基于股票收益的期权定价与实证分析

采用两种方法对传统的期权定价参数方法进行修正。一种是利用股票对数收益率的偏度与峰度对传统的期权定价方法计算出的期权价格进行修正,另一种是通过建立GARCH模型来预测股票收益的波动率,对传统定价方法中波动率为常数的假设进行修正。选取国电CWB1(580022)权证进行实证分析,结果表明修正得出的期权价格与实际的权证价格有很大的偏差,并对这样实证结果进行解释。     

交易量适合作为股价波动信息的代理变量吗?——来自中国沪深股市的证据

本文利用中国沪深股市日交易数据,采用多元GARCH模型从信息传递的角度进行实证研究,结果表明:股价对交易量具有显著的波动溢出效应,但交易量对股价的波动溢出效应不明显。这种波动的单向溢出说明在应对信息的冲击上股价比交易量能更快地做出反应,其后才通过波动溢出在交易量上得到反映,股价波动对成交量波动具有先导作用。因此,从波动冲击传导和信息传递的角度看,单纯地将交易量视为股价变动信息的代理变量还缺乏稳健的统计证据。     

基于GM(1,1)模型的市场碳交易价格预测——以北京、广东、湖北为例

社会各界对大气环境问题高度重视,使得国家和企业的低碳绿色环保意识不断增强,而碳交易价格属于国内新兴碳市场中的一项关键性因素,故论文利用GM(1,1)模型,选取北京、广东、湖北三个市场2015-2019年的年平均碳交易价格为研究对象进行短期预测。研究发现:GM(1,1)模型可较好地预测碳交易价格,拟合结果有较高的精度;未来三年,广东、湖北的碳价呈稳步性增长,北京的碳价每年均保持约20%的增长趋势,且2020-2022年的碳交易价格预测具有一定的可信度。     

Forecasting solar stock prices using tree-based machine learning classification: How important are silver prices?

Solar energy is one of the fastest growing sources of electricity generation. Forecasting solar stock prices is important for investors and venture capitalists interested in the renewable energy sector. This paper uses tree-based machine learning methods to forecast the direction of solar stock prices. The feature set used in prediction includes a selection of well-known technical indicators, silver prices, silver price volatility, and oil price volatility. The solar stock price direction prediction accuracy of random forests, bagging, support vector machines, and extremely randomized trees is much higher than that of logit. For a forecast horizon of between 8 and 20 days, random forests, bagging, support vector machines, and extremely randomized trees achieve a prediction accuracy greater than 85%. Although not as prominent as technical indicators like MA200, WAD, and MA20, oil price volatility and silver price volatility are also important predictors. An investment portfolio trading strategy based on trading signals generated from the extremely randomized trees stock price direction prediction outperforms a simple buy and hold strategy. These results demonstrate the accuracy of using tree-based machine learning methods to forecast the direction of solar stock prices and adds to the broader literature on using machine learning techniques to forecast stock prices.     

Option pricing with discrete time jump processes

In this paper we propose new option pricing models based on class of models with jumps contained in the Lévy-type based models (NIG-Lévy, Schoutens, 2003, Merton-jump, Merton, 1976 and Duan based model, Duan et al., 2007). By combining these different classes of models with several volatility dynamics of the GARCH type, we aim at taking into account the dynamics of financial returns in a realistic way. The associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel: we provide a characterization of the change in the probability measure using the Esscher transform and the Minimal Entropy Martingale Measure. We finally assess empirically the performance of this modelling approach, using a dataset of European options based on the S&P 500 and on the CAC 40 indices. Our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness. These results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist.     

成交量、持仓量对我国大豆类期货价差波动影响的实证分析

采用GARCH(1,1)模型就成交量、持仓量对大豆类期货价差波动率的影响进行实证分析,结果显示：当期成交量、持仓量对大豆期货价差波动的整体影响是显著的;滞后成交量、持仓量对大豆期货价差波动的整体影响也是显著的;当成交量、持仓量同时进入条件方差方程时,它们对大豆类期货价差波动的影响整体上也是显著的。这一结论揭示了我国大豆期货市场信息传递过程,验证了我国大豆期货市场的信息非有效性,对期货市场投资者以及期货市场监管者具有一定的借鉴意义。     

基于GARCH族模型的黄金价格收益率及波动性研究

文章应用GARCH族模型对黄金现货价格的收益率及波动性进行实证研究,实证结果表明黄金价格日收益率具有"尖峰厚尾"和"波动聚类"的特征。通过TGARCH及EGARCH模型发现我国黄金市场存在非对称性现象,正的冲击对黄金价格波动影响更大。     

Volatility estimation for stock index options: A GARCH approach

The objective of this paper is to compare the mispricing of option valuation models when alternate techniques are applied to the volatility estimation. Akgiray (1989) shows that out-of-sample forecasts of return variances of stock indices based on a GARCH model are superior predictors of the actual ex-post variances in comparison to forecasts generated using standard rolling regression methods. A second objective of this study is to examine if Akgiray's results carry over to option valuation. Although we find that the implied volatility technique results in the least mispricing, within the class of forecasts using only historic returns data, the use of GARCH models will also significantly reduce model mispricing.     

