Jump Testing Of Price Process With Microstructure Noise Based On High Frequency Financial Data And Its Application In The Study Of Volatility Arbitrage Strategy

Volatility prediction is relatively simple compared with stock return prediction.If an investor can predict volatility accurately,how he/she complete arbitrage?Investors generally choose to invest in a cross-option portfolio to arbitrage(such as dish opton).However,existing options in the financial market can not directly meet the demands of investors due to their poor liquidity and high transaction costs.The usual solution of this problem is replicating options with futures.In the process of replication,the delta hedge position of a single option is calculated by using the B-S formula,and the delta value of the option portfolio is obtained.Delta value of option portfolio is updated with daily data and future volatility is predicted by historical volatility(Return standard deviation).How to use more valuable high-frequency data to improve the returns of arbitrage portfolio is more vital for investors.Under the framework of high frequency data,the measurement of volatility is different for high frequency data with different characteristics.The common realized volatility(RV),the BiPower realized Volatility(BPV)to overcome the jump influence in the price process,the Threshold BiPower realized Volatility(TBPV)and so on.Appropriate volatility measurement is a prerequisition for the accurate prediction of volatility of assert return.Empirical analysis show that the price process often contains jumps,and the actual high-frequency data often contains microstructure noise.Therefore,the scientific methods of jump testing of price process have important application value for selecting appropriate volatility measurement,accurate prediction of volatility,accurate replication of options and option risk management(risk hedge).Meanwhile,the theoretical research of testing of jumping with microstructure noise in the frame of high frequency data is inadequate.Based on the high frequency data with microstructure noise,we will study the theoretical properties of the relevant statistics of the price process,verify whether the process has jump,and understand deeply the dynamic change law of the price process.We also will analyze the dynamic characteristics of the price process of the actual financial high frequency data,and understands the dynamic changes of the price process.We will be able to provide theoretical methods for the study of other dynamic characteristics of the price process with microstructure noise,enrich the theoretical contents of financial metrology,and provide certain technical methods for practical problems and actual financial data processing.That means,this jump test method based on financial high frequency data with microstructure noise further enriches the jump test correlation model,enriches the limit theory of related power variation and test statistics,and has important theoretical significance.The main contents of this paper will focus on this two parts:firstly,proposing the jump test method based on the financial high frequency data with microstructure noise;secondly,exploring the application of jump test method in volatility arbitrage strategy.In the first part,based on the financial high frequency data with microstructure noise,we proposing the test method and model to test whether the asset price process has jump or not.The actual high frequency data often contain microstructure noise due to the small sampling interval and so on,we test the jumps of the price process based on the noisy high frequency data.The main contents of first parts as follows:(1)Constructing Power variation based on Pre-average method.In order to make full use of the information of microstructure noise,the pre-average increment is established based on the pre-average method,and then the related realized power variation and the threshold power variation are established.The pre-average window of pre-average method is kn=cn?,we select a smaller adjusted parameter(a<1/2)of pre-average window compared with which(a=1/2)of classical literature(Ait-Sahalia,Jacod and Li(2012)).Therefore,the microstructure noise part and the jump test part will play a leading role in the pre-average increment.(2)Constructing test Statistics based on power variation.Constructing the two-scale ratio test statistics based on power variation using two-sacle ratio test statistics(Zhang,Mykland and Ait-Sahalia 62]).About Test Statistics,under the alternative hypothesis(price process has jumps),the test statistics tends to 1/2.Under the null hypothesis where the price process is continuous,the test statistic converges to another constant(differ quitely form 1/2).Then,Whether the sample path has jumps is distinguished by the significant difference in the asymptotic value of the test statistic.(3)Test Statistics and its related limit theory.Under the null hypothesis where the price process is continuous,the test statistic converges to a normal distribution,and under the alternative hypothesis where the price has jumps,the statistic converges to infinity.In order to make full use of the information of microstructure noise,a smaller pre-average window(a<1/2)is used in the process of constructing pre-average increment compared with the pre-average window(a=1/2)of Ait-Sahalia,Jacod and Li(2012).When the alternative hypothesis holds,that is,when the price process has jumps,the standardized test statistics tend to infinity at the rate of When the alternative hypothesis holds,the standardized test statistics(Ait-Sahalia,Jacod and Li(2012))tend to infinity at the rate of n1/4.Compared with the test of Ait-Sahalia,Jacod and Li(2012),our proposed statistic uses the information of the noise,enjoys faster rate to go to infinity under the alternative hypothesis,and has better power.