THE ECONOMIC VALUE OF USING REALIZED VOLATILITY IN FORECASTING FUTURE IMPLIED VOLATILITY

We examine the economic benefits of using realized volatility to forecast future implied volatility for pricing, trading, and hedging in the S&P 500 index options market. We propose an encompassing regression approach to forecast future implied volatility, and hence future option prices, by combining historical realized volatility and current implied volatility. Although the use of realized volatility results in superior performance in the encompassing regressions and out-of-sample option pricing tests, we do not find any significant economic gains in option trading and hedging strategies in the presence of transaction costs.     

A Likelihood Ratio Test of Price Volatilities: Comparing Stock Index Spot and Futures

This paper uses three methods to estimate the price volatility of two stock market indexes and their corresponding futures contracts. The classic variance measure of volatility is supplemented with two newer measures, derived from the Garman-Klass and Ball-Torous estimators. A likelihood ratio test is used to compare the classic variance measure of price volatilities of two stock market indexes and their corresponding futures contracts during the bull market of the 1980s. The stock market volatilities of the Standard & Poor's 500 (S&P 500) and New York Stock Exchange (NYSE) indexes were found to be significantly lower than their respective futures price volatilities. Since information may flow faster in the futures markets than in the corresponding stock market, our results support Ross's information-volatility hypothesis. It was also noted that the NYSE spot volatility was lower than the S&P 500 spot volatility. If the rate of information flow and firm size are positively related, then the lower NYSE spot volatility is explained by the size effect. The futures price volatilities for the two indexes were insignificantly different from each other. With stock index spot-futures price correlations approaching unity, one implication of our results for index futures activity is that smaller positions in futures contracts may suffice to achieve hedging or arbitrage goals.     

模糊厌恶下股指期货风险对冲策略设计及实证分析

投资者对股指期货与现货有着不同的模糊厌恶,本文首先将此假设条件引入带交易成本的Garleanu and Pederson (2013)投资模型中,并以指数基金对冲策略为例,构建了一个股指期货动态对冲的理论模型。与非对冲策略相比,基于上述模型设计的对冲策略投资绩效更好,动态最优成交额占目标交易额的比例更小,目标成交额对收益率预测因子的敏感性更大。借助上述模型,本文选取2010年4月至2021年6月的中国ETF指数基金和股指期货数据,并以2015年9月股指期货管理措施实施为界进行区间划分,实证研究发现:(1)中国A股市场的ETF投资组合进行股指期货对冲显著提升了投资绩效,但股指期货管理会削弱该作用;(2)投资绩效改善主要来源于交易成本的下降与目标成交额因子敏感性的提升,该机制受到股指期货管理的约束;(3)与Garleanu and Pederson (2013)、Zhang et al. (2017)相比,本文对冲策略保留“抗跌”特点的同时增加了“易涨”特性。本文研究结果表明,在当前大力发展机构投资者的背景下应不断丰富股指期货、股指期权产品谱系,降低股指期货交易成本并完善持仓约束。     

Is the realized volatility good for option pricing during the recent financial crisis?

The contributions of this paper are threefold. The first contribution is the proposed logarithmic HAR (log-HAR) option-pricing model, which is more convenient compared with other option pricing models associated with realized volatility in terms of simpler estimation procedure. The second contribution is the test of the empirical implications of heterogeneous autoregressive model of the realized volatility (HAR)-type models in the S&P 500 index options market with comparison of the non-linear asymmetric GARCH option-pricing model, which is the best model in pricing options among generalized autoregressive conditional heteroskedastic-type models. The third contribution is the empirical analysis based on options traded from July 3, 2007 to December 31, 2008, a period covering a recent financial crisis. Overall, the HAR-type models successfully predict out-of-sample option prices because they are based on realized volatilities, which are closer to the expected volatility in financial markets. However, mixed results exist between the log-HAR and the heterogeneous auto-regressive gamma models in pricing options because the former is better than the latter in times of turmoil, whereas it is worse during the rather stable periods.     

