论文标题
从黑色卡拉辛基到Verhulst模型，以适应非常规美联储的政策
From the Black-Karasinski to the Verhulst model to accommodate the unconventional Fed's policy
论文作者
论文摘要
在本文中，我们认为必须重新审视和修改一些最流行的短期兴趣模型，以更好地反映当前的市场状况。特别是，我们提出了对流行的黑色卡拉辛基模型的修改，该模型被从业人员广泛用于建模利率，信贷和商品。我们的调整引起了随机的Verhulst模型，该模型在人群动力学和流行病学中作为逻辑模型众所周知。我们证明，Verhulst模型的动态非常适合当前的经济环境和美联储的行动。此外，我们为BK和Verhulst模型的零息债券价格提供了新的积分方程。对于长达2年的BK模型，我们使用还原的差分转换方法来求解相应的积分方程。对于Verhulst积分方程，在某些温和的假设下，我们找到了封闭式解决方案。数值示例表明，从计算上讲，我们的方法比标准有限差异方法要高得多。
In this paper, we argue that some of the most popular short-term interest models have to be revisited and modified to reflect current market conditions better. In particular, we propose a modification of the popular Black-Karasinski model, which is widely used by practitioners for modeling interest rates, credit, and commodities. Our adjustment gives rise to the stochastic Verhulst model, which is well-known in the population dynamics and epidemiology as a logistic model. We demonstrate that the Verhulst model's dynamics are well suited to the current economic environment and the Fed's actions. Besides, we derive new integral equations for the zero-coupon bond prices for both the BK and Verhulst models. For the BK model for small maturities up to 2 years, we solve the corresponding integral equation by using the reduced differential transform method. For the Verhulst integral equation, under some mild assumptions, we find the closed-form solution. Numerical examples show that computationally our approach is significantly more efficient than the standard finite difference method.
