Modeling Time-to-Event Contingent Cash Flows: A Discrete-Time Survival Analysis Approach

Actuaries must often come up with risk estimates from incomplete data rapidly and accurately. One such example is predicting and pricing cash flows from a trust of individual contingent risks, such as an automobile lease consumer asset-backed security. We find that using a discrete-time product-limit estimator modified for random truncation and censoring to estimate a survival distribution for consumer automobile lease contracts along with our proposed cash flow model can effectively predict future cash flows. Furthermore, the combination of this lifetime estimator and our cash flow model allows for the derivation of direct formulas to consistently estimate the actuarial present value, its associated variance, and the conditional-tail-expectation of the full pool of contingent risks at a given point in time without the need for simulation. We also prove the modified discrete-time product-limitestimator yields an asymptotically multivariate normal estimation vector with independent components, which may be of use for small samples. The cash flow model and formulaic results perform well when applied to the Mercedes-Benz Auto Lease Trust (MBALT) 2017-A securitized bond. Keywords— Asymptotically Unbiased, Credit Risk, Lifetime Data, Risk Management