基于平稳过程的股票及期权交易研究

发布时间：2018-02-03 07:49

本文关键词： 严平稳过程强遍历定理板块联动股票高频联动看跌期权 B-S风险中性期权定价包含收益漂移项μ的期权定价统计套利　出处：《华东师范大学》2017年博士论文　论文类型：学位论文

【摘要】：金融市场中,套利是人们永恒追求的目标,但Fama在70年代提出的有效市场假说从理论角度阐述了套利在当今的市场环境中已经不可能。本文在承认市场有效性假说的前提下,利用一种新的套利方式——统计套利。统计套利虽然保证不了每次都有正向收益,但是提高交易次数之后,整体策略仍然有可观的正向稳定收益。本文的重点就是利用平稳过程在股票与期权中进行统计套利。板块联动是股票市场中经典的金融现象,其说明某些行业背景上相近的版块,其价格走势也会有相近的地方。如果通过数学方法确定了两个板块的先后关系,那么在此基础上通过相关板块走势寻找到未来可能爆发的版块就相对容易,因此该现象也是基本面分析的一个重要方向。但是这种基于日数据的股票版块分析方法其结果往往滞后于市场(因为市场应变时间充足,相关版块的走势基本一致)。本文试图用"放大镜"来放大股票价格数据,在放大后的高频数据中确定两只具有强相关性股票的相关关系,在市场未对这种价格形态做出反应的时候,先于市场"抓住"该套利机会。寻找高频联动点的方法依旧是通过技术指标的刻画,但是与以往不同的是,本文侧重于利用平稳过程技术指标来对价格走势的特定形态进行筛选。Wang、Zheng在书"High-Frequency Trading and Probability Theory"中首次提出用平稳化的技术指标进行统计套利,并在强遍历性定理的辅助下得到对数收益平均收敛的结论。本文在该思想的指导下,用平稳化的指标(同趋势指标CFI、异趋势指标DFI)寻找在中国股市最动荡的2015年,A股市场中两只有强相关性的股票(南方航空,东方航空)的高频联动现象,并通过该现象寻找统计套利机会。根据该方法的启示,很多基于日线的经典金融现象都可以在高频数据中重新发现,并结合平稳过程及强遍历性定理,发挥这些金融现象在未来收益中的预测作用。本文的另一个核心是平稳过程在期权的应用,该部分是在Zheng与Bao的启发及指导下得到的一种新的统计套利方法。期权因为其权利金相对金融标的资产偏低但收益与购买金融标的相同,有以小博大的意思,所以市场认可度很高。欧式期权与美式期权是期权的两个大类,其区别是:欧式期权必须在期权到期日行权,而美式期权可以在到期日之前工作时段的任意时间被执行。因为美式期权行权方式的非固定性,其价格要比相同条件下欧式期权要高。对于两种期权价格的计算,欧式期权定价中最著名的、使用最广泛的方法是Black-Scholes期权定价公式,其核心是风险中性条件下,计算期权未来收益的期望。美式期权没有标准化的计算方法,大部分是基于目前数据模拟计算出来的。在上述定义下,对于某些年化收益漂移项μ高于无风险收益率r的金融指数,其欧式看跌期权的权利金要比B-S看跌期权的权利金低;同理此条件下,欧式看涨期权的权利金要高于B-S看涨期权权利金。根据以上说明,如果真实期权权利金是参考B-S期权价格,并通过买卖双方博弈达成的,那么该价格就可能与包含收益漂移项μ的无偏期权价格不一致。在该思路下,每次都卖出看跌期权,那么随着时间的流逝,其收益有很大可能性为正。该思想也是本文期权套利的核心。在具体期权操作上,改变收益方式使其收益平稳可以提高策略的稳定性,即每次卖出期权价格分之一整数倍的期权,其单次收益序列构成平稳过程。根据强遍历性定理,策略收益的平均将收敛到某一特定值。本文为了跟标的价格(QQQ、DIA、SPY)做对比,设定初始资产为窗口日开始的价格,根据美国市场期权的保证金制度,每次卖出3份期权并累计计算收益结果。通过策略净值曲线与金融标的价格做对比,策略有稳定正向收益,虽然收益不能做到每时每刻都强于标的指数,但是策略风险被控制在允许的范围内。对套利策略进行优化,更改依次卖出看跌期权的策略为连续卖出看跌看涨期权策略,使策略从单向盈利变为双向盈利。把改进策略放到美国三大指数(QQQ、SPY、DIA)ETF期权中有:在B-S期权价格下,虽然新方法所带来的整体收益有所下降,但是该方法大幅降低了策略的风险(标准差、最大回撤),提高了策略夏普比率及Calmar比率,提升策略的整体表现;可是对于多只美国股票(飞利浦、可口可乐、丰田汽车),该做法并没有出现与前者相似的结果。
[Abstract]:In financial markets, arbitrage is the eternal pursuit of the people, but in 70s proposed Fama efficient market hypothesis from the perspective of the theory of arbitrage in today's market environment has been impossible. Based on the acknowledgement of the hypothesis of market efficiency by using a new type of statistical arbitrage arbitrage. Although the guarantee of statistical arbitrage not every time have positive returns, but increase the number of transactions, the overall strategy still has a positive and stable income considerable. The focus of this paper is to use the stationary process statistics in the stock and option arbitrage. Plate linkage is the classic financial phenomenon in the stock market, which shows that some industry background similar sections, the price trend there will be a similar place. If through the mathematical method to determine the two sector relationship has, so to find the future may be based on the relevant sector trend The outbreak of the forum is relatively easy, so an important direction for the analysis of the phenomenon is also fundamental. But this day the stock data section analysis method based on the results are often lag behind the market (because the market strain time, relevant section basically the same trend). This paper attempts to use the magnifying glass to enlarge the stock price data. To determine the correlation between two strong correlation of stock in the high frequency data of the amplified, when the market did not respond to the price form, first in the market to "seize" the arbitrage opportunity. For high frequency is still the linkage point through the characterization of the technical indicators, but it is different from the past, this paper focuses on the use of technology the index of stationary process to a specific form of price movements were.Wang, Zheng in the book "High-Frequency Trading and Probability Theory" was first proposed by smooth. Operation indicators for statistical arbitrage, and assisted in the strong ergodic theorem under the mean convergence of logarithmic return conclusion. In this paper, under the guidance of the thoughts, with