Zhu and Lian (Journal of Futures Markets, 2012) proposed the first closed-form formulas for VIX futures prices, whihch are conceptually appealing and easy to implement. Unfortunately, the paper is found to contain three kinds of errors. The main formula (9) for the price of futures misses the factor of 100 in two places. Consequently, the biggest reported RMSE of 3.230 by Zhu-Lian is significantly lower than the correct RMSE of 9.447; the biggest correct in-sample MPE of about 50% implies little practical value of Zhu-Lian. Further, the discretized equation set (14), which is used for estimating parameters, has variables with inconsistent units of time. As a result, the reported parameters could not be replicated. Lastly, the reported counts of VIX futures within three maturity-groups are bafflingly way off by between -26% and 48%. This short note corrects these mistakes, and tries to replicate the empirical work.
Zhu和Lian (Journal of Futures Markets, 2012)首次提出了VIX期货价格的封闭式公式，该公式在概念上具有吸引力，易于实施。不幸的是，这篇论文被发现有三种错误。期货价格的主公式(9)在两个地方漏掉了100因子。因此，朱莲报告的最大RMSE为3.230，显著低于正确的RMSE 9.447;样品内最大正确MPE约为50%，说明竹连的实用价值不大。此外，用于估计参数的离散化方程集(14)，其变量的时间单位不一致。因此，无法复制报告的参数。最后，报告的三个期限组的波动率指数期货数量相差了26%到48%，这令人困惑。这篇短文纠正了这些错误，并试图复制实证工作。
{"title":"An Analytical Formula for Vix Futures and Its Applications: Error Corrections and Replication","authors":"Qiang Liu, Shuxin Guo","doi":"10.2139/ssrn.3293437","DOIUrl":"https://doi.org/10.2139/ssrn.3293437","url":null,"abstract":"Zhu and Lian (Journal of Futures Markets, 2012) proposed the first closed-form formulas for VIX futures prices, whihch are conceptually appealing and easy to implement. Unfortunately, the paper is found to contain three kinds of errors. The main formula (9) for the price of futures misses the factor of 100 in two places. Consequently, the biggest reported RMSE of 3.230 by Zhu-Lian is significantly lower than the correct RMSE of 9.447; the biggest correct in-sample MPE of about 50% implies little practical value of Zhu-Lian. Further, the discretized equation set (14), which is used for estimating parameters, has variables with inconsistent units of time. As a result, the reported parameters could not be replicated. Lastly, the reported counts of VIX futures within three maturity-groups are bafflingly way off by between -26% and 48%. This short note corrects these mistakes, and tries to replicate the empirical work.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"832 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116146383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In December 2017, both the Chicago Board Options Exchange and the Chicago Mercantile Exchange introduced futures contracts on bitcoin. We investigate to what extent they provide useful information for the price discovery of bitcoin. We rely on the information share methodology of Hasbrouck (1995, J Finance, 50, pp. 1175–1199) and Gonzalo and Granger (1995, J Bus Econ Stat, 13, pp. 27–35) and find that the spot price leads the futures price. We attribute this result to the higher trading volume and the longer trading hours of the globally distributed bitcoin spot market, compared to the relatively restricted access to the US‐based futures markets.
2017年12月，芝加哥期权交易所和芝加哥商品交易所都推出了比特币期货合约。我们调查了它们在多大程度上为比特币的价格发现提供了有用的信息。我们依靠Hasbrouck (1995, J Finance, 50，第1175-1199页)和Gonzalo and Granger (1995, J Bus Econ Stat, 13，第27-35页)的信息共享方法，发现现货价格领先于期货价格。我们将这一结果归因于全球分布式比特币现货市场的更高交易量和更长的交易时间，而相比之下，美国期货市场的准入相对受限。
{"title":"Price Discovery in Bitcoin Spot or Futures?","authors":"D. Baur, T. Dimpfl","doi":"10.2139/ssrn.3171464","DOIUrl":"https://doi.org/10.2139/ssrn.3171464","url":null,"abstract":"In December 2017, both the Chicago Board Options Exchange and the Chicago Mercantile Exchange introduced futures contracts on bitcoin. We investigate to what extent they provide useful information for the price discovery of bitcoin. We rely on the information share methodology of Hasbrouck (1995, J Finance, 50, pp. 1175–1199) and Gonzalo and Granger (1995, J Bus Econ Stat, 13, pp. 27–35) and find that the spot price leads the futures price. We attribute this result to the higher trading volume and the longer trading hours of the globally distributed bitcoin spot market, compared to the relatively restricted access to the US‐based futures markets.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114729032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Early analysis of Bitcoin concluded that it did not meet the economic conditions to be classified as a currency. Since this conclusion, interest in Bitcoin has increased substantially. We investigate whether the introduction of futures trading in Bitcoin is able to resolve the issues that stopped Bitcoin from being considered a currency. Our analysis shows that spot volatility has increased following the appearance of futures contracts, that futures contracts are not an effective hedging instrument, and that price discovery is driven by uninformed investors in the spot market. We therefore argue that the conclusion that Bitcoin is a speculative asset rather than a currency is not altered by the introduction of futures trading.
