Estimating the time-to-event distribution for loan-level data within a consumer auto loan asset-backed security
Jackson P. Lautier, Vladimir Pozdnyakov, Jun Yan
The Annals of Applied Statistics · 2025 · Volume 19 · Issue 4
Abstract
The random cash flows of consumer auto asset-backed securities (ABS) depend critically on the time-to-event distribution of its 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 and exposure to left-truncation. We propose a parametric framework 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, we significantly simplify a complex multiparameter constrained optimization problem. These stationary points, shown to be the roots of an estimating equation, enable asymptotic normality and large-sample inference under suitable regularity conditions. For an actuarial policy limit geometric distribution, 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 methods are then applied to auto ABS data, including a likelihood ratio test to assess model specification, comparing various parametric distributions and contextualizing these results from the investor perspective.
Keywords
Asset-level disclosures; credit risk; incomplete data; Reg AB II; Survival analysis;
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