Asymmetric volatility spillover among Chinese sectors during COVID-19

Inter-sectoral volatility linkages in the Chinese stock market are understudied, especially asymmetries in realized volatility connectedness, accounting for the catastrophic event associated with the COVID-19 outbreak. In this paper, we examine the asymmetric volatility spillover among Chinese stock market sectors during the COVID-19 pandemic using 1-min data from January 2, 2019 to September 30, 2020. In doing so, we build networks of generalized forecast error variances by decomposition of a vector autoregressive model, controlling for overall market movements. Our results show evidence of the asymmetric impact of good and bad volatilities, which are found to be time-varying and substantially intense during the COVID-19 period. Notably, bad volatility spillover shocks dominate good volatility spillover shocks. The findings are useful for Chinese investors and portfolio managers constructing risk hedging portfolios across sectors and for Chinese policymakers monitoring and crafting stimulating policies for the stock market at the sectoral level.     

Forecasting aggregate stock market volatility with industry volatilities: The role of spillover index

In this paper, we aim to improve the predictability of aggregate stock market volatility with industry volatilities. The empirical results show that individual industry volatilities can provide useful predictive information, while the predictive contribution is limited. We further consider the spillover index between industry volatilities and find it displays strong predictive power for stock market volatility. Based on the portfolio exercise, we find that a mean-variance investor can achieve sizeable economic gains by using volatility forecasts of the spillover index. In addition, we conduct three extended analyses and further demonstrate the superior performance of the spillover index. Also, our results show robustness to a series of alternative settings. Finally, we investigate why the spillover index performs better and answer what information it contains. The results show that the spillover index can reflect and explain investor sentiments that are related to stock market volatility.     

The effect of mergers on implied volatility of equity options

This paper uses a sample of 25 large mergers from 1996 to 2004 to study the effect of mergers on the implied volatilities of equity options. The results indicate a statistically significant increase in volatility beyond the amount predicted if the transaction were effectively nothing more than a portfolio combination of the target and acquirer. The disparity suggests that, at least for the first 18 months after the transaction becomes effective, market participants expect mergers to increase risk. Integration risk and uncertainty about the extent to which efficiency gains and greater market power are realized are possible explanations for the discrepancy.     

Dynamic hedging with futures: a copula-based GARCH model with high-frequency data

Modeling the joint distribution of spot and futures returns is crucial for establishing optimal hedging strategies. This paper proposes a new class of dynamic copula-GARCH models that exploits information from high-frequency data for hedge ratio estimation. The copula theory facilitates constructing a flexible distribution; the inclusion of realized volatility measures constructed from high-frequency data enables copula forecasts to swiftly adapt to changing markets. By using data concerning equity index returns, the estimation results show that the inclusion of realized measures of volatility and correlation greatly enhances the explanatory power in the modeling. Moreover, the out-of-sample forecasting results show that the hedged portfolios constructed from the proposed model are superior to those constructed from the prevailing models in reducing the (estimated) conditional hedged portfolio variance. Finally, the economic gains from exploiting high-frequency data for estimating the hedge ratios are examined. It is found that hedgers obtain additional benefits by including high-frequency data in their hedging decisions; more risk-averse hedgers generate greater benefits.     

备兑权证风险对冲策略分析

我国资本市场金融创新产品接连推出,备兑权证也再次被提上议程。在备兑权证的风险管理上,现有文献多集中于权证定价模型上的Delta对冲策略,却忽视了交易成本与间断交易,也没有深入分析影响该策略的各个因素。本文通过仿真实验Leland模型下的动态Delta对冲策略,发现交易成本、对冲间隔、行权价格以及波动率的变化都会显著影响对冲结果,但发行商仍有机会获取对冲收益,建议发行商略微溢价（5％）发行备兑权证,认为第三方对冲监管和差别对待的机制设计可确保市场繁荣。     

An approximate distribution of delta-hedging errors in a jump-diffusion model with discrete trading and transaction costs

We introduce a jump-diffusion model for asset returns with jumps drawn from a mixture of normal distributions and show that this model adequately fits the historical data of the S&P500 index. We consider a delta-hedging strategy (DHS) for vanilla options under the diffusion model (DM) and the proposed jump-diffusion model (JDM), assuming discrete trading intervals and transaction costs, and derive an approximation for the probability density function (PDF) of the profit-and-loss (P&L) of the DHS under both models. We find that, under the log-normal model of Black–Scholes–Merton, the actual PDF of the P&L can be well approximated by the chi-squared distribution with specific parameters. We derive an approximation for the P&L volatility in the DM and JDM. We show that, under both DM and JDM, the expected loss due to transaction costs is inversely proportional to the square root of the hedging frequency. We apply mean–variance analysis to find the optimal hedging frequency given the hedger's risk tolerance. Since under the JDM it is impossible to reduce the P&L volatility by increasing the hedging frequency, we consider an alternative hedging strategy, following which the P&L volatility can be reduced by increasing the hedging frequency.     

