The Research Of Risk Measurement Model And Algorithm On Chinese Convertible Bonds

Convertible bond is a hybrid financial derivative which has dual character of bonds andoptions. Its form of value is quite complex, and has become an important derivative financialinstrument in the capital market of China. At present, there are only19ordinary convertiblebonds can be traded in the market, the embarrassed convertible bonds market has lookingforward to expansion for a long time. The convertible bonds risk measurement research is stillat the exploratory stage. It currently doesn’t have a mature and convenient measurementmodel to measure the risk of convertible bonds reasonably. This paper explores to build aconvertible bonds risk measurement model for the financial market of China, and gives thecorresponding algorithm and empirical analysis. This paper studies the risk measurementmodel of convertible bonds from the following three aspects:First of all, the random Faure sequences, variance reduction technique and Moroalgorithm are applied to the risk measurement model of convertible bonds, and then thequasi-Monte Carlo (QMC) method for measuring convertible bonds is established on base ofthe methods mentioned above. Finally, an empirical study based on TangGang convertiblebonds is presented. These results illustrate that the risk measurement model, which is basedon the quasi-Monte Carlo method, performs well since the standard deviation of Value-at-Riskand Expected Shortfall are small enough, the computational efficiency is higher, and itsestimator matches the actual loss exactly.Secondly, through introducing the theory of fuzzy mathematics into the risk measurementof convertible bonds, we consider the risk measurement problem of convertible bonds byassumpting that the initial stock price of convertible bonds, volatility, and rate of return arefuzzy numbers. The risk measurement model of fuzzy Quasi-Monte Carlo is obtained bycombining the improved Monte Carlo method. In order to evaluate the performance of therisk measurement model, a new evaluation index, namely BSR, is constructed and theanalysis is also provided. Finally, an empirical study based on xingang convertible bond ispresented. These results illustrate that our risk measurement model, which is based on fuzzyquasi-Monte Carlo method, performs well since the standard deviation is small enough andthe estimator matches the actual loss exactly.Further more, we explore to introduce the fractal market hypothesis theory to theconvertible bond risk measurement model for the financial markets of China. The MonteCarlo simulation shows that the Whittle method overcome the defects of precision andstability from R/S method, modify R/S method, V/S method, DFA method and other methods which are commonly used. With the Whittle method and the Quasi Monte Carlo algorithmbased on fractal market hypothesis, we proposed a risk measurement model of convertiblebonds under the assumptions that the process of underlying stock price is obey to fractalBrownian motion. Through the indicators of BSR, the empirical results show that the riskmeasurement model based on fractal market hypothesis is not only effective but also hasvalue for further research.