Estimating Asset Parameters Using Levy’s Moment Matching Method

Abstract

Conventionally, the unknown parameters in Merton’s model are set using a calibration method that estimates the current asset value and volatility from observable stock prices. This paper describes a completely different approach for estimating these asset parameters. The proposed approach uses Levy’s moment matching method to derive an equation for the asset value based on the sum of equity and debt on the balance sheet, with the current debt value treated as an unknown and estimated from stock prices. Empirical analysis reveals that this method results in simpler calculations than the calibration method and can estimate the asset parameters and default probability to the same degree of accuracy. An additional advantage of the proposed method is that it estimates the asset correlation if the current debt value is known, allowing Merton’s model to be extended to multiple companies. The asset correlation obtained by the proposed method is estimated from multiple parameters related to equity, debt, and the evaluation period, which is useful when the influence of equity volatility, leverage, and time must be considered in estimating asset correlations based on equity correlations.