  In this paper, we relax the power parameter of instantaneous variance and
develop a new stochastic volatility plus jumps model that generalize the Heston
model and 3/2 model as special cases. This model has two distinctive features.
First, we do not restrict the new parameter, letting the data speak as to its
direction. The Generalized Methods of Moments suggests that the newly added
parameter is to create varying volatility fluctuation in different period
discovered in financial market. Moreover, upward and downward jumps are
separately modeled to accommodate the market data. Our model is novel and
highly tractable, which means that the quasi-closed-form solutions for future
and option prices can be effectively derived. We have employed data on VIX
future and corresponding option contracts to test this model to evaluate its
ability of performing pricing and capturing features of the implied volatility.
To sum up, the free stochastic volatility model with asymmetric jumps is able
to adequately capture implied volatility dynamics and thus it can be seen as a
superior model relative to the fixed volatility model in pricing VIX
derivatives.