smooth index (CFI index with the trend, trend of differentiation index DFI) looking at the China stock market turmoil in 2015, has a strong correlation of A stock market in two the stock (China Southern Airlines, China Eastern Airlines) high-frequency linkage phenomenon, and the phenomenon of finding statistical arbitrage opportunities. According to the method of the enlightenment, many of the classic financial phenomenon based on the daily can be found again in high frequency data, and combined with the stationary process and strong ergodic theorem, play these financial phenomenon to predict future earnings the core of this paper. Another option is a stationary process in the application, this part is a new kind of statistics in the inspiration and guide the Zheng and Bao under the arbitrage method. Because the right option means The financial asset is low but the income and the purchase of financial standard is the same as that of has a small broad meaning, so the market acceptance is very high. The European option and American option are two kinds of options, the difference is: the European option must be on the maturity date of the option exercise at any time, and the American option to work in before the date of expiry period is executed. Because the non fixed way of American option, the price to be higher than the European option under the same conditions. The calculation for the two option price of European option pricing is the most famous, the most widely used method is the Black-Scholes option pricing formula, its core is the risk neutral condition the calculation of future earnings expectations, option. American option calculation methods have not standardized, most are based on the current data simulation. In the above definition, for some years yield drift was higher than those without The risk return rate of R financial index, the European option premium than the B-S option premiums low; in this condition, European call option premiums than the B-S option premium. According to the above description, if real option premium is the price reference period B-S right, and by both parties a game, so the price may be included and return the drift Mu unbiased option price is not consistent. In this way, every time a put option to sell, then with the passage of time, there is a great possibility for the return. The core thought is also the option of arbitrage. In the specific operating options, change the return of its steady income can improve the stability of a strategy, namely each sell option price of integer option, the single return sequence consisting of stationary process. According to the strong ergodic theorem, return strategy The average will converge to a certain value. This paper in order to price (QQQ, DIA, SPY) to do comparison, setting the initial asset window beginning on price, according to the U.S. market option margin system, each sold 3 copies and accumulated income option results. Through the strategy of value curve compared with financial net the price of mark, a stable positive income strategy, although income can not do at all times stronger than the underlying index, but the policy risk is controlled in the permitted range. The arbitrage strategy optimization, in order to change the put option to sell strategy for continuous sell bearish call strategy, the strategy of profit from one-way to two-way profit. The improvement strategy into the United States three index (QQQ, SPY, DIA) ETF: B-S option in the option price, although the overall income brought by the new method has decreased, but the method greatly reduces the strategy Risk (standard deviation, maximum retracement) improved the ratio of strategy SHARP ratio and Calmar ratio, and promoted the overall performance of the strategy. However, for many American stocks (PHILPS, Coca-Cola, TOYOTA car), there was no similar result with the former.

【学位授予单位】：华东师范大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：F831.51;F831.53

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