Improving the realized GARCH’s volatility forecast for Bitcoin with jump-robust estimators

This study employs the realized GARCH (RGARCH) model to estimate the volatility of Bitcoin returns and measure the benefits of various scaled realized measures in forecasting volatility. Empirical results show that considerable price jumps occurred in the Bitcoin market, suggesting that a jump-robust realized measure is crucial to estimate Bitcoin volatility. The RGARCH model, especially the one with tri-power variation, outperforms the standard GARCH model. Additionally, the RGARCH model with jump-robust realized measures can provide steady forecasting performance. This study is timely given that the CME may release a Bitcoin option product and our results are relevant to option pricing     

Options and earnings announcements: an empirical study for the European Options Exchange

In this paper we give an introduction in option pricing theory and explicitly specify the Black-Scholes model. Although market participants use this and similar models to price options, they violate one of the fundamental assumptions of the model. They do not set a constant value for the volatility of the underlying asset over time, but change the volatility even during a day. By means of event study methodology we investigate the volatility of the underlying asset and the volatility implicit in option prices around earnings announcements by firms. We find that the volatility in option prices increases before the announcement date and drops sharply afterwards. The volatility of the underlying stocks is higher only at the announcement dates and we do not observe a higher volatility around these dates. Hence, the constant volatility of the underlying asset, which is one of the assumptions in the Black-Scholes model, does not hold. However, the market seems to correctly anticipate the change in volatility, by correcting option prices.     

The impact of option listing on the price volatility and trading volume of underlying OTC stocks

This paper examines the impact of an initial option listing on the price volatility and trading volume of underlying OTC stocks. The sample is divided by market value to determine whether larger firms are impacted differently by option listing than smaller firms. We find relative trading volume increases significantly, with the small and medium market value firms showing the largest gain. However, the tests show no evidence of changes in price volatility following option listing. No significant changes were found in either the firms' betas or variance following option initiation. The results provide further evidence that option listing does not destabilize the market for the underlying stock.     

Volatility estimation from observed option prices

It is well established that the standard Black-Scholes model does a very poor job in matching the prices of vanilla European options. The implied volatility varies by both time to maturity and by the moneyness of the option. One approach to this problem is to use the market option prices to back out a local volatility function that reproduces the market prices. Since option price observations are only available for a limited set of maturities and strike prices, most algorithms require a smoothing technique to implement this approach. In this paper we modify the implementation of Andersen and Brotherton-Ratcliffe to provide another way of dealing with this issue. Numerical examples indicate that our approach is reasonably successful in reproducing the input prices.     

Crack spread hedging: accounting for time‐varying volatility spillovers in the energy futures markets

Crude oil, heating oil, and unleaded gasoline futures contracts are simultaneously analysed for their effectiveness in reducing price volatility for an energy trader. A conceptual model is developed for a trader hedging the ‘crack spread’. Various hedge ratio estimation techniques are compared to a Multivariate GARCH model that directly incorporates the time to maturity effect often found in futures markets. Modelling of the time‐variation in hedge ratios via the Multivariate GARCH methodology, and thus taking into account volatility spillovers between markets is shown to result in significant reductions in uncertainty even while accounting for trading costs. Copyright © 2002 John Wiley & Sons, Ltd.     

涨跌停板制度对期货市场价格发现过程及波动性的影响--基于上海期货交易所的实证研究

本文通过检验在出现涨跌停板之后一个交易日的期货价格及其波动性的变化情况，研究了涨跌停板制度对上海期货交易所期货价格变动的影响。研究结果显示，对不同的期货品种，涨跌停板制度的影响存在一定的差异，但总体而言，涨跌停板制度并没有起到防范价格过度反应和降低市场波动性的作用。相反，在一定程度上延缓了期货市场价格发现功能的发挥，增大了市场的波动性。     

基于波动效应与价格发现的期指仿真交易研究

沪深300股指期货仿真交易的推出,对我国现货市场的影响如何以及这种影响是否有利于现货效率的改进。首次采用修正的GARCH模型和向量误差修正模型(VEC)将股指期货推出后现货市场波动性的变化和股指期货与现货市场的价格发现功能结合起来进行对比研究。结果表明,期指仿真交易的推出对于现货市场效率的改进确实存在正面的影响。其引入在短期内加大了现货市场的波动,但这一波动正是市场信息流动加速的反映,因而提高了市场信息的传递效率。同时期货价格领先于现货价格,存在由期货市场到现货市场长期的单向因果关系,说明期货价格具有引导现货价格向均衡方向调整的功能,从而在经验上支持了股指期货市场的开放政策。     

How should a local regime-switching model be calibrated?

