本文關(guān)鍵詞： 嚴(yán)平穩(wěn)過程 強(qiáng)遍歷定理 板塊聯(lián)動 股票高頻聯(lián)動 看跌期權(quán) B-S風(fēng)險(xiǎn)中性期權(quán)定價(jià) 包含收益漂移項(xiàng)μ的期權(quán)定價(jià) 統(tǒng)計(jì)套利　出處：《華東師范大學(xué)》2017年博士論文　論文類型：學(xué)位論文

【摘要】：金融市場中,套利是人們永恒追求的目標(biāo),但Fama在70年代提出的有效市場假說從理論角度闡述了套利在當(dāng)今的市場環(huán)境中已經(jīng)不可能。本文在承認(rèn)市場有效性假說的前提下,利用一種新的套利方式——統(tǒng)計(jì)套利。統(tǒng)計(jì)套利雖然保證不了每次都有正向收益,但是提高交易次數(shù)之后,整體策略仍然有可觀的正向穩(wěn)定收益。本文的重點(diǎn)就是利用平穩(wěn)過程在股票與期權(quán)中進(jìn)行統(tǒng)計(jì)套利。板塊聯(lián)動是股票市場中經(jīng)典的金融現(xiàn)象,其說明某些行業(yè)背景上相近的版塊,其價(jià)格走勢也會有相近的地方。如果通過數(shù)學(xué)方法確定了兩個(gè)板塊的先后關(guān)系,那么在此基礎(chǔ)上通過相關(guān)板塊走勢尋找到未來可能爆發(fā)的版塊就相對容易,因此該現(xiàn)象也是基本面分析的一個(gè)重要方向。但是這種基于日數(shù)據(jù)的股票版塊分析方法其結(jié)果往往滯后于市場(因?yàn)槭袌鰬?yīng)變時(shí)間充足,相關(guān)版塊的走勢基本一致)。本文試圖用"放大鏡"來放大股票價(jià)格數(shù)據(jù),在放大后的高頻數(shù)據(jù)中確定兩只具有強(qiáng)相關(guān)性股票的相關(guān)關(guān)系,在市場未對這種價(jià)格形態(tài)做出反應(yīng)的時(shí)候,先于市場"抓住"該套利機(jī)會。尋找高頻聯(lián)動點(diǎn)的方法依舊是通過技術(shù)指標(biāo)的刻畫,但是與以往不同的是,本文側(cè)重于利用平穩(wěn)過程技術(shù)指標(biāo)來對價(jià)格走勢的特定形態(tài)進(jìn)行篩選。Wang、Zheng在書"High-Frequency Trading and Probability Theory"中首次提出用平穩(wěn)化的技術(shù)指標(biāo)進(jìn)行統(tǒng)計(jì)套利,并在強(qiáng)遍歷性定理的輔助下得到對數(shù)收益平均收斂的結(jié)論。本文在該思想的指導(dǎo)下,用平穩(wěn)化的指標(biāo)(同趨勢指標(biāo)CFI、異趨勢指標(biāo)DFI)尋找在中國股市最動蕩的2015年,A股市場中兩只有強(qiáng)相關(guān)性的股票(南方航空,東方航空)的高頻聯(lián)動現(xiàn)象,并通過該現(xiàn)象尋找統(tǒng)計(jì)套利機(jī)會。根據(jù)該方法的啟示,很多基于日線的經(jīng)典金融現(xiàn)象都可以在高頻數(shù)據(jù)中重新發(fā)現(xiàn),并結(jié)合平穩(wěn)過程及強(qiáng)遍歷性定理,發(fā)揮這些金融現(xiàn)象在未來收益中的預(yù)測作用。本文的另一個(gè)核心是平穩(wěn)過程在期權(quán)的應(yīng)用,該部分是在Zheng與Bao的啟發(fā)及指導(dǎo)下得到的一種新的統(tǒng)計(jì)套利方法。期權(quán)因?yàn)槠錂?quán)利金相對金融標(biāo)的資產(chǎn)偏低但收益與購買金融標(biāo)的相同,有以小博大的意思,所以市場認(rèn)可度很高。歐式期權(quán)與美式期權(quán)是期權(quán)的兩個(gè)大類,其區(qū)別是:歐式期權(quán)必須在期權(quán)到期日行權(quán),而美式期權(quán)可以在到期日之前工作時(shí)段的任意時(shí)間被執(zhí)行。因?yàn)槊朗狡跈?quán)行權(quán)方式的非固定性,其價(jià)格要比相同條件下歐式期權(quán)要高。對于兩種期權(quán)價(jià)格的計(jì)算,歐式期權(quán)定價(jià)中最著名的、使用最廣泛的方法是Black-Scholes期權(quán)定價(jià)公式,其核心是風(fēng)險(xiǎn)中性條件下,計(jì)算期權(quán)未來收益的期望。美式期權(quán)沒有標(biāo)準(zhǔn)化的計(jì)算方法,大部分是基于目前數(shù)據(jù)模擬計(jì)算出來的。在上述定義下,對于某些年化收益漂移項(xiàng)μ高于無風(fēng)險(xiǎn)收益率r的金融指數(shù),其歐式看跌期權(quán)的權(quán)利金要比B-S看跌期權(quán)的權(quán)利金低;同理此條件下,歐式看漲期權(quán)的權(quán)利金要高于B-S看漲期權(quán)權(quán)利金。根據(jù)以上說明,如果真實(shí)期權(quán)權(quán)利金是參考B-S期權(quán)價(jià)格,并通過買賣雙方博弈達(dá)成的,那么該價(jià)格就可能與包含收益漂移項(xiàng)μ的無偏期權(quán)價(jià)格不一致。在該思路下,每次都賣出看跌期權(quán),那么隨著時(shí)間的流逝,其收益有很大可能性為正。該思想也是本文期權(quán)套利的核心。在具體期權(quán)操作上,改變收益方式使其收益平穩(wěn)可以提高策略的穩(wěn)定性,即每次賣出期權(quán)價(jià)格分之一整數(shù)倍的期權(quán),其單次收益序列構(gòu)成平穩(wěn)過程。根據(jù)強(qiáng)遍歷性定理,策略收益的平均將收斂到某一特定值。本文為了跟標(biāo)的價(jià)格(QQQ、DIA、SPY)做對比,設(shè)定初始資產(chǎn)為窗口日開始的價(jià)格,根據(jù)美國市場期權(quán)的保證金制度,每次賣出3份期權(quán)并累計(jì)計(jì)算收益結(jié)果。通過策略凈值曲線與金融標(biāo)的價(jià)格做對比,策略有穩(wěn)定正向收益,雖然收益不能做到每時(shí)每刻都強(qiáng)于標(biāo)的指數(shù),但是策略風(fēng)險(xiǎn)被控制在允許的范圍內(nèi)。對套利策略進(jìn)行優(yōu)化,更改依次賣出看跌期權(quán)的策略為連續(xù)賣出看跌看漲期權(quán)策略,使策略從單向盈利變?yōu)殡p向盈利。把改進(jìn)策略放到美國三大指數(shù)(QQQ、SPY、DIA)ETF期權(quán)中有:在B-S期權(quán)價(jià)格下,雖然新方法所帶來的整體收益有所下降,但是該方法大幅降低了策略的風(fēng)險(xiǎn)(標(biāo)準(zhǔn)差、最大回撤),提高了策略夏普比率及Calmar比率,提升策略的整體表現(xiàn);可是對于多只美國股票(飛利浦、可口可樂、豐田汽車),該做法并沒有出現(xiàn)與前者相似的結(jié)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.

【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：F831.51;F831.53

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本文編號：1486831