Disagreement and equilibrium option trading volume

Using a complete market equilibrium model, we present results concerning the effect disagreement has on equilibrium option trading volume and positioning. We find that if agents agree on volatility, total option volume is independent of wealth distribution and average optimism. We also find option volume increasing in drift disagreement and decreasing in risk aversion and volatility. Pessimists are shown to write most options. With volatility disagreement, the results are less clear; however, we show agents with high volatility beliefs write deep out of the money options and buy close to the money options. Numerical comparative statics are also performed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.     

The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets

In this paper we examine the extent of the bias between Black and Scholes (1973)/Black (1976) implied volatility and realized term volatility in the equity and energy markets. Explicitly modeling a market price of volatility risk, we extend previous work by demonstrating that Black-Scholes is an upward-biased predictor of future realized volatility in S&P 500/S&P 100 stock-market indices. Turning to the Black options-on-futures formula, we apply our methodology to options on energy contracts, a market in which crises are characterized by a positive correlation between price-returns and volatilities: After controlling for both term-structure and seasonality effects, our theoretical and empirical findings suggest a similar upward bias in the volatility implied in energy options contracts. We show the bias in both Black-Scholes/Black implied volatilities to be related to a negative market price of volatility risk. JEL Classification G12 · G13     

Short‐Term Market Risks Implied by Weekly Options

We study short‐maturity (“weekly”) S&P 500 index options, which provide a direct way to analyze volatility and jump risks. Unlike longer‐dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment. Adopting a novel seminonparametric approach, we uncover variation in the negative jump tail risk, which is not spanned by market volatility and helps predict future equity returns. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events that are not always “signaled” by the level of market volatility and elude standard asset pricing models.     

Dynamic volatility spillovers and investment strategies between the Chinese stock market and commodity markets

Building on the increased interest in the volatility spillover effects between Chinese stock market and commodity markets, this paper investigates the dynamic volatility spillovers of Chinese stock market and Chinese commodity markets based on the volatility spillover index under the framework of TVP-VAR. The result shows that there is a highly dependent relationship between the stock market and commodity markets. On average, the Chinese stock market is the net recipient of spillover, non-ferrous metals and chemical industry have a very obvious spillover impact on the stock market. The degree of total volatility spillover is different in different periods. After major crisis events, the volatility correlation between markets increases. Since the outbreak of COVID-19, the spillover effect of the stock market on the commodity market has been significantly enhanced. Then optimal portfolio weights and hedge ratios are calculated for portfolio diversification and risk management. The result shows that the ability of most commodities to hedge against risks is significantly reduced when the crisis occurs; NMFI (precious metals) and CRFI (grain) still have good hedging ability after the crisis, but the effectiveness of hedging risk is relatively low. Besides, the combination of CRFI and SHCI (the Shanghai composite index) is the most effective for risk reduction.     

Disagreement and asset prices

How do differences of opinion affect asset prices? Do investors earn a risk premium when disagreement arises in the market? Despite their fundamental importance, these questions are among the most controversial issues in finance. In this paper, we use a novel data set that allows us to directly measure the level of disagreement among Wall Street mortgage dealers about prepayment speeds. We examine how disagreement evolves over time and study its effects on expected returns, return volatility, and trading volume in the mortgage-backed security market. We find that increased disagreement is associated with higher expected returns, higher return volatility, and larger trading volume. These results imply that there is a positive risk premium for disagreement in asset prices. We also show that volatility in and of itself does not lead to higher trading volume. Instead, only when disagreement arises in the market is higher uncertainty associated with more trading. Finally, we are able to distinguish empirically between two competing hypotheses regarding how information in markets gets incorporated into asset prices. We find that sophisticated investors appear to update their beliefs through a rational expectations mechanism when disagreement arises.     

On the systematic volatility of unpriced earnings

Some important puzzles in macro finance can be resolved in a model featuring systematically varying volatility of unpriced shocks to firms? earnings. In the data, the correlation between corporate debt and stock market valuations is low. The model accounts for this via the opposing effect of unpriced earnings risk on levered debt and equity prices. The model also explains the low (or nonexistent) risk-reward relation for the market portfolio of levered equity via the opposing effects of unpriced and priced uncertainty (both components of stock volatility) on the levered equity risk premium. Versions of the model calibrated to empirical measures of both types of fundamental risk can quantitatively substantiate these explanations. Variation in residual earning dispersion accounts for a significant fraction of observed disagreement between debt and equity valuations and of realized stock volatility. The implication that the two components of risk should forecast the levered equity risk premium with opposite signs is also supported in the data. The results are a notable advance for risk-based asset pricing.     

S&P 100 Index Option Volatility

Using transaction data on the S&P 100 index options, we study the effect of valuation simplifications that are commonplace in previous research on the timeseries properties of implied market volatility. Using an American-style algorithm that accounts for the discrete nature of the dividends on the S&P 100 index, we find that spurious negative serial correlation in implied volatility changes is induced by nonsimultaneously observing the option price and the index level. Negative serial correlation is also induced by a bid/ask price effect if a single option is used to estimate implied volatility. In addition, we find that these same effects induce spurious (and unreasonable) negative cross-correlations between the changes in call and put implied volatility.     

Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?

This paper examines the relation between net buying pressure and the shape of the implied volatility function (IVF) for index and individual stock options. We find that changes in implied volatility are directly related to net buying pressure from public order flow. We also find that changes in implied volatility of S&P 500 options are most strongly affected by buying pressure for index puts, while changes in implied volatility of stock options are dominated by call option demand. Simulated delta‐neutral option‐writing trading strategies generate abnormal returns that match the deviations of the IVFs above realized historical return volatilities.     

Can we forecast the implied volatility surface dynamics of equity options? Predictability and economic value tests

We examine whether the dynamics of the implied volatility surface of individual equity options contains exploitable predictability patterns. Predictability in implied volatilities is expected due to the learning behavior of agents in option markets. In particular, we explore the possibility that the dynamics of the implied volatility surface of individual stocks may be associated with movements in the volatility surface of S&P 500 index options. We present evidence of strong predictable features in the cross-section of equity options and of dynamic linkages between the volatility surfaces of equity and S&P 500 index options. Moreover, time-variation in stock option volatility surfaces is best predicted by incorporating information from the dynamics in the surface of S&P 500 options. We analyze the economic value of such dynamic patterns using strategies that trade straddle and delta-hedged portfolios, and find that before transaction costs such strategies produce abnormal risk-adjusted returns.     

The intraday behaviors and relationships with its underlying assets: evidence on option market in Taiwan

In this paper, we use daily data to investigate the information asymmetric effects and the relationships between the trading volume of options and their underlying spot trading volume. Our results reveal that options with higher liquidity are near-the-money and expiration periods with 2 to 4 weeks have higher trading activity. We classify them into two parts with the ARIMA model: the expected trading activity impact and the unexpected trading activity impact. Using the bivariate generalized autoregressive conditional heteroscedasticity (GARCH) model, we investigate the trading activity effect and information asymmetric effect. In conclusion, the trading volume volatility of the spot and options markets move together, and a greater expected and unexpected trading volume volatility of the spot (options) market is associated with greater volatility in the options (spot) market. However, both markets generate higher trading volume volatility when people expect such an impact rather than when they do not. We also find that there are feedback effects within these two markets. Furthermore, when the spot (options) market has negative innovations, it generates a greater impact on the options (spot) market than do positive innovations. Finally, the conditional correlation coefficient between the spot and the option markets changes over time based on the bivariate GARCH model.     

The Informational Role of Option Trading Volume in Equity Index Options Markets

This paper examines the dynamic relations between future price volatility of the S&P 500 index and trading volume of S&P 500 options to explore the informational role of option volume in predicting the price volatility. The future volatility of the index is approximated alternatively by implied volatility and by EGARCH volatility. Using a simultaneous equation model to capture the volume-volatility relations, the paper finds that strong contemporaneous feedbacks exist between the future price volatility and the trading volume of call and put options. Previous option volumes have a strong predictive ability with respect to the future price volatility. Similarly, lagged changes in volatility have a significant predictive power for option volume. Although the volume-volatility relations for individual volatility and volume terms are somewhat different under the two volatility measures, the results on the predictive ability of volume (volatility) for volatility (volume) are broadly similar between the implied and EGARCH volatilities. These findings support the hypothesis that both the information- and hedge-related trading explain most of the trading volume of equity index options.     

Does vega-neutral options trading contain information?

This study suggests a novel approach for decomposing net options demands into the options order imbalances with and without volatility risk. By analyzing a high-frequency index futures and options dataset, we examine the information content of (i) the direction-motivated order imbalance induced by a single option type, which is exposed to volatility risk, and (ii) that constructed by both calls and puts, which is vega-neutral. The aggregate options order imbalance does not convey information after controlling for futures market trading. However, the intraday options order imbalance by trading without volatility risk significantly predicts spot index returns, though its longer-horizon forecasting ability is relatively weak because of a possible cross-market hedging effect. The predictive abilities of informed foreigners’ trades and out-of-the-money options trading are prominent. Our empirical results suggest that the vega-neutral options trading conveys additional information distinct from the futures order imbalance.     

波动溢出网络视角的金融风险传染研究

当前各类经济风险交叉关联,金融系统的风险溢出效应备受关注,为刻画我国金融系统性风险传染的路径特征,本文从波动溢出网络的视角分析金融系统内部的风险传染机制。首先使用广义动态因子模型对收益波动的共同波动率成分和特质性波动率成分进行区分。然后,根据货币市场、资本市场、大宗商品交易市场、外汇市场、房地产市场和黄金市场之间的特质性波动溢出效应,利用基于TVP-VAR模型的方差分解溢出指数分析金融系统波动溢出的动态联动性和风险传递机制。在分析方向性波动溢出效应的基础上,采用方差分解网络方法构建起信息溢出复杂网络,从网络视角分析金融系统内部的风险传染特征。实证研究发现,房地产市场和外汇市场的净溢出效应绝对值相较于其他市场更大,其受其他市场风险冲击的影响强于对外风险溢出效应,而股票市场的单向对外风险溢出效应强度最大。在波动溢出的基础上,进一步考虑股市波动率指数与其他市场波动率指数进行投资组合的资产配置权重,计算了波动率指数投资组合的最优组合权重和对冲策略。研究结论有助于更好地理解我国金融系统的风险传染机制,对监管机构加强宏观审慎监管、投资者规避投资风险具有重要意义。     

