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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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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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description	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.
doi_str_mv	10.1007/s10700-024-09431-z
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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
title	Valuation of convertible bond based on uncertain fractional differential equation
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