Yoon Youngin, Kim Jeong-Hoon
Department of Mathematics, Yonsei University, Seoul, 03722 Republic of Korea.
Comput Econ. 2023;61(1):429-450. doi: 10.1007/s10614-021-10214-6. Epub 2021 Nov 27.
As is well known, multi-factor stochastic volatility models are necessary to capture the market accurately in pricing financial derivatives. However, the multi-factor models usually require too many parameters to be calibrated efficiently and they do not lead to an analytic pricing formula. The double Heston model is one of them. The approach of this paper for this difficulty is to rescale the double Heston model to reduce the number of the model parameters and obtain a closed form analytic solution formula for variance swaps explicitly. We show that the rescaled double Heston model is as effective as the original double Heston model in terms of fitting to the VIX market data in a stable condition and yet the computing time is much less than that under the double Heston model. However, in a turbulent situation after the start of the COVID-19 pandemic in 2020, we acknowledge that even the double Heston model fails to capture the market accurately.
众所周知，多因素随机波动率模型对于在金融衍生品定价中准确捕捉市场是必要的。然而，多因素模型通常需要校准过多参数才能有效进行，并且它们无法得出解析定价公式。双赫斯顿模型就是其中之一。本文针对这一难题的方法是对双赫斯顿模型进行重新缩放，以减少模型参数数量，并明确获得方差互换的封闭形式解析解公式。我们表明，在稳定条件下拟合VIX市场数据方面，重新缩放后的双赫斯顿模型与原始双赫斯顿模型一样有效，但其计算时间比双赫斯顿模型下的计算时间少得多。然而，在2020年新冠疫情开始后的动荡时期，我们承认即使是双赫斯顿模型也无法准确捕捉市场。