{"title":"Bitcoin Futures - What Use are They?","authors":"S. Corbet, B. Lucey, M. Peat, S. Vigne","doi":"10.2139/ssrn.3197634","DOIUrl":"https://doi.org/10.2139/ssrn.3197634","url":null,"abstract":"Early analysis of Bitcoin concluded that it did not meet the economic conditions to be classified as a currency. Since this conclusion, interest in Bitcoin has increased substantially. We investigate whether the introduction of futures trading in Bitcoin is able to resolve the issues that stopped Bitcoin from being considered a currency. Our analysis shows that spot volatility has increased following the appearance of futures contracts, that futures contracts are not an effective hedging instrument, and that price discovery is driven by uninformed investors in the spot market. We therefore argue that the conclusion that Bitcoin is a speculative asset rather than a currency is not altered by the introduction of futures trading.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126670946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is a contango with VIX ≈ 12% and a long-term futures price V∞ ≈ 20%. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity and through a multi-factor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically-sure profits if it is assumed that CMFs are stationary and ergodic (see Proposition 3.1). To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies, but also indicate that the latter have modest Sharpe ratios, of the order of SR = 0.5 or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are experienced sporadically, but also inevitably, in the volatility futures market.
{"title":"Statistics of VIX Futures and Their Applications to Trading Volatility Exchange-Traded Products","authors":"M. Avellaneda, A. Papanicolaou","doi":"10.2139/ssrn.3028910","DOIUrl":"https://doi.org/10.2139/ssrn.3028910","url":null,"abstract":"We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is a contango with VIX ≈ 12% and a long-term futures price V∞ ≈ 20%. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity and through a multi-factor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically-sure profits if it is assumed that CMFs are stationary and ergodic (see Proposition 3.1). To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies, but also indicate that the latter have modest Sharpe ratios, of the order of SR = 0.5 or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are experienced sporadically, but also inevitably, in the volatility futures market.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126889186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is often asserted that futures investors periodically pay or receive the difference in futures prices across contracts with different delivery dates. This "roll yield" is mythical - no such cash flow occurs, at the time of "roll" trades or on any other date. While the term is a misnomer, the "roll yield" does contain useful information. It explains when futures gains exceed or fall short of spot price changes, and for storable assets it provides information regarding benefits to the marginal holder of a spot position. This paper clarifies the actual role of the "roll yield".
{"title":"The 'Roll Yield' Myth","authors":"H. Bessembinder","doi":"10.2139/ssrn.3011634","DOIUrl":"https://doi.org/10.2139/ssrn.3011634","url":null,"abstract":"It is often asserted that futures investors periodically pay or receive the difference in futures prices across contracts with different delivery dates. This \"roll yield\" is mythical - no such cash flow occurs, at the time of \"roll\" trades or on any other date. While the term is a misnomer, the \"roll yield\" does contain useful information. It explains when futures gains exceed or fall short of spot price changes, and for storable assets it provides information regarding benefits to the marginal holder of a spot position. This paper clarifies the actual role of the \"roll yield\".","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126767621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Flash Crash of May 6, 2010, shook the confidence of market participants and raised questions about the market structure of electronic markets. In these markets, intraday intermediation has been increasingly provided by market participants without formal obligations to do so. We examine intraday intermediation in the E-mini S&P 500 stock index futures market before and during the Flash Crash. We discuss the evolution of trading from human to electronic environments and the implications of our results for market design.
{"title":"Automation, Intermediation and the Flash Crash","authors":"A. Kirilenko, A. Kyle, M. Samadi, Tugkan Tuzun","doi":"10.2139/ssrn.3119363","DOIUrl":"https://doi.org/10.2139/ssrn.3119363","url":null,"abstract":"The Flash Crash of May 6, 2010, shook the confidence of market participants and raised questions about the market structure of electronic markets. In these markets, intraday intermediation has been increasingly provided by market participants without formal obligations to do so. We examine intraday intermediation in the E-mini S&P 500 stock index futures market before and during the Flash Crash. We discuss the evolution of trading from human to electronic environments and the implications of our results for market design.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114142768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estimate VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 historical data, evaluate the effect of adding jumps into asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.