Delta-Hedged Gains and the Negative Market Volatility Risk Premium

We investigate whether the volatility risk premium is negativeby examining the statistical properties of delta-hedged optionportfolios (buy the option and hedge with stock). Within a stochasticvolatility framework, we demonstrate a correspondence betweenthe sign and magnitude of the volatility risk premium and themean delta-hedged portfolio returns. Using a sample of S&P500 index options, we provide empirical tests that have thefollowing general results. First, the delta-hedged strategyunderperforms zero. Second, the documented underperformanceis less for options away from the money. Third, the underperformanceis greater at times of higher volatility. Fourth, the volatilityrisk premium significantly affects delta-hedged gains, evenafter accounting for jump fears. Our evidence is supportiveof a negative market volatility risk premium.     

Inflation breakeven in the Jarrow and Yildirim model and resulting pricing formulas

The Jarrow and Yildirim model for pricing inflation-indexed derivatives is still the main reference technique adopted in the inflation market. Despite its popularity it has some shortcomings, the most immediate of which is the difficulty of calibrating to market prices of options due to the large number of parameters involved. Since the market trades options on the inflation rate or index, we reformulate their model in terms of the notion of breakeven inflation. The first main advantage is the possibility of describing the prices of the most popular inflation derivatives as functions of just three parameters: breakeven volatility, the volatility of the CPI price index and the correlation between them. Secondly, the resulting Black–Scholes-implied volatilities are very straightforward to implement and the geometric interpretation of the model makes it intuitive to calibrate. Lastly, the model permits us to reproduce a realistic picture of the current state of the art of the derivatives market and, in particular, due to its simplicity, it is able to estimate the risk premium priced by the inflation market.     

New evidence on the implied-realized volatility relation

We consider the relation between the volatility implied in an option's price and the subsequently realized volatility. Earlier studies on stock index options have found biases and inefficiencies in implied volatility as a forecast of future volatility. More recently, Christensen and Prabhala find that implied volatility in at-the-money one-month OEX call options on the S&P 100 index in fact is an unbiased and efficient forecast of ex-post realized index volatility after the 1987 stock market crash. In this paper, the robustness of the unbiasedness and efficiency result is extended to a more recent period covering April 1993 to February 1997. As a new contribution, implied volatility is constructed as a trade weighted average of implied volatilities from both in-the-money and out-of-the-money options and both puts and calls. We run a horse race between implied call, implied put, and historical return volatility. Several robustness checks, including a new simultaneous equation approach, underscore our conclusion, that implied volatility is an efficient forecast of realized return volatility.     

Smile and default: the role of stochastic volatility and interest rates in counterparty credit risk

In this research, we investigate the impact of stochastic volatility and interest rates on counterparty credit risk (CCR) for FX derivatives. To achieve this we analyse two real-life cases in which the market conditions are different, namely during the 2008 credit crisis where risks are high and a period after the crisis in 2014, where volatility levels are low. The Heston model is extended by adding two Hull–White components which are calibrated to fit the EURUSD volatility surfaces. We then present future exposure profiles and credit value adjustments (CVAs) for plain vanilla cross-currency swaps (CCYS), barrier and American options and compare the different results when Heston-Hull–White-Hull–White or Black–Scholes dynamics are assumed. It is observed that the stochastic volatility has a significant impact on all the derivatives. For CCYS, some of the impact can be reduced by allowing for time-dependent variance. We further confirmed that Barrier options exposure and CVA is highly sensitive to volatility dynamics and that American options’ risk dynamics are significantly affected by the uncertainty in the interest rates.     

Generic pricing of FX,inflation and stock options under stochastic interest rates and stochastic volatility

We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/inflation/stock index with both stochastic volatility and stochastic interest rates yields a realistic model that is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed form under Schöbel and Zhu [Eur. Finance Rev., 1999, 4, 23–46] stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston [Rev. Financial Stud., 1993, 6, 327–343] model. Finally, we investigate the quality of this approximation numerically and consider a calibration example to FX and inflation market data.     

Market Reform and Efficiency: The Case of KOSPI200 Options

The Korean government and exchange have identified a need to regulate excessive speculative trading and to protect domestic individual investors from foreign and professional traders. As such, they have proposed an options market reform that requires higher levels of margin accounts for options trading and that increases the basic options multipliers in the KOSPI200 options market. This study examines how this market reform affects the price disagreement and adjustment behaviors of the index options market. Our analyses indicate that the efficiency and information quality of out-of-the-money options trades have increased since the reform took effect.