Abstract Implied volatility and implied vol-of-vol are two different sources of risk but the latter has been generally neglected. However, recent studies show the importance of both risk factors for investment strategies. The elasticity of vol-of-vol is focused on in this paper. We propose a revised Heston model reflecting the random nature of vol-of-vol and obtain pricing formulas of variance swaps for simple returns. We use a perturbation technique to transform the problem into a partial differential equation problem and then use the Green function and Fourier transform methods to derive explicitly a quasi-closed form approximation of the fair strike price. Subsequent result shows a comparison with the Heston result and the impact of the stochastic elasticity of vol-of-vol on the variance swap price.

中文翻译：

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vol-of-vol 的随机弹性和方差掉期的定价

摘要 隐含波动率和隐含波动率波动率是两种不同的风险来源，但后者通常被忽视。然而，最近的研究表明这两个风险因素对投资策略的重要性。vol-of-vol 的弹性是本文的重点。我们提出了一个修正的 Heston 模型，反映了 vol-of-vol 的随机性，并获得了简单收益的方差掉期定价公式。我们使用扰动技术将问题转化为偏微分方程问题，然后使用格林函数和傅立叶变换方法明确推导出公平执行价格的准封闭形式近似值。随后的结果显示了与 Heston 结果的比较以及 vol-of-vol 的随机弹性对方差互换价格的影响。