Fuzzy option pricing advances green bond valuation under carbon risk and policy uncertainty
image: It shows the fuzzy price interval of bond prices with climate risks, which corresponds to the membership function u and the price interval. It can be seen that due to the existence of fuzzy information, the bond price with consideration of climate risk is a fuzzy interval, and people can choose an appropriate value based on the information they obtain, which is convenient for decision-making.
Credit: Chengli Zheng (Central China Normal University,China) Jiayu Jin (Central University of Finance and Economics, China) Liyan Han (Beihang University, China)
Background and Motivation
As global warming accelerates and climate policy ambitions intensify, green finance has become central to the transition toward low-carbon and sustainable economic growth. Green bonds are at the forefront, channelling funds into projects for energy conservation, emissions reduction, and environmental innovation. Yet, pricing these instruments remains challenging due to the inherent uncertainty of future climate policies, evolving green technologies, and subjective investor beliefs. Traditional pricing models often fail to capture these unique risks and the resulting fuzziness in asset valuation. China Finance Review International (CFRI) brings you a new article titled ‘Reduced interest option pricing for green bonds’, which investigates a new fuzzy option pricing framework for green bonds under carbon risk and policy uncertainty.
Methodology and Scope
This study builds on Merton’s classic corporate bond option pricing model and incorporates a jump-diffusion process to reflect the unpredictable impact of climate policy and technological innovation on firm asset values. The model further integrates fuzzy logic—specifically, Choquet expectation and λ-additive fuzzy measures—to account for uncertainties and subjective factors in bond pricing. Analytical and approximation techniques are developed to provide explicit price ranges and coupon rate intervals for green bonds, factoring in different scenarios of policy tightening, technological progress, and investor subjectivity. Scenario and sensitivity analyses illustrate how environmental standards, technological breakthroughs, and loss severity influence green bond values and pricing intervals.
Key Findings and Contributions
- Propose a fuzzy option pricing model for green bonds: The authors introduce a model that combines jump-diffusion asset processes with fuzzy logic, capturing both the volatility and uncertainty stemming from carbon policies and technological change.
- Provide analytical solutions for price intervals: The study develops explicit, scenario-based analytical pricing formulas and shows how they can deliver price and coupon rate ranges rather than single-point estimates, improving decision-making for issuers and investors.
- Demonstrate that policy tightening and loss severity drive price variability: Sensitivity analysis reveals that stricter environmental standards and higher potential losses from non-compliance have the largest impact on bond value intervals.
- Highlight the importance of subjective and fuzzy information: By incorporating investor subjectivity and information fuzziness, the model aligns more closely with real-world decision-making and market dynamics.
- Advance practical tools for the green bond market: The approach allows for flexible, scenario-specific pricing, supporting more robust risk management, policy design, and green investment under uncertainty.
Why It Matters
Accurately pricing green bonds is crucial for steering investment towards sustainable projects and for managing climate-related financial risk. By integrating jump-diffusion processes and fuzzy logic, this research equips market participants with tools to price green bonds more realistically—reflecting not only observable risks but also policy shifts and subjective uncertainties. This can help drive capital into the green sector, support the achievement of carbon neutrality goals, and strengthen financial market stability amid the transition to a low-carbon future.
Practical Applications
- For Researchers: This model provides a rigorous and innovative framework for analysing the pricing of green financial instruments, supporting future theoretical and empirical studies on climate risk and financial market uncertainty.
- For Investors: The fuzzy pricing method offers investors more accurate risk assessment and practical coupon rate intervals, enhancing decision-making under conditions of policy and technological uncertainty.
- For Policymakers: The findings suggest that clear and enforceable emission standards, along with effective economic penalties and incentives for technological breakthroughs, can shape green bond pricing and direct funds toward genuine low-carbon investments.
- For Issuing Enterprises: The methodology helps companies better understand how technological upgrades and compliance strategies impact their financing costs, and how to position themselves in the evolving green bond market.
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