Realized Volatility Options

Abstract We survey four approaches to pricing options on quadratic variation (“realized variance”) and on its square root (“realized volatility”). The first approach uses Fourier analysis to price realized volatility/variance options, assuming the availability of the characteristic function of realized variance; it leads to explicit formulas in, for instance, the Heston model and lévy models. The second approach does not assume a model for the realized variance, but instead prices volatility/variance options in terms of European options, under an independence assumption. The third approach assumes the availability of volatility and/or variance swap quotes, and prices volatility/variance options in terms of the swaps. The fourth approach assumes only the continuity of the underlying returns process; it finds lower and upper bounds, as well as subreplicating and superreplicating hedges of variance options, by use of model‐free strategies involving European options.