Convertible Bonds Pricing Models For Uncertainty Theory

Convertible bonds play an important role in capital markets in Western developed countries as a sophisticated financial instrument for more than one hundred years. With the development of China's capital market, people pay more and more attention to convertible bonds which developed very rapidly in recent years and have become the important financing tool for China's listed com-panies as well as one of the major investment products in the secondary market. It's important to evaluate convertible bonds accurately for the reasonable design of issuers, the rational investment of investors and the health development of the financial markets.Along with the economic globalization, financial market becomes increasingly mature and complete. While generally, the financial market is fraught with uncertainty. In order to better study the financial markets, Professor Liu Baoding established uncertainty theory in 2007. Uncertainty theory combined random theory and fuzzy theory together can better describe the behavior of uncertain phenomena and give more realistic financial derivatives pricing models. Uncertainty theory is a branch of mathematics by introducing uncertain variables, uncertain measure, uncertain process and other new content.This dissertation is intended to study the convertible bond pricing model for the uncertainty theory. Suppose the enterprise value is described by a geometric canonical process and the con-vertible bonds are composed of bonds and options. It tries to get more precise convertible bonds pricing models by using the uncertainty theory to better characterize the uncertainty of convertible bonds markets.First, this paper has an overview of convertible bonds in the basic theory, characteristics, his-tory of the development and research situation at home and abroad; Chapter 2 introduces the basic concepts and related knowledge of uncertainty theory; In Chapter 3 the definition of arbitrage and some basic properties of no arbitrage in fuzzy financial markets are given; In chapter 4, we con-structed the formula of convertible bonds pricing, bonds pricing with credit risks and convertible bonds pricing with interest and dividends regarding the convertible bonds as a portfolio of bonds, European call options and European put options based on the assumption that enterprise value follows the geometric canonical process. In Chapter 5, we analyze the pricing of redeemable convertible bonds and convertible bonds which can be sold back to company and give out the expression of market interest rate under uncertainty theory.