Pricing of volatility derivatives using 3/2-stochastic models

Analytic solutions are found for prices of both variance and volatility swaps and VIX options under new 3/2- stochastic models for the dynamics of the underlying assets. The main features of the new stochastic differential equations are an empirically validated cv3/2 diffusion term, a nonlinear drift providing a balancing effect of a stronger mean reversion with high volatility, and for the case of the variance and volatility swaps, a free function of time as a moving target in the reversion term, allowing additional flexibility for model calibration against market data.