Estimating volatility in the Merton model: The KMV estimate is not maximum likelihood
比较了默顿模型中两种资产波动率估计方法（最大似然和KMV迭代法），发现两者不等价，并给出了等价条件，数值显示该条件对实值期权近似成立。
Abstract We compare two methods for estimating the asset volatility in the Merton model using observed equity prices: maximum likelihood and an iterative method commonly referred to as the KMV method. The two methods often yield extremely similar estimates, which has led to the conjecture that the two methods are equivalent. We show that this is not true and we provide a necessary and sufficient condition that the inverse of the equity pricing function would have to satisfy for the two methods to be equivalent. Moreover, we show numerically that this condition is very close to being true for in‐the‐money options.