Multiscale stochastic volatility for variance swaps with constant elasticity of variance

Abstract Variance swap is one of volatility derivatives popularly used for the risk management of financial instruments traded in volatile market. An appropriate choice of a volatility model should be an important part of the risk management. In this paper, we consider a hybrid model of constant elasticity of variance and multiscale (fast and slow) stochastic volatility. Based on this framework, we obtain a closed form solution formula for the approximate fair strike values of continuous time variance swaps and compute the solution. The theoretical formula is validated by numerical solution given by MonteCarlo simulation. The multiscale effect and the predictability of the strike price movements are investigated for a given information about the underlying asset and volatility.