论文标题
分数Heston跳跃扩散模型的分解公式
A decomposition formula for fractional Heston jump diffusion models
论文作者
论文摘要
我们在随机波动率模型中为欧洲期权提供了一个期权定价公式。特别是，使用扩散过程的分数积分来定义波动过程，股票价格和波动率过程都有跳跃，以捕获称为杠杆作用的市场效应。我们展示了如何计算波动率过程中的Martingale代表。最后，使用ItôCilculus进行不连续轨迹的过程，我们为期权价格开发了一阶近似公式。在传统定价方法中使用这种近似公式有两个主要优点。首先，为了提高计算效率，其次是对模型参数变化的期权价格变化有更深入的了解。
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility processes have jumps in order to capture the market effect known as leverage effect. We show how to compute a martingale representation for the volatility process. Finally, using Itô calculus for processes with discontinuous trajectories, we develop a first order approximation formula for option prices. There are two main advantages in the usage of such approximating formulas to traditional pricing methods. First, to improve computational effciency, and second, to have a deeper understanding of the option price changes in terms of changes in the model parameters.
