The Study Of Stock And Option Trading Strategies Based On Stationary Process

In the financial market,arbitrage is the eternal goal.In the 70s the efficient market hypothesis proposed by Fama illustrated from the theoretical perspective that arbitrage is impossible in current market environment.In this paper,under the premise of the recognition of the market efficiency hypothesis,a new method of arbitrage——statistical arbitrage is used.Although the statistical arbitrage can not guarantee a positive return each time,but after the increase in the number of transactions,the overall strategy is still considerable positive stable income.The key point of this paper is to use the stationary process to carry on the statistical arbitrage in the stock and the option.Board linkage is a typical financial phenomenon in the stock market,which explains that for boards that have strong correlations with field background,their trends have strong correlations,and this is also an important direction for basic analysis.This analytic method based on stock board daily data is always fallen behind the market,and the board linkage based on daily data rises and falls concurrently,is there a relation of time order between them?Even such a relation exists,it will not be discovered by analysis of daily data,because the market has already reacted to such a form with obvious benefits.This article tries to use a "magnifying glass" to magnify stock price data,and seeks linkage opportunities of two stocks with high correlations among high-frequency data,,and "seize" an arbitrage opportunity before the market when it has not reacted to this kind of price form.The way of searching high-frequency linkage points is still to descript by technolog-ical indicators,while unlike previous methods,this article chooses tranquil technological indicators for filtering price forms.Wang,Zheng proposed of counting arbitrage by tran-quil indicators for the first time in the book "High-Frequency Trading and Probability Theory",and obtains characteristics of logarithmic yield average convergence under the strong ergodic theory.With the aid of this thought,this article uses tranquil indicators(same trend indicator CFI,different trend indicator DFI)to search high-frequency link-age phenomenon of two stocks(Southern Airlines,Eastern Airlines)in the A share market in the most turbulent year for Chinese stock market 2015,and through this phenomenon seeks stochastic arbitrage opportunities,in the end proves that in "second-scale" data there is indeed more obvious linkage phenomenon.Many typical financial phenomenon based on the date line can be rediscovered in high-frequency data,and due to the amount of data,these financial phenomenon appear ten more times or dozens of times in the most,but in high-frequency data they might appear hundreds even thousands of times,and sample amount increases to a multiple of geometric growth,again with stationary process and the strong ergodic theory,these financial phenomenon can dig out its function of directing and predicting from the convergent value of corresponding strategy gains.Another center of this article is the use of stationary process in options.Because options have lower assets of premiums than financial marks,and same gains as purchasing stocks,investors can achieve reasonable asset disposition with low costs,which is a reason that options become more and more popular in the market.By type options can be divided into European options and American options,and European options can only be exercised when the time expires,while American options can be exercised any time before the time due,because of the casualty,American options generally have higher prices than European options.The most famous and widely used formula for the pricing of European options is the Black-Scholes equation,the core of it is the expectation of option future gain under the risk-neutral condition.For ordinary exponential and blue-chip stocks,its annualized return ? is high than non-risk return r,thus the price of put options is lower considering the return drift ? than under the risk-neutral condition.If the real option premiums is achieved through game by two sides of trades taking the B-S formula as the reference,then its price is likely to be higher than actual option,prices.In this way,sells put options every time,then as the time goes,its gain has much possibility to be plus.In specific option operations,making single gains tranquil can improve the stability of strategies,that is,sells options taking up a certain percent of the price of options every time,then its single gain sequences form a stationary process,and according to the strong ergodic theory,the average gain will converge to a certain value,and the effectiveness of option selling strategies can be judged by this convergence value.This article sets the initial asset as the price when the window day starts for comparing to indicator prices(QQQ,DIA,SPY),and according to the premium rule of American market option,calculates gains every time three options are sold.Through the comparison between prices of this strategy net value curve and financial marks,strategies have steady positive gains,and though gains cannot guarantee to be higher than indicator exponential of every time,the strategy risk is controlled in a very small range.Improve this arbitrage strategy,replace selling put options only of selling call op-tions and put options at the same time,turns single direction benefits into two-direction benefits.Carry out the new strategy in three major American exponential ETF option-s(QQQ,DIA,SPY),and show results by gain graphics,it can be seen that though total benefits brought by the new strategy has a decrease to some degree,the risk of strategy is decreased greatly(standard deviation,maximum drawdown),strategy Sharp ratio and Calmar ration is increased,the overall strategy performance is improved;but according to some American stocks(Philips,Coca cola,Toyota)options price,the improved strategy don't get the same result.