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 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.