(4)Monte Carlo Simulation and empirical analysis.The simulation results confirm the theoretical results and empirical research based on high-frequency financial data at home and abroad have jumps.The second part,based on the jump test method and model proposed in the first part,we explore the application of jump test in volatility arbitrage strategy.Based on the jump test model proposed in the front part,we make a jump test on the domestic financial high frequency data,and the empirical results show that the domestic asset price process often has jumps.This part we study how to use the financial high-frequency data of the price process to improve the return of cross-option portfolio.Based on the high-frequency financial data with jumps,the BiPower realized Volatility(BPV)is often used as a measure of asset volatility.When the price process has jumps,from the perspective of volatility prediction of financial high frequency data,the Delta replication of combination-cross option with futures,combined with the idea of moving average,which constructs the weekly average of the BiPower realized Volatility(BPVtW),the monthly average of the BiPower realized Volatility(BPVtM),the seasonal average of the BiPower realized Volatility(BPVtQ).We establish the prediction model of this four volatility sequences based on ARFIMA model.The volatility prediction value is used twice in the option arbitrage strategy.The first time the volatility prediction value is used to judge the market volatility timing,and the second time the volatility prediction value is used to calculate the delta value of a single option and option portfolio.Combined with the five forecasted volatility(including the standard deviation of return),we can construct 25(5 x 5)kinds of replication strategy and the corresponding volatility arbitrage strategy.The empirical study shows that,compared with the original strategy which uses daily volatility standard deviation twice,the strategy which uses quarterly average BiPower realized Volatility(BPvtQ)enjoys bigger Sharp value,the value at risk(VaR)is the smallest,the investment cost is the smallest,and the comprehensive investment effect is the best.At the same time,in order to study whether the processing jump can improve the return of the option replication strategy,we also define the Threshold BiPower realized variation(TBPV)and realized volatility(RV).Similar to the case where the strategy based on BiPower realized Volatility(BPV),we establishes 25(5x 5)kinds of futures delta replication strategy and the corresponding volatility arbitrage strategy,respectively,based on the Threshold BiPower realized variation(TBPV)and realized volatility(RV).And the 25 strategies are studied systematically.The empirical study shows that,compared with the original strategy which uses daily volatility standard deviation twice,the strategy which uses quarterly average Threshold BiPower realized variation and realized volatility enjoys bigger Sharp value,quarterly average BiPower realized Volatility.At the same time,we compare the BiPower realized Volatility(BPV)with the Threshold BiPower realized variation(TBPV)and realized volatility(RV).respectively.The results show that the profitability of the optimal volatility correlation strategy based on BiPower realized variation(BPV)is better than that based on Threshold BiPower realized variation(TBPV)and on realized variation(RV).Finally,the sensitivity analysis of market timing parameters(R?)and option execution price parameters(RK)shows that when the market timing parameter(R,)is more than 90%and the option execution price parameter(RK)is about 0.1,the profit effect of the optimal strategy is the best.This paper mainly studies the jump test of high-frequency financial data with microstructure noise and its the application of volatility arbitrage strategy.In theory,the test statistics constructed in this paper make full use of the microstructure noise information and have better statistical properties and stronger test efficiency than the that in Ait-Sahalia,Jacod and Li(2012).In order to make full use of the information of microstructure noise,the classical pre-average statistical method is reformed,and the average window width is selected as a smaller number.Using the two-scale method for reference,the test statistics are constructed.Under H0 holds,the price is continuous,the statistics will tend to the standard normal distribution.Under H1 holds,when the price process contains jumps,the test statistics will tend to infinite.Compared with classical literature in Ait-Sahalia,Jacod and Li(2012),the testing statistical has a higher limit rate with H1 holds,showing better statistical properties and test efficacy In practice,based on the perspective of financial high-frequency data volatility prediction,this paper constructs and studies the volatility arbitrage strategy of futures replication options,and systematically analyses the risk and return of arbitrage strategy.Using jump test statisticsto analyze the actual data,it shows that the actual financial high-frequency data often have jumps.It is necessary to use the volatility estimators such as BPV or TBPV to estimate the volatility.In order to carry out systematic analysis,this paper uses four methods of high frequency data volatility BPV,TBPV,RV and low frequency volatility to measure volatility.Each kind of high frequency data volatility constructs four kinds of volatility measurement,including daily measurement,weekly measurement,monthly measurement and quarterly measurement.On the premise of accurately predicting volatility,option portfolio can be constructed to arbitrage.Because of the low activity of option trading,the return structure of butterfly option can be duplicated by futures.Using futures replication options to carry out volatility arbitrage strategy requires two times to use the predicted volatility.To build ARFIMA model to predict volatility,based on BPV high frequency volatility measurement and low frequency volatility measurement,we can construct 25 kinds of arbitrage strategies.Therefore,there are 75(25×3)strategies.This paper constructs an evaluation index of profit and risk of the strategy,and makes a systematic analysis of 75 arbitrage strategies.Empirical results show that BPV and TBPV measurement-related strategies based on processing jumps are superior to RV measurement-related strategies without processing jumps,and volatility arbitrage strategies based on the most accurate quarterly volatility series are optimal.