Based upon the fact that a constant long-term mean could not provide a good description of the term structure of the implied volatility and variance swap curve, as suggested by Byelkina and Levin (in: Sixth world congress of the Bachelier Finance Society, Toronto, 2010) and Forde and Jacquier (Appl Math Finance 17(3):241–259, 2010), this paper presents a new stochastic volatility model, by assuming the long-term mean of the volatility in the Heston model be stochastic. An important feature of our model is that it still preserves the essential advantage of the Heston model, i.e., the analytic tractability, because a closed-form pricing formula for European options can be derived, which could not only facilitate the risk management process but also help save plenty of time in terms of model calibration. The effect of the newly introduced stochastic long-term mean is demonstrated through the numerical comparison with the Heston model. It is also shown that the current model can overall lead to more accurate option prices than the Heston model, through a carefully designed empirical study.

基于一个恒定的长期均值不能很好地描述隐含波动率和方差互换曲线的期限结构的事实，正如Byelkina和Levin所建议的那样（在：多伦多Bachelier金融学会第六届世界大会上， 2010年）以及Forde和Jacquier（Appl Math Finance 17（3）：241–259，2010年）中，本文假设Heston模型中的波动率的长期均值是随机的，从而提出了一种新的随机波动率模型。我们模型的一个重要特征是，它仍然保留了Heston模型的基本优势，即分析可处理性，因为可以得出欧洲期权的封闭式定价公式，这不仅可以促进风险管理流程，而且可以帮助节省大量的模型校准时间。通过与Heston模型进行数值比较，证明了新引入的随机长期均值的影响。通过精心设计的实证研究，还表明，与Heston模型相比，当前模型总体上可以导致更精确的期权价格。