How asymmetric is U.S. stock market volatility?

This paper explores differences in the impact of equally large positive and negative surprise return shocks in the aggregate U.S. stock market on: (1) the volatility predictions of asymmetric time-series models, (2) implied volatility, and (3) realized volatility. Following large negative surprise return shocks, both asymmetric time-series models (such as the EGARCH and GJR models) and implied volatility predict an increase in volatility and, consistent with this, ex post realized volatility normally rises as predicted. Following large positive return shocks, asymmetric time-series models predict an increase in volatility (albeit a much smaller increase than following a negative shock of the same magnitude), but both implied and realized volatilities generally fall sharply. While asymmetric time-series models predict a decline in volatility following near-zero returns, both implied and realized volatility are normally little changed from levels observed prior to the stable market. The reasons for the differences are explored.     

The information frown in option prices

In the S&P 500 options market, the information content of implied volatilities differs by strike in a frown pattern that is a rough mirror image of the implied volatility smile. Implied volatilities calculated from moderately high strike price options are both unbiased and efficient predictors of future volatility. Implied volatilities calculated from low and at-the-money strikes are biased and less efficient. This bias cannot be explained by market imperfections but is consistent with the hedging pressure argument of Bollen and Whaley [J. Finan. 59 (2004) 711] and Ederington and Guan [J. Derivat. 10 (2002) (Winter) 9]. We also find that a serious estimation bias results when the relations are estimated using panel data.     

Forecasting oil price realized volatility using information channels from other asset classes

Motivated from Ross (1989) who maintains that asset volatilities are synonymous to the information flow, we claim that cross-market volatility transmission effects are synonymous to cross-market information flows or “information channels” from one market to another. Based on this assertion we assess whether cross-market volatility flows contain important information that can improve the accuracy of oil price realized volatility forecasting. We concentrate on realized volatilities derived from the intra-day prices of the Brent crude oil and four different asset classes (Stocks, Forex, Commodities and Macro), which represent the different “information channels” by which oil price volatility is impacted from. We employ a HAR framework and estimate forecasts for 1-day to 66-days ahead. Our findings provide strong evidence that the use of the different “information channels” enhances the predictive accuracy of oil price realized volatility at all forecasting horizons. Numerous forecasting evaluation tests and alternative model specifications confirm the robustness of our results.     

The information content of risk-neutral skewness for volatility forecasting

The paper investigates whether risk-neutral skewness has incremental explanatory power for future volatility in the S&P 500 index. While most of previous studies have investigated the usefulness of historical volatility and implied volatility for volatility forecasting, we study the information content of risk-neutral skewness in volatility forecasting model. In particular, we concentrate on Heterogeneous Autoregressive model of Realized Volatility and Implied Volatility (HAR-RV-IV). We find that risk-neutral skewness contains additional information for future volatility, relative to past realized volatilities and implied volatility. Out-of-sample analyses confirm that risk-neutral skewness improves significantly the accuracy of volatility forecasts for future volatility.     

An Empirical Comparison of Two Stochastic Volatility Models using Indian Market Data

We conduct an empirical comparison of hedging strategies for two different stochastic volatility models proposed in the literature. One is an asymptotic expansion approach and the other is the risk-minimizing approach applied to a Markov-switched geometric Brownian motion. We also compare these with the Black–Scholes delta hedging strategies using historical and implied volatilities. The derivatives we consider are European call options on the NIFTY index of the Indian National Stock Exchange. We compare a few cases with profit and loss data from a trading desk. We find that for the cases that we analyzed, by far the better results are obtained for the Markov-switched geometric Brownian motion.     

Neural network volatility forecasts

We analyse whether the use of neural networks can improve ‘traditional’ volatility forecasts from time-series models, as well as implied volatilities obtained from options on futures on the Spanish stock market index, the IBEX-35. One of our main contributions is to explore the predictive ability of neural networks that incorporate both implied volatility information and historical time-series information. Our results show that the general regression neural network forecasts improve the information content of implied volatilities and enhance the predictive ability of the models. Our analysis is also consistent with the results from prior research studies showing that implied volatility is an unbiased forecast of future volatility and that time-series models have lower explanatory power than implied volatility. Copyright © 2008 John Wiley & Sons, Ltd.     

