Real option valuation using Weibull distribution: a new framework for depreciation risk management

• Published in: Seonmul yeongu (Online) Vol. 33; no. 2; pp. 110 - 130
• Main Author: Ko, Seok Bin
• Format: Journal Article
• Language: English
• Published: Bingley Emerald Publishing Limited 12.05.2025; Emerald Group Publishing Limited; Emerald Publishing; 한국파생상품학회
• Subjects: Automobile leasing; Car leases; Depreciation; Derivatives; Expected values; Finance companies; Flexibility; Funding; Institutional investments; Investors; Leases; Left-skewed distribution; Parameter estimation; Product development; Put & call options; Put option formula; Random variables; Real option valuation; Risk management; Securities prices; Skewness; Stochastic models; Valuation; Volatility; Weibull distribution; 경영학; Left-skewed distribution; Put option formula; Car leases; Weibull distribution; Real option valuation
• ISSN: 1229-988X; 2713-6647; 2713-6647; 1229-988X
• DOI: 10.1108/JDQS-10-2024-0041

This study aims to develop an accurate option pricing model for car leases by introducing a put option valuation framework based on the Weibull distribution. Traditional models typically assume asset values follow a lognormal distribution, failing to capture the left-skewed nature and bounded dynamics. To address this limitation, this study compares the performance of the Weibull distribution with that of the lognormal model using residual value data from two popular car models in South Korea, evaluating each model’s ability to reflect unique depreciation patterns. The findings demonstrate that the Weibull distribution provides a superior fit to the data, leading to more precise option pricing. This enhanced accuracy is crucial for auto finance companies navigating uncertainties in used car prices, particularly as the mobility services and car leasing markets continue to expand. Moreover, the practical implications of this research extend beyond the auto finance industry; insights from this study can inform sectors dealing with skewed or bounded assets, such as insurance products and financial derivatives, thereby enabling improved risk assessment and decision-making processes. This research introduces a novel approach to modeling put option values using the Weibull distribution, filling a significant gap in the existing literature on car lease option pricing. However, as this is the first study to model put option values using the Weibull distribution, further research is necessary. Specifically, investigating volatility patterns over the lifecycle of used cars could significantly enhance the value of this framework.