| In a wide variety of products in the financial markets, convertible bonds, although not the most compelling products, but after 170 years of history of baptism points, shares of its convertible bonds, bonds and options of the three properties of the unique advantages of rolled into one, still plays in corporate finance, financial market development role. Therefore, the convertible bonds Pricing Model, is able to reflect its value and in line with market needs.This paper describes the meaning of convertible bonds and characteristics of convertible bonds for stock nature of the special bonds and options are described, including, convertible bonds, options, or maturity can be implemented in advance of the American option This is also the product characteristics of convertible bonds, the decision of the product in terms of the convertible bonds, in addition to the general price, time period, conversion rights, profit rate, it also contains redeemable in particular the right to sell back to the right Protection of the terms of the complex variable, so this has increased the difficulty of pricing convertible bonds. Subsequently, the paper of convertible bonds in China’s market had documentation to explain the development of China’s history of convertible bonds, both issued products on the market process, but also includes convertible bonds in China for the development process of legislation. Convertible bonds in China from 1992 to the current market, the first issue circulation of only 10 a few, our market were issued 77 convertible bonds, convertible bonds issued by the size and quality are changing dramatically, convertible bonds Market has also been a great specification. Legislation, the first convertible bond for the definition and the provisions of company law carried out only in those expounded. In 1997, the State Council Securities Commission issued the "Interim Office of the Convertible Bonds, "and began to carry out non-listed companies in the broader area of the pilot issue of convertible bonds. In 2001, the "Convertible Bonds listed companies to implement, "the"listed companies application for the issuance of convertible corporate bonds document ","Convertible bond prospectus," and the "Convertible Bonds Listing Announcements" corresponding promulgated, China Convertible bonds formally embarked on a fast track, the amount of convertible bond issues has been further expanded. Analysis of the development process of the convertible bond can be subdivided into four stages.1991-1997-year exploration phase; 1997-2001 year pilot phase; 2001-2002 in the specification phase; and the 2002 stage of development after the market track. Subsequently, the paper summarizes the convertible bond market of the general characteristics, specific mainly small; China issued convertible bonds in the enterprise and industry distribution is uneven, mostly found in construction, energy and financial sectors; the terms of issue of convertible bonds Design convergence, companies can not form issued by the difference can be transferred and can not cause the market’s attention. At the same time, our system of convertible bond issues is a reason for restricting market development, China has adopted a system of examination and approval system, greatly improving the distribution requirements. China’s public offering in the form of convertible bonds issue is the lack of private equity in the form, so it also hindered the expansion of the market space. In addition, even though China launched a short-mechanism, but the matching system is imperfect, hindering arbitrage activities of institutional investors.Subsequently, the paper studies the pricing of convertible bonds involving domestic and international documentation. Foreign research, the paper start with the Black-Scholes option pricing formula, the research on the options in the options for the nature of convertible bonds were studied. First of all the BS pricing formula Ingersoll Queen to the pricing of convertible bonds and convertible bonds have been closed form solution, and the value of the company based variables, the single factor model. Brennan & Schwart On this basis, the company established a value-based interest rates and variable two-factor model, and concluded that the price of convertible bonds is not sensitive to interest rates. Mihir Bhattacharya & Zhu convertible bonds through the study found that although the market is not sensitive to interest rates, but is sensitive to changes in stock prices, so you can stock as a base variable, construct single-factor model. Subsequently, relevant scholars in the model and added back to the sales conditions, credit risk and redemption policies, the pricing of convertible bonds were studied. Some scholars from the market phenomena, analyzing the market price is undervalued convertible bonds reason. Some scholars in the aspects of convertible bonds, arbitrage activities investigated the impact of the relevant stock market. Domestic research, scholars in China Pricing of convertible bonds late start, and because of the convertible bond market imperfections, did not have the research conditions. The earliest of pricing convertible bonds is equal to the use of Lin Yi-Black-Scholes pricing model for pricing convertible bonds. Later scholars of convertible bonds for a further analysis, speaking of convertible bonds into ordinary bonds and the value of the options had to consider enterprises in the non-callable and callable situation. Some scholars are of the redeemable convertible bond issuers and investors, dynamic game between the process of construction pricing. Some scholars from the numerical simulation algorithm, based on variables such as stock price perspective study of convertible bonds. According to foreign scholars, research ideas, some scholars have found empirical test of the Convertible Bonds are not sensitive to interest rates. Subsequently, some scholars from the stochastic interest rate, the risk of bankruptcy and the controlling shareholders in decision-making behavior on the side of the angle the pricing of convertible bonds were studied. Recent scholars, mainly related to the market price is found to be underestimated, as well as convertible bonds pricing control equation.The focus of this paper squares Monte Carlo simulation method (LSM) in the use of pricing convertible bonds. In the literature, the start of foreign Longstaff & Schwartz first proposed LSM start, they use LSM method of pricing American options, creating a LSM method is used to set a precedent for pricing derivatives In the next few years, various scholars of American options LSM approach has been improved, for example, American Put LSM method for the numerical results show that the choice of different alternative polynomials is stable and requires less Basic function; sampling variance reduction techniques; the number of basis functions of different