Study Of The Optimal Parameter In The CEV Model

After more than ten year development, Chinese stock market has obtained impressive achievement. With the effort of all participants, the market is becoming more and more mature and perfect, and the research of the market behaviour is close to the root. Although stocks' returns are the main concerns for almost all of the academical researches about stock market, returns' random processes are even more important for correct investment decision making, because they provide the basic information about capital risk. This paper analyzed the characteristics of the distribution of stock market returns serial.After browian motion being introduced in the analysis of stock price behaviour by Bachelier in 1900, it was gradually used in a series of classic model, including famous Black-Schole model and CAPM. But people began to find that the basic assumption'(log) return was IID normal variable"can not be met, because the financial data was not subject to normal distribution, and has the characteristics of leptokurtic, fat tails, asymmetry and long-term memory. As a result, Black-Schole model and other model which based on this assumption is flawed. As a consequence, a lot of correction and modification have been made. This paper analysed the optimal parameter in the CEV model which was used in option pricing, taking account of the special nature of Chinese stock market, determined the optimal beta in each period, provide accurate estimation in future option pricing and risk management.This paper find that past researchs using CEV model in exotic option pricing(including rainbow option, Asian option, etc.) were not appropriate. In these papers, they only provided numerical solution, or simply used beta=0.5, beta=1 in the model, failed to use the optimal parameter in each period and take into account the spacial nature of Chinese stock market. Policy change has great influence in the Chinese stock development, in the period between the foundation of market and implementation of price change limitation policy, the optimal beta is about 0.7, which is close to 0.7 in American stock market, after the implementation of price change limitation, the optimal beta decrease dramatically to 0.3 or 0.4 , reflecting the great policy influence, and after the stock market structure reform, optimal beta is increasing, showing the irrational development in this period. As a conclusion, choosing the optimal parameter in each period divided by policy change is critical in stock pricing, derivative pricing and risk management.