Convertible Bond Pricing Model In Fractional Brownian Motion Environment

Convertible bonds is a form of bonds in nature, so it still issues as bonds. Thedifference is that the issued companies have regulated in the beginning thatbondholders can choose whether to convert their holdings of convertible bonds intoshares of the issuing company at the agreed conversion ratio on the date of maturity orbefore. It has gradually become a new financial derivative product since it both hasthe characteristics of bonds and options and can create a win-win benefit for issuersand holders. Fractional Brownian motion fits the financial markets because of itsrelevance, the long-range correlation and self-similarity, and is gradually developinginto a new mainstream financial research tool.This thesis is based on the financial market model in Fractional Brownian motionenvironment. We mainly study on the value composition of the convertible bonds andthe pricing formula. The thesis includes eight chapters.In chapter one, we introduced the current research results, developments,research significance of the convertible bonds as well as the main research content.In chapter two, we first introduced the concept and nature of fractional Brownianmotion, the theory of stochastic analysis on fractional Brownian motion. Then wegave the definition of convertible bond model.In chapter three, we assumed that interest rate, volatility, dividend are constant,established mathematical models of financial markets in the fractional Brownianmotion environment where the stock price process follows a geometric fractionalBrownian motion, obtained the pricing formula with transaction costs.In chapter four, we assumed that the risk-free interest rate, expected rate of return,stock volatility and dividend rate are time function, established mathematical modelsof financial markets in the fractional Brownian motion environment and pricingformula with dividends by the use of fractional Brownian random analysis theory.In chapter five, we assumed that random interest rate follows Vasicek model andthe stock price follows a geometric fractional Brownian motion, established financialmarkets models, obtained the pricing formula of convertible bonds with bonus andrandom interest rate using actuarial method.In chapter six, we assumed that the stock price follows a geometric fractionalBrownian motion, interest rate meets the Vasicek model, established financial marketmodel under fractional jump-diffusion environment, built the pricing formula ofconvertible bonds with dividends and random interest rate using actuarial method and stochastic analysis of fractional Brownian motion theory.In chapter seven, we assumed that the stock price and the value of corporateassets follow the stochastic differential equations driven by fractional Brownianmotion, interest rate is time function, established the financial markets model infractional Brownian motion environment, and obtained the pricing formula ofconvertible bond with default risk using actuarial method.In chapter eight, we summarized the main results, and further research questions.