Analytically pricing volatility swaps under stochastic volatility

Papers focusing on analytically pricing discretely-sampled volatility swaps are rare in literature, mainly due to the inherent difficulty associated with the nonlinearity in the pay-off function. In this paper, we present a closed-form exact solution for the pricing of discretely-sampled volatility swaps, under the framework of Heston (1993) stochastic volatility model, based on the definition of the so-called average of realized volatility. By working out such a closed-form exact solution for discretely-sampled volatility swaps, this work represents a substantial progress in the field of pricing volatility swaps, as it has: (1) significantly reduced the computational time in obtaining numerical values for the discretely-sampled volatility swaps; (2) improved the computational accuracy of discretely-sampled volatility swaps, comparing with the continuous sampling approximation, especially when the time interval between sampling points is large; (3) enabled all the hedging ratios of a volatility swap to be analytically derived.