本文關(guān)鍵詞：基于Copula-SV模型的國(guó)債期貨跨期套利研究　出處：《西南財(cái)經(jīng)大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 國(guó)債期貨 跨期套利 Copula 隨機(jī)波動(dòng)模型 協(xié)整分析 MCMC

【摘要】：國(guó)債期貨本身是一個(gè)利率衍生品,對(duì)利率市場(chǎng)會(huì)產(chǎn)生顯著的影響。它不僅是整個(gè)利率體系很重要的環(huán)節(jié),同時(shí)也是整個(gè)利率市場(chǎng)化的“基石”。由于國(guó)債期貨對(duì)利率市場(chǎng)有著極其深刻的影響和意義,2012年2月13日,中金所啟動(dòng)5年期國(guó)債期貨交易測(cè)試,經(jīng)過近一年的仿真試行,2013年9月6日,5年期國(guó)債期貨合約正式在中金所上市。作為國(guó)內(nèi)首款利率衍生品,國(guó)債期貨的推出將對(duì)市場(chǎng)和投資者具有積極的意義,其推出后的定價(jià)和套利策略必將成為市場(chǎng)關(guān)注和研究的熱點(diǎn)。 由于我國(guó)在上個(gè)世紀(jì)九十年代初就開辦了國(guó)債期貨試點(diǎn),因此國(guó)內(nèi)與之相關(guān)的研究也不在少數(shù),概括起來主要可以分為兩個(gè)階段：一是國(guó)債期貨被叫停時(shí)期的反思階段,二是國(guó)債恢復(fù)重啟推出仿真交易后的策略運(yùn)用階段。與國(guó)內(nèi)研究相比,國(guó)外關(guān)于跨期套利的研究起點(diǎn)更早內(nèi)容更加豐富。本文結(jié)合相關(guān)文獻(xiàn)并考慮到我國(guó)國(guó)債期貨當(dāng)前的具體情況,本文的研究?jī)?nèi)容將主要集中在套利策略方面。 對(duì)于國(guó)債期貨來說,和股指期貨一樣,在正式推出前,中金所向市場(chǎng)提供了國(guó)債期貨的仿真交易。由于國(guó)債期貨正式上市至今才一個(gè)季度,TF09合約甚至都還沒開始交易,市場(chǎng)還不夠活躍,交易價(jià)格和現(xiàn)貨價(jià)格尚不存在明顯的聯(lián)動(dòng)性,期現(xiàn)套利的價(jià)差也因此不具有合理性,因此用當(dāng)前的交易數(shù)據(jù)來進(jìn)行期現(xiàn)套利的分析,在現(xiàn)階段不具有其現(xiàn)實(shí)意義。另一方面,不同于股指期貨簡(jiǎn)單的現(xiàn)金交割,國(guó)債期貨期現(xiàn)套利涉及到現(xiàn)貨市場(chǎng)CTD的可獲得性、交個(gè)標(biāo)的隨交割時(shí)間變化而變化、國(guó)債久期和轉(zhuǎn)換因子的計(jì)算、以及現(xiàn)貨交割對(duì)市場(chǎng)的沖擊、摩擦和交易成本等諸多問題,在實(shí)際的操作中都還有待研究和解決。因此,就目前的情況來看,把研究重心放在跨期套利上是比較合理的。 在大部分的文獻(xiàn)中,關(guān)于期貨套利分析的研究方法主要分為持有成本理論和價(jià)差波動(dòng)模型兩種。但是這兩種方法一是忽略了現(xiàn)實(shí)中的隨機(jī)因素對(duì)價(jià)差的影響,二是對(duì)模型的假設(shè)都較為嚴(yán)格,然而,在現(xiàn)實(shí)中的數(shù)據(jù)往往較難達(dá)到如此理想的情形。因此,本文換了一個(gè)角度,避開以往模型中一系列嚴(yán)苛的假設(shè)條件,從資產(chǎn)組合入手,將國(guó)債期貨跨期套利組合看作是一個(gè)資產(chǎn)組合,從而進(jìn)行國(guó)債期貨的跨期套利分析。本文通過對(duì)國(guó)債期貨定價(jià)及套利策略進(jìn)行深入的分析研究并結(jié)合前人研究的成果提出了以資產(chǎn)組合思想為基礎(chǔ)的Copula-SV國(guó)債期貨跨期套利模型。 