A0615
Title: Estimating the time-to-event distribution for loan-level data within a consumer auto loan asset-backed security
Authors: Jackson Lautier - Bentley University (United States) [presenting]
Jun Yan - University of Connecticut (United States)
Vladimir Pozdnyakov - University of Connecticut (United States)
Abstract: The random cash flows of consumer auto asset-backed securities (ABS) depend critically on the time-to-event distribution of the individual, securitized assets. Estimating this distribution has historically been challenged by limited data. Recent regulatory changes reversed this, however, and asset-level auto ABS data is now publicly available to investors for the first time. The idiosyncrasies of this ABS data present new difficulties in estimating the loan-level lifetime distribution due to its discrete-time structure, finite support, and exposure to left truncation. A parametric framework is proposed for estimating the loan-level lifetime distribution while leaving the left-truncation time distribution unspecified. Through theorems developed to identify the stationary points of the likelihood, a complex multiparameter-constrained optimization problem is significantly simplified. These stationary points, shown to be the roots of an estimating equation, enable asymptotic normality and large-sample inference to follow. In the special case of a finite geometric distribution via an actuarial policy limit, closed-form maximum likelihood estimates may be derived. These theoretical results are further generalized to accommodate right-censoring and validated through numerical and simulation studies. These efficient and accurate estimation methods are then applied to data from two Ally Auto Receivables Trust ABS bonds, which can offer potentially valuable insights to investors.