polynomial function changes and low differences in sequence can improve the accuracy of LSM. Others through control variables to reduce variance, or the path generated by improving the initial LSM state variables. LSM applied to domestic pricing of American options early in 2008 to study the pricing of American options LSM method a specific algorithm. Some scholars and LSM method of pricing of convertible bonds was related to empirical test and found that China’s undervalued convertible bonds. Some scholars put the LSM approach has been applied to insurance pricing insurance and financial products.After a literature review, that is the focus of the third part of this article. Convertible bonds as a derivative product, the paper first describes the convertible bond pricing theory. These are derivatives in the theory or theoretical assumptions, mainly in convertible bonds with equity features, the stock is a Wiener process, satisfying a normal distribution; in the financial markets, if set Profit opportunity, the influx of investors will eventually digest the arbitrage profits, so in theory, assuming the financial market is to meet the no arbitrage theory; BS option pricing model is the foundation of all is the basis of the convertible bond pricing; risk Neutral pricing means all investors are risk neutral.Monte Carlo simulation could have been in mathematics or physics method, but when it is executed with the option to taking into account the uncertain time. Monte Carlo simulation method is introduced to option pricing is an excellent method. This paper gives a general definition of Monte Carlo simulation, and then introduced the principle of Monte simulation test slightly, that is based on the probability characteristics of the object, the use of computer-generated sample of the results and then calculate the parameter values. Monte Carlo simulation accuracy and simulation times is closely related to the higher simulation times higher identified, but we must consider the calculation of the amount of time to do a balance. In the Monte Carlo simulation, the simulation will produce variance. Variance for the simulation to study the dual variables obtained by technology, the control variable technique, stratified sampling technique, moment matching technique and conditions of Monte Carlo simulation methods were modified. This paper describes the basic steps of Monte Carlo simulation, the proposed Monte Carlo simulation of the two major drawbacks:First, slow convergence, the more complex derivative products have the estimation error and the estimated time is substantially increased; followed Monte Carlo simulation with path dependence, the characteristics of forward simulation, the iterative search for the feature after the American option has a certain degree of difficulty of analog.Monte Carlo simulation for these two defects, we introduce the least squares Monte Carlo (LSM) method. LSM method from the former two aspects were improved and developed. One is to improve the simulation of the estimation error reduction technologies, specifically to reduce the statistical error and discretization error. Statistical error can be achieved by stratified sampling method. Discretization error is simulated by changing the path of dependence to achieve. Subsequently, the paper first describes the LSM method described and American options in the specific processes and methods, and then combine the characteristics of convertible bonds proposed LSM method in convertible bond pricing how. Convertible bonds are more complicated than the American options, this article continues to discuss the conversion, put, call, forced conversion and continue to hold such circumstances, investors can execute the conditions and limitations, and draw profit and loss income.The improved method of analysis of LSM focus on variance reduction of the technology. Also divided into control variables technique, the dual variable technology, based on importance sampling and stratified sampling, Latin Hypercube techniques. Technology is the control variable for the variable and the correlation between the variables, one of the variables in that case, the variable can be constructed by another unknown variable to control for unknown variables. Of course, the control variables in the process of computing the amount of the larger operation, so the need to consider time and improve accuracy of the comparison between. Technology is the dual variable by setting the two samples, two kinds of simulation. One set of samples used in random sampling, and is in general based on the Monte Carlo simulation, while the other set of samples is the use of dual random sample. Then, the sum of the two simulation results averaged. Technology can eliminate the dual variable number of variance swaps in the non-singular part of the function. Moreover, uniform or non-uniform distribution for the process of dual technology can have a good effect. Importance sampling technique is a variance under the probability measure, under the probability measure into another variance, that is to change the sample path generated by simulation, by changing the path generation process, to change the probability measure, thus reducing the variance. Importance sampling techniques are generally applied to small probability simulation of events in derivatives pricing, for example, the pricing of portfolio credit derivatives, barrier options under jump diffusion and derivative pricing. Stratified sampling is stratified by the total sample, and samples of special importance to assign a greater proportion of the sample layer on the emergence of a large amount more. Variance to compare the size of the improved in order to adjust to the variance reduction effect of the best point. Latin Hypercube Sampling is the use of no replacement stratified sampling technique, divide it into Dengfen, and then each Dengfenzhiyou Yici chance of selection, it is the image of the advantage lies more the shape of the response for samples.At last, the paper concluded that the variance of technological improvements can play a large effect of improving simulation accuracy of LSM. But there are not ideal, I believe that this was mainly due to convertible bond market in China is immature, so the market price can not be found. Convertible bonds issued by the pricing bias is possible, and the model does not take into account the market rate, redemption rights, the right to sell back to the characteristics of convertible bonds. So, this is only LSM method to improve this convertible bond pricing in a simple try. Taking into account the characteristics of convertible bonds and convertible bonds in China’s market characteristics. Improvement of LSM can still be worthy of study, found that the real price of convertible bonds, which can be studied and investors have been pursuing. |
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