GED Compound Poisson Model And Application

The launch of margin trading and short selling business satisfies the objective possibility of pairing arbitrage trading in China ’s capital market.In the process of constructing the pair trading strategy,the research on the volatility model of the pair spread has completed the transformation from the fixed conditional variance to the time-varying conditional variance,and the widely used GARCH cluster model has limitations in the application of financial time series.The common conditional heteroscedasticity model is no longer suitable for financial markets with frequent asset price jump risks.It is necessary to find a new jump model to fit financial data.Pair trading strategy is based on the estimation of the conditional variance of the portfolio spread to select the timing of the transaction,and the choice of the volatility model largely determines the pairing income.Therefore,in order to estimate the conditional variance more accurately,it is the purpose of this paper to construct a model that can capture the new distribution of jump risk and identify the aggregation of jump risk.The main work of this paper is divided into the following four parts.In the first part,based on the idea of compound Poisson distribution in the total loss model,the generalized error compound Poisson(GECP)distribution is proposed for the first time by taking the generalized error distribution as the compound object.The mathematical expressions of the numerical characteristics such as mean,variance and probability density function of GECP distribution are calculated.The GECP distribution makes the basic distribution of the traditional total loss model continuous and expands its support to the real field,which expands the application scope of the compound Poisson distribution and improves the limitation of the total loss model.The second part calculates the probability density function of the sub-distribution of the GECP distribution-normal compound Poisson(NORMCP)distribution.Based on the NORMCP distribution,it is assumed that the Poisson distribution parameters obey the ARMA model,and the normal distribution parameters change with time.Construct a normal compound Poisson process and give a parameter estimation process.In the third part,the selection criteria and position allocation method of paired trading targets are given.The NORMCP distribution is used to estimate the conditional variance of the comprehensive price difference of the portfolio and determine the trading threshold multiple,so as to establish the paired trading strategy.The fourth part takes the shares of Bank of China,Agricultural Bank of China,Industrial and Commercial Bank of China and Construction Bank in China ’s A-share market as the target assets,and empirically tests the effectiveness of the paired trading strategy based on NORMCP distribution.The empirical results show that compared with the paired trading strategy based on GARCH model,the trading strategy proposed in this paper performs better in terms of annualized return rate,Sharpe ratio and negative return ratio.The research on the generalized error compound Poisson distribution in this paper enriches the probability distribution theory to a certain extent and broadens the application range of the compound Poisson distribution in financial time series.Applying this distribution to measure the spread volatility in financial asset matching transactions and constructing a jump risk model based on the new distribution further provides a reference for the estimation of financial risks.