為了驗(yàn)證模型的有效性,本文采用數(shù)據(jù)模擬的方法,通過計(jì)算機(jī)模擬模擬出平穩(wěn)和非平穩(wěn)的套利價(jià)差序列,然后分別用Copula-SV模型與傳統(tǒng)的價(jià)差波動(dòng)模型對(duì)價(jià)差序列進(jìn)行建模,估計(jì)套利區(qū)間,再運(yùn)用本文的套利策略進(jìn)行模擬交易,對(duì)比兩種模型最終的績(jī)效后發(fā)現(xiàn)：在套利組合價(jià)差平穩(wěn)的情形下,傳統(tǒng)價(jià)差波動(dòng)模型和Copula-SV模型各有優(yōu)劣,運(yùn)用傳統(tǒng)的價(jià)差波動(dòng)模型進(jìn)行套利顯得更加穩(wěn)健,風(fēng)險(xiǎn)更低,但是收益相對(duì)較低；另一方面,由于Copula-SV模型是直接對(duì)分布進(jìn)行估計(jì),對(duì)價(jià)差波動(dòng)特征的刻畫更為細(xì)致,因此在套利組合價(jià)差平穩(wěn)情形下運(yùn)用Copula-SV模型進(jìn)行套利時(shí),獲得的收益會(huì)比傳統(tǒng)價(jià)差波動(dòng)模型要高,但是由于交易次數(shù)的增多,模型的勝率也因之下降,交易成本也因此高于傳統(tǒng)套利模型。當(dāng)套利組合價(jià)差為非平穩(wěn)序列時(shí),基于平穩(wěn)假設(shè)的傳統(tǒng)價(jià)差波動(dòng)模型將會(huì)失效,由于Copula-SV模型是直接對(duì)每一個(gè)時(shí)點(diǎn)的分布進(jìn)行估計(jì),因此從理論上來說可以適用于價(jià)差序列非平穩(wěn)的情形,但是,由于是基于統(tǒng)計(jì)套利的思想,此時(shí)運(yùn)用Copula-SV模型進(jìn)行套利的結(jié)果將大不如價(jià)差平穩(wěn)的情形,不僅收益降低,勝率也隨之下降。綜上分析,不論是在套利組合價(jià)差平穩(wěn)還是非平穩(wěn)的情形下,Copula-SV模型都可以對(duì)套利區(qū)間進(jìn)行估計(jì),從而輔助套利者進(jìn)行套利策略的實(shí)施。而且在套利價(jià)差平穩(wěn)條件下Copula-SV模型對(duì)套利區(qū)間的估計(jì)更加精確,可以為套利者帶來更多的潛在收益；在套利價(jià)差非平穩(wěn)條件下Copula-SV模型仍可適用,這也彌補(bǔ)了傳統(tǒng)價(jià)差波動(dòng)模型失效的空白。 另外,在對(duì)模型的績(jī)效和適用性進(jìn)行分析和檢驗(yàn)后,本文運(yùn)用Copula-SV模型,從跨期套利的角度,對(duì)5年期國(guó)債期貨合約套利組合進(jìn)行了實(shí)證分析：首先通過協(xié)整分析發(fā)現(xiàn)國(guó)債期貨近期合約和遠(yuǎn)期合約的價(jià)格序列通過協(xié)整檢驗(yàn),二者存在著長(zhǎng)期均衡的關(guān)系。同時(shí)本文通過協(xié)整回歸方程得到了5年期國(guó)債期貨跨期套利組合的套利頭寸比。其次,考慮到套利組合實(shí)質(zhì)上可以看作是一個(gè)資產(chǎn)組合,因此從資產(chǎn)組合方向入手,在單個(gè)期貨合約的角度,選擇三種厚尾的隨機(jī)波動(dòng)模型分別進(jìn)行估計(jì)和對(duì)比后發(fā)現(xiàn)SV-GED和SV-t模型對(duì)近期合約和遠(yuǎn)期合約的收益率波動(dòng)和邊際分布的擬合程度最高。然后,根據(jù)極大似然法對(duì)橢圓函數(shù)族中的正態(tài)Copula函數(shù)和t-Copula函數(shù)以及阿基米德函數(shù)族中的ClaytonCopula、FrankCopula和GumbelCopula函數(shù)的參數(shù)值進(jìn)行估計(jì),通過對(duì)比模型的極大似然值,發(fā)現(xiàn)t-Copula函數(shù)的擬合程度最好,并以此估計(jì)出最終套利組合的聯(lián)合分布。在得到聯(lián)合分布后,再采用MCMC的方法模擬出套利組合的置信區(qū)間,套利組合的置信區(qū)間實(shí)際上也就是價(jià)差的置信區(qū)間,然后再利用統(tǒng)計(jì)套利的思想結(jié)合具體的開平倉(cāng)點(diǎn)設(shè)置,止盈止損點(diǎn)的選擇等套利策略確定出最佳的套利區(qū)間,從而得到最終的5年期國(guó)債期貨套利模型。 