Multiscale stochastic volatility for variance swaps with constant elasticity of variance

Abstract

The 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 is an important part of the risk management. One of desirable considerations should be given to the fact that the volatility varies on several characteristic time scales. Stochastic volatility models can reflect this feature by introducing multiscale volatility factors. However, pure stochastic volatility models cannot capture the whole volatility surface accurately although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. So, we choose a hybrid model of constant elasticity of variance type of local volatility and fast and slow scale stochastic volatility for evaluating the fair strikes of variance swaps. We obtain a closed-form solution formula for the approximate fair strike values of continuously sampled variance swaps and compute the solution. The theoretical formula is validated through Monte Carlo simulation. The predictability of the strike price movements is discussed in terms of the sensitive effects of the stochastic volatility and the elasticity of variance parameters for a given partial information about the underlying asset and volatility.