{"title":"Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models","authors":"A. Swishchuk, Zijiao Wang","doi":"10.2139/ssrn.3084186","DOIUrl":"https://doi.org/10.2139/ssrn.3084186","url":null,"abstract":"In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estimate VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 historical data, evaluate the effect of adding jumps into asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130970059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study comprehensively examines pairs trading in Chinese commodity futures markets, which, although less researched, represents an important scenario for analysing commodity price behaviour. Based on a sample of daily future returns from 2006 to 2016, we propose a cointegration model that employs an adaptive learning process, and we show that our model yields an average annualised return of 26.94 percent before trading costs, using a closed‐loop strategy. Our results are robust to various tests, including parameter uncertainty, holding period constraints, trading period selection and trading costs.
{"title":"Pairs Trading in Chinese Commodity Futures Markets: An Adaptive Cointegration Approach","authors":"Danni Chen, Jing Cui, Yan Gao, Leilei Wu","doi":"10.1111/acfi.12335","DOIUrl":"https://doi.org/10.1111/acfi.12335","url":null,"abstract":"This study comprehensively examines pairs trading in Chinese commodity futures markets, which, although less researched, represents an important scenario for analysing commodity price behaviour. Based on a sample of daily future returns from 2006 to 2016, we propose a cointegration model that employs an adaptive learning process, and we show that our model yields an average annualised return of 26.94 percent before trading costs, using a closed‐loop strategy. Our results are robust to various tests, including parameter uncertainty, holding period constraints, trading period selection and trading costs.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"282 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114609013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michail Anthropelos, Christos Bouras, Evangelos S. Malmpanzi
This paper studies the dynamic relationship between the CBOE VIX index spot and futures returns by applying multi-period, non-parametric, Granger non-causality tests and measurements on conditional distributions. In contrast to the related empirical studies, it is found that VIX futures returns are strong causal for VIX spot returns, not only in the short run, but also at higher time horizons. The predictive content of the VIX futures varies widely with the prediction horizon and maturity. In particular, the returns of VIX futures with low maturities have intense predictive ability for VIX spot returns in the short run, while the causal effects from VIX futures with longer maturities are found to last longer. Evidence of bidirectional causation at multiple time horizons is also documented between VIX spot returns and the returns of futures with medium and long-term maturities. An out-of-sample forecasting exercise also supports our main findings.
{"title":"Long Term Causality in VIX Markets","authors":"Michail Anthropelos, Christos Bouras, Evangelos S. Malmpanzi","doi":"10.2139/ssrn.3203029","DOIUrl":"https://doi.org/10.2139/ssrn.3203029","url":null,"abstract":"This paper studies the dynamic relationship between the CBOE VIX index spot and futures returns by applying multi-period, non-parametric, Granger non-causality tests and measurements on conditional distributions. In contrast to the related empirical studies, it is found that VIX futures returns are strong causal for VIX spot returns, not only in the short run, but also at higher time horizons. The predictive content of the VIX futures varies widely with the prediction horizon and maturity. In particular, the returns of VIX futures with low maturities have intense predictive ability for VIX spot returns in the short run, while the causal effects from VIX futures with longer maturities are found to last longer. Evidence of bidirectional causation at multiple time horizons is also documented between VIX spot returns and the returns of futures with medium and long-term maturities. An out-of-sample forecasting exercise also supports our main findings.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126062038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the log-linear relationship between futures contracts and their underlying assets and show that in the classical Brownian semi-martingale (BSM) framework the two series must, by no-arbitrage, have the same integrated variance. We then introduce the concept of noise cancelling and propose a generally applicable methodology to assess the performance of realized measures when the variable of interest is latent, overcoming the problem posed by the lack of a true value for the integrated variance. Using E-mini index futures contracts, we carry out formal testing of several realized measures in the presence of noise. Moreover, a thorough simulation analysis is employed to evaluate the estimators' sensitivity to different price and noise processes, and sampling frequencies.
{"title":"Inference from the Futures: Ranking the Noise Cancelling Accuracy of Realized Measures","authors":"G. Mirone","doi":"10.2139/ssrn.2993234","DOIUrl":"https://doi.org/10.2139/ssrn.2993234","url":null,"abstract":"We consider the log-linear relationship between futures contracts and their underlying assets and show that in the classical Brownian semi-martingale (BSM) framework the two series must, by no-arbitrage, have the same integrated variance. We then introduce the concept of noise cancelling and propose a generally applicable methodology to assess the performance of realized measures when the variable of interest is latent, overcoming the problem posed by the lack of a true value for the integrated variance. Using E-mini index futures contracts, we carry out formal testing of several realized measures in the presence of noise. Moreover, a thorough simulation analysis is employed to evaluate the estimators' sensitivity to different price and noise processes, and sampling frequencies.","PeriodicalId":306457,"journal":{"name":"ERN: Futures (Topic)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133733382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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