero drift. The realized third and fourth moments variations
computed from high frequency return series are good approximations to
corresponding actual moments of the return distribution. An investor holding an
asset with skewed or fat-tailed distribution is able to hedge the tail risk by
contracting the third or fourth moment swap under which the float leg of
realized variation and the predetermined fixed leg are exchanged. Thus
constructed portfolio follows more Gaussian-like distribution and hence the
investor effectively hedge the tail risk.