本文通過對(duì)5年期國(guó)債期貨跨期套利組合中的近期合約和遠(yuǎn)期合約進(jìn)行相關(guān)性分析發(fā)現(xiàn),在市場(chǎng)的單邊行情較不明朗,出現(xiàn)長(zhǎng)期震蕩時(shí),5年期國(guó)債期貨套利組合中近期合約與遠(yuǎn)期合約具有很強(qiáng)的相關(guān)性,因此震蕩行情下進(jìn)行國(guó)債期貨跨期套利可以保證較高的收益和較低的風(fēng)險(xiǎn),同時(shí)也具有較好的操作準(zhǔn)確性。另一方面,當(dāng)市場(chǎng)出現(xiàn)大幅的上漲或下跌,表現(xiàn)為明顯的單邊行情時(shí),在熊市行情中進(jìn)行國(guó)債期貨跨期套利的情形下,5年期國(guó)債期貨套利組合中近期合約與遠(yuǎn)期合約的相關(guān)性相較于牛市行情表現(xiàn)的更為強(qiáng)烈,此時(shí)進(jìn)行套利交易可以保證較高的收益。 本文利用2013/11/7—-2014/1/22期間的國(guó)債期貨交易數(shù)據(jù)對(duì)估計(jì)出的模型進(jìn)行了測(cè)試,發(fā)現(xiàn)最終計(jì)算出的模型的年華收益率為12.96%,大大超出了市場(chǎng)上一般理財(cái)產(chǎn)品的收益能力,說明模型的設(shè)定和測(cè)試結(jié)果非常理想。另一方面,本文利用估計(jì)出的模型對(duì)樣本期內(nèi)的數(shù)據(jù)進(jìn)行檢驗(yàn),并列舉實(shí)例介紹了模型在現(xiàn)實(shí)國(guó)債期貨跨期套利交易中的具體操作方法。 綜上所述,由于國(guó)債期貨在我國(guó)正式上市還不到半年,國(guó)內(nèi)外對(duì)其進(jìn)行的研究還相對(duì)較少,特別是對(duì)國(guó)債期貨進(jìn)行套利策略研究的文獻(xiàn)幾乎沒有。因此本文從跨期套利的角度,通過理論推導(dǎo)和計(jì)算機(jī)模擬的方法對(duì)國(guó)債期貨所適用的套利模型進(jìn)行了深入的對(duì)比和研究,發(fā)現(xiàn)本文提出的Copula-SV模型不僅能彌補(bǔ)傳統(tǒng)模型對(duì)數(shù)據(jù)要求過于嚴(yán)格的不足,而且運(yùn)用Copula-SV模型進(jìn)行實(shí)際套利操作中還能獲得令人滿意的套利結(jié)果。而后運(yùn)用本文提出的模型對(duì)國(guó)債期貨上市以來的交易數(shù)據(jù)進(jìn)行了實(shí)證檢驗(yàn),發(fā)現(xiàn)模型的效果確實(shí)較為理想,暫時(shí)彌補(bǔ)了我國(guó)在國(guó)債期貨跨期套利實(shí)證研究方面所存在的空白。
[Abstract]:Treasury bond futures is an interest rate derivatives, will have a significant impact on the interest rate market. It is not only a part of the interest rate system is very important, but also the interest rate market "cornerstone". Because the bond futures have a profound influence and significance of the interest rate market in February 13, 2012, gold in the starting 5 year bonds futures trading test, after the trial, the simulation for nearly a year in September 6, 2013, the 5 year bond futures contract officially listed in the gold. As the first domestic interest rate derivatives, treasury bond futures will have positive significance to the market and investors, the launch of the pricing and arbitrage strategy will become the focus of market attention and research.
