Weibull option Greeks for managing residual value risk in automotive finance

Abstract

This study proposes a Weibull-based framework for managing residual value (RV) risk in automotive leasing and demonstrates its direct applicability to key business decisions. Unlike lognormal option models, the Weibull specification captures the asymmetric and fat-tailed nature of used-car values, or more broadly, depreciating asset values, enabling finance companies to quantify exposures more realistically. The framework embeds option-theoretic sensitivities into five operational metrics, including the offset budget, offer-timing score, volatility guardrail, scale guardrail and composite distributional alert, and applies them to Hyundai Sonata transactions in South Korea. The results show that these tools support managerial use by guiding incentive allocation, customer outreach timing and guarantee adjustments in response to rate and volatility shocks. Robustness checks confirm the stability of the metrics under bootstrap sampling and rolling parameter estimates, as well as the consistency of the Weibull-based sensitivities across vehicle models relative to lognormal and gamma benchmarks. Year-by-year tests spanning turbulent COVID-era conditions through the subsequent normalization period further show that the Weibull specification maintains a reliably strong fit. The study concludes that the framework provides practical value for auto finance companies and offers fertile directions for future work on time-varying models, as well as opportunities to extend the approach to industries where extreme, outlier-driven losses are central to risk management.