The Martingale Pricing For Convertible Bond

Compounding portfolio is a kind of portfolio that connecting many basic elements (interest rates, exchange rates, contingent claims, goods, etc.) with the market, also existing in the structure of those elements. Positioning the price of compound portfolio reasonably and suitably is an important subject which has theoretical practical value in financial mathematic study.Interest rates/contingent claims compounded portfolio is a portfolio that mixed the elements of interest rate contingent claims into the integral profit of portfolio. The paper present 3 innovations toward the Interest rates/contingent claims compounded portfolio- convertible bond under the completed and continuous market module. Under the assumption that convertible has back buy treaty, back sell treaty ,also in the case of stochastic interest, the stock has dividend-paying, 3 pricing formulas of the convertible bond are evolved by means of martingale approach(risk-neutral valuation).The main innovatory results as follows:1.Under the assumption that the process of asset price is lognormal distribution, the pricing formulas of the convertible bond are obtained, also the characteristic of price wave and risks can be detected.2.The pricing formulas of the convertible bond with back buy treaty are evolved, and it's characteristics in price wave and risks be detected, then compare the value of the innovatory convertible bond with that of the ordinary convertible bond.3.The pricing formulas of the convertible bond with back sell treaty are evolved, and it's characteristics in price wave and risks be detected , then compare the value of the innovatory convertible bond with that of the ordinary convertible bond.4.Under the assumption of stochastic interest, and the stock has dividend-paying, the pricing formulas of the convertible bond are obtained.