Since China started pilot bond futures in the last century at the beginning of 90s, the domestic research related is not in the minority, mainly can be divided into two stages: one is the reflection phase of treasury bond futures was halted during the period of two, the national debt recovery restart launched after the transaction using the simulation stage. Compared with the domestic and foreign research on the starting point of research, earlier content of intertemporal arbitrage is more abundant. This article combined with the relevant literature and considering the specific circumstances of China's treasury bond futures at present, the research content of this paper will mainly focus on the aspects of the arbitrage strategy.
For bond futures, and stock index futures, before the official launch, the gold market to provide the simulation trading of treasury bond futures. Because bond futures officially listed so far only a quarter, TF09 contracts have not even started trading, the market is not active, the transaction price and the spot price there is no obvious linkage the spread of arbitrage is therefore not reasonable, so the current transaction data to analyze arbitrage, does not have its practical significance in the present stage. On the other hand, the stock index futures is different from the simple cash settlement, bond futures arbitrage involves spot market CTD availability make a mark with the delivery time of the change of bond duration and conversion factor is calculated, and the impact of spot delivery on the market, many problems of friction and transaction costs, in the actual operation still need further research Therefore, as far as the current situation is concerned, it is reasonable to put the center of gravity on the Interperiod arbitrage.
In most of the literature, research methods of futures arbitrage analysis is mainly divided into the cost theory and price volatility model two. But the two method is ignoring the influence of random factors in the reality of the spread, two assumptions of the model are more stringent, however, in reality, the data is often to reach such an ideal situation. Therefore, we avoid the previous model in a series of rigorous assumptions, starting from the portfolio, the bond futures arbitrage portfolio as a portfolio, intertemporal arbitrage analysis and bond futures. Through in-depth analysis and Research on Treasury bond futures pricing and arbitrage strategy combined with the results of previous studies proposed by portfolio based Copula-SV bond futures arbitrage model.
In order to verify the validity of the model, this paper uses the method of data simulation, through computer simulation to simulate the stationary and non-stationary sequence and then use arbitrage spreads, price volatility model Copula-SV model and the traditional model of spread sequence, and then use the arbitrage arbitrage interval estimation, this paper simulated trading strategy, performance comparison of two models the final found: in the case of stable arbitrage spreads, the traditional price difference model and Copula-SV model have advantages and disadvantages, the use of price fluctuations of the traditional model of arbitrage is more stable, lower risk, but the income is relatively low; on the other hand, the Copula-SV model is directly on the distribution of the estimates, description of the characteristics of spread the fluctuation is more detailed, so in the case of steady spread of arbitrage portfolio using Copula-SV model arbitrage, the gains will be better than the traditional Price volatility model must be high, but due to the increase in the number of transactions, the model for winning percentage decline, transaction costs and therefore higher than traditional arbitrage model. When arbitrage portfolio spreads for non-stationary series, will the traditional spread volatility model based on failure of the stationary assumption, the Copula-SV model is directly distributed to every point of estimation, thus theoretically can be applied to the spread of non-stationary series, but because it is based on the idea of statistical arbitrage, this time using the Copula-SV model results will not spread arbitrage steady situation, not only to reduce income, winrate drops. In conclusion, whether in steady or spread arbitrage portfolio non stationary case, Copula-SV model can estimate the arbitrage interval, thus supporting the arbitrage arbitrage strategy and arbitrage spreads in the stable. Under the condition of Copula-SV model, the arbitrage interval estimation is more accurate, which can bring more potential benefits for the arbitrators. Under the non-stationary condition of arbitrage spread, Copula-SV model can still be applied, which also makes up for the blank of the traditional price difference volatility model.
