Estimating Volatility in the Merton Model: The KMV Estimate is not Maximum Likelihood

Benjamin Christoffersen, David Lando*, Søren Feodor Nielsen

*Corresponding author for this work

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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.
Original languageEnglish
JournalMathematical Finance
Issue number4
Pages (from-to)1214-1230
Number of pages17
Publication statusPublished - Oct 2022


  • Distance-to-default
  • EM-algorithm
  • KMV method
  • Merton model

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