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

Abstract

Prudent management of insurance investment portfolios requires competent asset pricing of fixed-income assets with time-to-event contingent cash flows, such as consumer asset-backed securities (ABS). Current market pricing techniques for these assets either rely on a non-random time-to-event model or may not utilize detailed asset-level data that is now available with most public transactions. We first establish a framework capable of yielding estimates of the time-to-event random variable from securitization data, which is discrete and often subject to left-truncation and right-censoring. We then show that the vector of discrete-time hazard rate estimators is asymptotically multivariate normal with independent components, which has not yet been done in the statistical literature in the case of both left-truncation and right-censoring. The time-to-event distribution estimates are then fed into our cash flow model, which is capable of calculating a formulaic price of a pool of time-to-event contingent cash flows vis-\'{a}-vis calculating an expected present value with respect to the estimated time-to-event distribution. In an application to a subset of 29,845 36-month leases from the Mercedes-Benz Auto Lease Trust 2017-A (MBALT 2017-A) bond, our pricing model yields estimates closer to the actual realized future cash flows than the non-random time-to-event model, especially as the fitting window increases. Finally, in certain settings, the asymptotic properties of the hazard rate estimators allow investors to assess the potential uncertainty of the price point estimates, which we illustrate for a subset of 493 24-month leases from MBALT 2017-A.