Estimating the time-to-event distribution for loan-level data within a consumer auto loan asset-backed security

Music City Center 

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. 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 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.

Asset-level disclosures

Incomplete data

Reg AB II

Structured Finance

Survival analysis