Sequential Itô–Taylor expansions and characteristic functions of stochastic volatility models
提出一种通过序贯使用伊藤-泰勒展开来推导一般随机波动率模型特征函数的新方法，适用于非仿射和带跳跃的模型，可数值反演出概率密度函数，用于定量金融中的定价和对冲，尤其适合中长到期权。
Abstract This study proposes a new approach to derive the characteristic function of a general stochastic volatility model by sequentially utilizing the Itô–Taylor expansions. In particular, our method applies to non‐affine stochastic volatility models with jumps, for which the corresponding characteristic functions do not have closed‐form expressions. Numerically inverting these characteristic functions can yield accurate probability density functions of stochastic volatility models to serve for various pricing and hedging purposes in quantitative finance. The proposed sequential Itô–Taylor expansion allows us to handle derivatives with medium to long maturities. Numerical experiments illustrate the accuracy and effectiveness of our approach.