论文标题
一个新的自我兴奋的跳转过程，用于期权定价
A new self-exciting jump-diffusion process for option pricing
论文作者
论文摘要
我们提出了一个新的跳投过程，即Heston-Queue-Hawkes（HQH）模型，结合了著名的Heston模型和最近引入的排队霍克斯（Q-Hawkes）跳跃过程。像霍克斯的过程一样，HQH模型可以捕获自我激发和传染的影响。但是，由于HQH过程的特征函数是在封闭形式中已知的，因此可以使用该模型完全利用基于傅立叶的快速定价算法（如COS方法）。此外，我们表明，通过使用特征函数的部分积分，这也是HQH过程明确闻名的，我们可以降低COS方法的维度，从而减少其数值复杂性。欧洲和百慕大选项的数值结果表明，与BATES模型相比，HQH模型提供了更广泛的波动性微笑，而其计算负担远小于Heston-Hawkes（HH）过程。
We propose a new jump-diffusion process, the Heston-Queue-Hawkes (HQH) model, combining the well-known Heston model and the recently introduced Queue-Hawkes (Q-Hawkes) jump process. Like the Hawkes process, the HQH model can capture the effects of self-excitation and contagion. However, since the characteristic function of the HQH process is known in closed-form, Fourier-based fast pricing algorithms, like the COS method, can be fully exploited with this model. Furthermore, we show that by using partial integrals of the characteristic function, which are also explicitly known for the HQH process, we can reduce the dimensionality of the COS method, and so its numerical complexity. Numerical results for European and Bermudan options show that the HQH model offers a wider range of volatility smiles compared to the Bates model, while its computational burden is considerably smaller than that of the Heston-Hawkes (HH) process.