The hedging effect of green bonds on carbon market risk

This paper explores effective hedging instruments for carbon market risk. Examining the relationship between the carbon futures returns and the returns of four major market indices, i.e., the VIX index, the commodity index, the energy index and the green bond index, we find that the connectedness between the carbon futures returns and the green bond index returns is the highest and this connectedness is extremely pronounced during the market's volatile period. Further, we develop and evaluate hedging strategies based on three dynamic hedge ratio models (DCC-APGARCH, DCC-T-GARCH, and DCC-GJR-GARCH models) and the constant hedge ratio model (OLS model). Empirical results show that among the four market indices the green bond index is the best hedge for carbon futures and performs well even in the crisis period. The paper also provides evidence that the dynamic hedge ratio models are superior to the OLS model in the volatile period as more sophisticated models can capture the dynamic correlation and volatility spillover between the carbon futures and market index returns.     

Options markets, self-fulfilling prophecies, and implied volatilities

This paper answers the following often asked question in option pricing theory: if the underlying asset's price does not satisfy a lognormal distribution, can market prices satisfy the Black-Scholes formula just because market participants believe it should? In complete markets, if the underlying asset's objective distribution is not lognormal, then the answer is no. But, in an incomplete market, if the underlying asset's objective distribution is not lognormal and all traders believe it is, then the answer is yes! The Black-Scholes formula can be a self-fulfilling prophecy. The proof of this second assertion consists of generating an economy where self-confirming beliefs sustain the Black-Scholes formula as an equilibrium. An asymmetric information model is provided, where the underlying asset's price has stochastic volatility and drift. This model is distinct from the existing pricing models in the literature, and it provides new empirical implications concerning Black-Scholes implied volatilities and the bid/ask spread. Similar to stochastic volatility models, this model is consistent with the implied volatility “smile” pattern in strike prices. In addition, it is consistent with implied volatilities being biased predictors of future volatilities.     

How important is the term structure in implied volatility surface modeling? Evidence from foreign exchange options

We claim that previously proposed parametric specifications that linearly approximate the term structure of the implied volatility surface (IVS) in option prices fail to capture important information regarding the expectations of market participants. This paper proposes a parametric specification for describing the IVS that allows flexible modeling of the term structure through a Nelson and Siegel (1987) factorization, recently proposed by Diebold and Li (2006) in the context of yield curve modeling. The specification is tested on implied volatilities from the over-the-counter foreign exchange options market, where contracts with long expiries are actively traded and thus the term structure dimension of the surface should be very important. We first show that the proposed volatility specification can consistently and remarkably improve our ability to describe the surface on any given day. We then establish the economic relevance of the incremental information captured by our proposed specification by showing that it can produce more accurate forecasts of implied volatility that can support long-term profitable trading strategies in the absence of transaction costs.     

Learning minimum variance discrete hedging directly from the market

Option hedging is a critical risk management problem in finance. In the Black–Scholes model, it has been recognized that computing a hedging position from the sensitivity of the calibrated model option value function is inadequate in minimizing variance of the option hedge risk, as it fails to capture the model parameter dependence on the underlying price (see e.g. Coleman et al., J. Risk, 2001, 5(6), 63–89; Hull and White, J. Bank. Finance, 2017, 82, 180–190). In this paper, we demonstrate that this issue can exist generally when determining hedging position from the sensitivity of the option function, either calibrated from a parametric model from current option prices or estimated nonparametricaly from historical option prices. Consequently, the sensitivity of the estimated model option function typically does not minimize variance of the hedge risk, even instantaneously. We propose a data-driven approach to directly learn a hedging function from the market data by minimizing variance of the local hedge risk. Using the S&P 500 index daily option data for more than a decade ending in August 2015, we show that the proposed method outperforms the parametric minimum variance hedging method proposed in Hull and White [J. Bank. Finance, 2017, 82, 180–190], as well as minimum variance hedging corrective techniques based on stochastic volatility or local volatility models. Furthermore, we show that the proposed approach achieves significant gain over the implied BS delta hedging for weekly and monthly hedging.