This paper aims to develop a new free stochastic volatility model, joint with jumps. By freeing the power parameter of instantaneous variance, this paper takes Heston model and 3/2 model for special examples, and extends the generalizability. This model is named after free stochastic volatility model, and it owns two distinctive features. First of all, the power parameter is not constrained, so as to enable the data to voice its authentic direction. The Generalized Methods of Moments suggest that the purpose of this newly-added parameter is to create various volatility fluctuations observed in financial market. Secondly, even upward and downward jumps are separately modeled to accommodate the market data, this paper still provides the quasi-closed-form solutions for futures and option prices. Consequently, the model is novel and highly tractable. Here, it should be noted that the data on VIX futures and corresponding option contracts is employed to evaluate the model, in terms of its pricing and implied volatility features capturing performance. To sum up, the free stochastic volatility model with asymmetric jumps is capable of adequately capturing the implied volatility dynamics. Thus, it can be regarded as a model advantageous in pricing VIX derivatives with fixed power volatility models.

中文翻译：

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使用自由随机波动率模型对VIX衍生产品定价

本文旨在开发一种具有跳跃联合的新的随机随机波动率模型。通过释放瞬时方差的幂参数，本文以Heston模型和3/2模型为特殊示例，并扩展了推广性。该模型以自由随机波动率模型命名，具有两个鲜明的特征。首先，功率参数不受限制，以便使数据能够表达其真实方向。广义矩方法建议，此新添加的参数的目的是创建在金融市场中观察到的各种波动性波动。其次，即使向上和向下跳动也被分别建模以适应市场数据，本文仍然为期货和期权价格提供准封闭形式的解决方案。因此，该模型新颖且易于处理。在这里，应该注意的是，根据其价格和隐含的波动率特征来捕捉表现，采用了VIX期货和相应的期权合约的数据来评估该模型。综上所述，具有非对称跳跃的自由随机波动率模型能够充分捕捉隐含波动率动态。因此，它可以被视为有利于以固定功率波动率模型对VIX衍生产品进行定价的模型。