A calibration study of the Merton model

In this paper we estimate the Merton model by three widely-used methods: KMV, maximum likelihood estimation and Markov chain Monte Carlo; we aim to ascertain their estimation performance and prove their (non)equivalence. The Merton model assumes the asset value to be observable, whereas in practice it remains latent and so do its parameters. As the problem of unobservability poses interesting challenges, we investigate them and attempt to provide useful insights. To our knowledge, a comparison of the three estimation methods combined, in terms of accuracy and equivalence, has not yet been made. For this comparative work we conduct a simulation study. Additionally, we extend the Merton model by masking equity prices with trading noise and estimate it using a state-space framework. Combined with earlier work, we prove that all three methods are equivalent in their update of the drift parameter and find from our simulation study that KMV (Markov chain Monte Carlo) is the most accurate estimation method (after accounting for microstructure noise). In conclusion, credit institutions may use any of the three estimation methods to estimate a firm’s growth rate. Theoretically, its estimates should coincide and we find that this too is the case, empirically.