Pricing Convertible Bonds With Reset

Convertible bonds are the corporate bonds with the right of coversion,which renders the right to the holder that can covert the security to that company's stock with the pre-specified conversion price in the fixed period. Hence, convertible bonds are the stock derivative financial instrument, which has the characters of equity and bond. In the investors'position, they can obtain the infinite interest. However, in the issuers'position, they can obtain the low cost of financing through selling the implied option. Therefor after it's bornd, convertible bonds are widely and increasingly concerned by investors and issues.Now, it has becomed the important part of the cpital market.In our country,the convertible bonds'market began developing in the early 1990s.After ten years, it has made considerable development not only in issuing amount but also in issuing scale, becoming the important supplementary part of the China's capital market.In order to attracting investors,the attached clauses become diverse, so these don't get the pricing of convertible bonds once for all. Particularly, the reset clause (that's in the fixed period, if the pre-specified conversion price is lower than the stock price, we must reset the conversion price) is similar with the reset option in this point. Many investors are attracted by this clause, because it protects the value of convertible bonds decreasing when the stock price comes down. But the clause makes the pricing of convertible bonds becoming more complex.The thesis specially researches the convertible bonds with reset clause. Assume that the convertible bonds haven't credit risk, the risk-free rate is constant, the underlying stock receives no dividends and the interest is payed until the maturity. Under these assumptions, no conversion occurs prior to maturity, that's to say the convertible bonds must necessarily be the European type. Moreover, if the stock price is lower in a long time, we can reset the conversion price and promote the value of convertible bonds. In such circumstances, the put clause doesn't happen. Under these presupposition, we gain the solution of the value of convertible bonds with one reaet, multiple reset, the geometric average reset, and then pricing the convertible bonds with arithmetic average reset can benefit by using the formula as the control variant in Monte Carlo simulation.This thesis includes six parts:Introduct and chapter one, the author introduce the development of convertible bonds at home and abroad, the definition and the caulses of convertible bonds, and then analyzes the factors that affec their value, finally studies the foreign and domestic achievements concerning the thory of pricing convertible bonds. At the same time, the author gives the research ideas of the thesis, the creative point and the related theories.Chapter two, the author perfects the Toshikazu Kimura and Toshio Shinohara's discussion of the value of European convertible bonds with one reset, and gives the solution of the value of convertible bonds and then discusses the result. In order to adapt to the reality, the author prices convertible bonds with multiple reset and obtains the solution.Chapter three, the author firstly analysis the character of the geometric average of the stock price, and then assumes that the stock price follow the geometric Brownian motion. Under this assumption, the geometric average of the stock price also follows the geometric Brownian motion. On the basis, the author obtains the solution of the value of convertible bonds with geometric average reset.Finally the author compares it with the value of convertible bonds with one reset.Chapter four, the author introduces the thory of Monte Carlo simulation, and then pricing the convertible bonds with arithmetic average reset can benefit by using the result of the third chapter as the control variant in Monte Carlo simulation. Finally the author draws a conclusion that for the convertible bonds, the difference between geometric average reset and arithmetic average reset is very subtle.At last, the author makes the conclusion and points out the future research direction.