Valuation of convertible bond based on uncertain fractional differential equation

Convertible bond is a hybrid financial derivative with the properties of debt and equity, which provides the holder with a right to convert bond into the issuer’s stock at a prescribed ratio in the future. This paper analyzes the valuation problems of convertible bond on the basis of uncertain fract...

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Bibliographic Details
Published in:Fuzzy optimization and decision making 2024-12, Vol.23 (4), p.513-538
Main Authors: Wang, Weiwei, Ralescu, Dan A., Zhang, Panpan
Format: Article
Language:English
Subjects:
Artificial Intelligence
Calculus of Variations and Optimal Control
Optimization
Criteria
Differential equations
Expected values
Fractional calculus
Interest rates
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Parameter estimation
Probability Theory and Stochastic Processes
Securities prices
Stochastic models
Uncertainty analysis
Valuation
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Summary:Convertible bond is a hybrid financial derivative with the properties of debt and equity, which provides the holder with a right to convert bond into the issuer’s stock at a prescribed ratio in the future. This paper analyzes the valuation problems of convertible bond on the basis of uncertain fractional differential equation. Then the prices of convertible bond are obtained by means of expected value criterion and optimistic value criterion, respectively. Besides, numerical examples are given to compare expected value models with optimistic value models. Finally, an empirical study is provided to illustrate that the uncertain fractional stock model is superior to the classical stochastic model.
ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-024-09431-z