基于Copula-SV模型的国债期货跨期套利研究

发布时间：2018-01-13 08:40

本文关键词：基于Copula-SV模型的国债期货跨期套利研究　出处：《西南财经大学》2014年硕士论文　论文类型：学位论文

【摘要】：国债期货本身是一个利率衍生品,对利率市场会产生显著的影响。它不仅是整个利率体系很重要的环节,同时也是整个利率市场化的“基石”。由于国债期货对利率市场有着极其深刻的影响和意义,2012年2月13日,中金所启动5年期国债期货交易测试,经过近一年的仿真试行,2013年9月6日,5年期国债期货合约正式在中金所上市。作为国内首款利率衍生品,国债期货的推出将对市场和投资者具有积极的意义,其推出后的定价和套利策略必将成为市场关注和研究的热点。由于我国在上个世纪九十年代初就开办了国债期货试点,因此国内与之相关的研究也不在少数,概括起来主要可以分为两个阶段：一是国债期货被叫停时期的反思阶段,二是国债恢复重启推出仿真交易后的策略运用阶段。与国内研究相比,国外关于跨期套利的研究起点更早内容更加丰富。本文结合相关文献并考虑到我国国债期货当前的具体情况,本文的研究内容将主要集中在套利策略方面。对于国债期货来说,和股指期货一样,在正式推出前,中金所向市场提供了国债期货的仿真交易。由于国债期货正式上市至今才一个季度,TF09合约甚至都还没开始交易,市场还不够活跃,交易价格和现货价格尚不存在明显的联动性,期现套利的价差也因此不具有合理性,因此用当前的交易数据来进行期现套利的分析,在现阶段不具有其现实意义。另一方面,不同于股指期货简单的现金交割,国债期货期现套利涉及到现货市场CTD的可获得性、交个标的随交割时间变化而变化、国债久期和转换因子的计算、以及现货交割对市场的冲击、摩擦和交易成本等诸多问题,在实际的操作中都还有待研究和解决。因此,就目前的情况来看,把研究重心放在跨期套利上是比较合理的。在大部分的文献中,关于期货套利分析的研究方法主要分为持有成本理论和价差波动模型两种。但是这两种方法一是忽略了现实中的随机因素对价差的影响,二是对模型的假设都较为严格,然而,在现实中的数据往往较难达到如此理想的情形。因此,本文换了一个角度,避开以往模型中一系列严苛的假设条件,从资产组合入手,将国债期货跨期套利组合看作是一个资产组合,从而进行国债期货的跨期套利分析。本文通过对国债期货定价及套利策略进行深入的分析研究并结合前人研究的成果提出了以资产组合思想为基础的Copula-SV国债期货跨期套利模型。为了验证模型的有效性,本文采用数据模拟的方法,通过计算机模拟模拟出平稳和非平稳的套利价差序列,然后分别用Copula-SV模型与传统的价差波动模型对价差序列进行建模,估计套利区间,再运用本文的套利策略进行模拟交易,对比两种模型最终的绩效后发现：在套利组合价差平稳的情形下,传统价差波动模型和Copula-SV模型各有优劣,运用传统的价差波动模型进行套利显得更加稳健,风险更低,但是收益相对较低；另一方面,由于Copula-SV模型是直接对分布进行估计,对价差波动特征的刻画更为细致,因此在套利组合价差平稳情形下运用Copula-SV模型进行套利时,获得的收益会比传统价差波动模型要高,但是由于交易次数的增多,模型的胜率也因之下降,交易成本也因此高于传统套利模型。当套利组合价差为非平稳序列时,基于平稳假设的传统价差波动模型将会失效,由于Copula-SV模型是直接对每一个时点的分布进行估计,因此从理论上来说可以适用于价差序列非平稳的情形,但是,由于是基于统计套利的思想,此时运用Copula-SV模型进行套利的结果将大不如价差平稳的情形,不仅收益降低,胜率也随之下降。综上分析,不论是在套利组合价差平稳还是非平稳的情形下,Copula-SV模型都可以对套利区间进行估计,从而辅助套利者进行套利策略的实施。而且在套利价差平稳条件下Copula-SV模型对套利区间的估计更加精确,可以为套利者带来更多的潜在收益；在套利价差非平稳条件下Copula-SV模型仍可适用,这也弥补了传统价差波动模型失效的空白。另外,在对模型的绩效和适用性进行分析和检验后,本文运用Copula-SV模型,从跨期套利的角度,对5年期国债期货合约套利组合进行了实证分析：首先通过协整分析发现国债期货近期合约和远期合约的价格序列通过协整检验,二者存在着长期均衡的关系。同时本文通过协整回归方程得到了5年期国债期货跨期套利组合的套利头寸比。其次,考虑到套利组合实质上可以看作是一个资产组合,因此从资产组合方向入手,在单个期货合约的角度,选择三种厚尾的随机波动模型分别进行估计和对比后发现SV-GED和SV-t模型对近期合约和远期合约的收益率波动和边际分布的拟合程度最高。然后,根据极大似然法对椭圆函数族中的正态Copula函数和t-Copula函数以及阿基米德函数族中的ClaytonCopula、FrankCopula和GumbelCopula函数的参数值进行估计,通过对比模型的极大似然值,发现t-Copula函数的拟合程度最好,并以此估计出最终套利组合的联合分布。在得到联合分布后,再采用MCMC的方法模拟出套利组合的置信区间,套利组合的置信区间实际上也就是价差的置信区间,然后再利用统计套利的思想结合具体的开平仓点设置,止盈止损点的选择等套利策略确定出最佳的套利区间,从而得到最终的5年期国债期货套利模型。本文通过对5年期国债期货跨期套利组合中的近期合约和远期合约进行相关性分析发现,在市场的单边行情较不明朗,出现长期震荡时,5年期国债期货套利组合中近期合约与远期合约具有很强的相关性,因此震荡行情下进行国债期货跨期套利可以保证较高的收益和较低的风险,同时也具有较好的操作准确性。另一方面,当市场出现大幅的上涨或下跌,表现为明显的单边行情时,在熊市行情中进行国债期货跨期套利的情形下,5年期国债期货套利组合中近期合约与远期合约的相关性相较于牛市行情表现的更为强烈,此时进行套利交易可以保证较高的收益。本文利用2013/11/7—-2014/1/22期间的国债期货交易数据对估计出的模型进行了测试,发现最终计算出的模型的年华收益率为12.96%,大大超出了市场上一般理财产品的收益能力,说明模型的设定和测试结果非常理想。另一方面,本文利用估计出的模型对样本期内的数据进行检验,并列举实例介绍了模型在现实国债期货跨期套利交易中的具体操作方法。综上所述,由于国债期货在我国正式上市还不到半年,国内外对其进行的研究还相对较少,特别是对国债期货进行套利策略研究的文献几乎没有。因此本文从跨期套利的角度,通过理论推导和计算机模拟的方法对国债期货所适用的套利模型进行了深入的对比和研究,发现本文提出的Copula-SV模型不仅能弥补传统模型对数据要求过于严格的不足,而且运用Copula-SV模型进行实际套利操作中还能获得令人满意的套利结果。而后运用本文提出的模型对国债期货上市以来的交易数据进行了实证检验,发现模型的效果确实较为理想,暂时弥补了我国在国债期货跨期套利实证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.

【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51;F224

【参考文献】