Local regime-switching models are a natural consequence of combining the concept of a local volatility model with that of a regime-switching model. However, even though Elliott et al. (2015) have derived a Dupire formula for a local regime-switching model, its calibration still remains a challenge, primarily due to the fact that the derived volatility function for each state involves all the state price variables whereas only one market price is available for model calibration, and a direct implementation of Elliott et al.’s formula may not yield stable results. In this paper, a closed system for option pricing and data extraction under the classical regime-switching model is proposed with a special approach, splitting one market price into two “market-implied state prices”. The success of our approach hinges on the recovery of the two local volatility functions being transformed into an optimal control problem, which is solved through the Tikhonov regularization. In addition, an efficient algorithm is proposed to obtain the optimal solution by iteration. Our numerical experiments show that different shapes of local volatility functions can be accurately and stably recovered with the newly-proposed algorithm, and this algorithm also works quite well with real market data.     

Day trading and stock price volatility

When an investor buys and sells the same stock on the same day, he is said to have made a day trade. Using the trading records of Finnish traders, this paper examines whether day trading is related to volatility of stock prices. I find a strong positive time-series relation between the number of day trades by individual investors and intraday volatility among heavily day traded stocks. This effect is robust after controlling for a previously documented volume–volatility relation. The result suggests that the joint hypothesis of price pressure and volatility induced day trading dominates the liquidity effects of day trading.     

A reduced form framework for modeling volatility of speculative prices based on realized variation measures

Building on realized variance and bipower variation measures constructed from high-frequency financial prices, we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility. We decompose the total daily return variability into the continuous sample path variance, the variation arising from discontinuous jumps that occur during the trading day, as well as the overnight return variance. Our empirical results, based on long samples of high-frequency equity and bond futures returns, suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long-memory HAR–GARCH model, while the overnight returns may be modeled by an augmented GARCH type structure. The dynamic dependencies in the non-parametrically identified significant jumps appear to be well described by the combination of an ACH model for the time-varying jump intensities coupled with a relatively simple log-linear structure for the jump sizes. Finally, we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out-of-sample forecasts for the total return volatility.     

Dynamic volatility modelling of Bitcoin using time-varying transition probability Markov-switching GARCH model

Bitcoin (BTC), as the dominant cryptocurrency, has attracted tremendous attention lately due to its excessive volatility. This paper proposes the time-varying transition probability Markov-switching GARCH (TV-MSGARCH) models incorporated with BTC daily trading volume and daily Google searches singly and jointly as exogenous variables to model the volatility dynamics of BTC return series. Extensive comparisons are carried out to evaluate the modelling performances of the proposed model with the benchmark models such as GARCH, GJRGARCH, threshold GARCH, constant transition probability MSGARCH and MSGJRGARCH. Results reveal that the TV-MSGARCH models with skewed and fat-tailed distribution predominate other models for the in-sample model fitting based on Akaike information criterion and other benchmark criteria. Furthermore, it is found that the TV-MSGARCH model with BTC daily trading volume and student-t error distribution offers the best out-of-sample forecast evaluated based on the mean square error loss function using Hansen’s model confidence set. Filardo’s weighted transition probabilities are also computed and the results show the existence of time-varying effect on transition probabilities. Lastly, different levels of long and short positions of value-at-risk and the expected shortfall forecasts based on MSGARCH, MSGJRGARCH and TV-MSGARCH models are also examined.     

Forecasting value at risk with intra-day return curves

Methods for incorporating high resolution intra-day asset price data into risk forecasts are being developed at an increasing pace. Existing methods such as those based on realized volatility depend primarily on reducing the observed intra-day price fluctuations to simple scalar summaries. In this study, we propose several methods that incorporate full intra-day price information as functional data objects in order to forecast value at risk (VaR). Our methods are based on the recently proposed functional generalized autoregressive conditionally heteroscedastic (GARCH) models and a new functional linear quantile regression model. In addition to providing daily VaR forecasts, these methods can be used to forecast intra-day VaR curves, which we considered and studied with companion backtests to evaluate the quality of these intra-day risk measures. Using high-frequency trading data from equity and foreign exchange markets, we forecast the one-day-ahead daily and intra-day VaR with the proposed methods and various benchmark models. The empirical results suggested that the functional GARCH models estimated based on the overnight cumulative intra-day return curves exhibited competitive performance with benchmark models for daily risk management, and they produced valid intra-day VaR curves.