In addition, test and Analysis on the performance and applicability of the model, this paper uses the Copula-SV model, from the perspective of intertemporal arbitrage, the empirical analysis of 5 year bond futures contract arbitrage portfolio: firstly, through cointegration analysis found that the Treasury bond futures price series recently or forward contracts through the cointegration test, two there is a long-term equilibrium relationship. At the same time, through the cointegration regression equation obtained 5 year bond futures arbitrage arbitrage positions ratio. Secondly, considering the arbitrage portfolio in essence can be regarded as a portfolio, so from the portfolio of futures contracts in a single direction, angle, selection of stochastic volatility three kinds of models of thick tail are estimated and compared the fitting degree of SV-GED and SV-t model on short-term or forward contracts of volatility and the highest marginal distribution. Then, the root According to the elliptic function family of the normal Copula function and t-Copula function and Archimedes function in the ClaytonCopula maximum likelihood method, the parameters FrankCopula and GumbelCopula function values were estimated by the maximum likelihood model comparison value, find the best fitting degree of t-Copula function, and to estimate the joint distribution of the final arbitrage portfolio. Get in the joint distribution, and then use MCMC method to simulate the confidence interval of the arbitrage portfolio arbitrage portfolio, the confidence interval is actually the confidence interval spreads, and then using the idea of statistical arbitrage with specific Kaiping points set, full stop point selection of arbitrage strategies determine optimal arbitrage interval, in order to get the model the end of the 5 year bond futures arbitrage.
Based on the 5 year treasury bond futures arbitrage portfolio in short-term contracts and forward contracts for correlation analysis found that in the market unilateral market more uncertain, long-term shocks, 5 year bond futures arbitrage portfolio in recent contract and long-term contract has a strong correlation, so the market shocks of bond futures intertemporal arbitrage can guarantee high returns and low risk, but also has good accuracy. On the other hand, when the market sharply rise or fall, showed unilateral market, treasury bond futures in the bear market arbitrage situation in recent contract and long-term correlation combination contract 5 year bond futures arbitrage compared to the bull market performance is more intense, the carry trade can ensure higher returns.
This paper is tested by using 2013/11/7 - bond futures trading data during -2014/1/22 to estimate the model, found the final calculated model year rate of return of 12.96%, greatly exceeded the market average return of financial products, that model is set up and the test result is very ideal. On the other hand, based on the sample period the data were tested using the estimated model, and illustrated the specific methods of operation model of intertemporal arbitrage in real bond futures.
In summary, the Treasury bond futures officially listed in China is still less than half a year, domestic and foreign research on it is relatively less, especially for bond futures arbitrage strategy of almost no literature. So this paper from the perspective of intertemporal arbitrage, arbitrage model by means of theoretical derivation and computer simulation of treasury bond futures for a comparison and research in-depth, found that the Copula-SV model proposed in this paper can not only make up for the traditional model of the problem of too strict requirements for data, and use the Copula-SV model to the actual arbitrage operation also can arbitrage with satisfactory results. And then use the proposed model to the transaction data since the Treasury futures market of the empirical test, the effect is indeed an ideal model, temporarily make up for the existing in our country's national debt futures arbitrage in the empirical study Blank.

【學(xué)位授予單位】：西南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F832.51;F224

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