High Moment Variations and Their Application

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 moment 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 hedges the tail risk. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:1040–1061, 2014