The implied volatility smirk

This paper provides an industry standard on how to quantify the shape of the implied volatility smirk in the equity index options market. Our local expansion method uses a second-order polynomial to describe the implied volatility–moneyness function and relates the coefficients of the polynomial to the properties of the implied risk-neutral distribution of the equity index return. We present a formal, two-way representation of the link between the level, slope and curvature of the implied volatility smirk and the risk-neutral standard deviation, skewness and excess kurtosis. We then propose a new semi-analytical method to calibrate option-pricing models based on the quantified implied volatility smirk, and investigate the applicability of two option-pricing models.     

How Spanish options market smiles in summer: an empirical analysis for options on IBEX-35

This paper examines the behaviour of the smile in the Spanish Stock Exchange during 2011 and 2012 summers. In these periods, the value of the main index of the Spanish Stock Exchange market IBEX-35 had fallen down a maximum of 2103.60 points in summer 2011, which made a drop of 20.05% in this period. On the contrary, in summer 2012, it had raised a maximum of 2165.70 points. That means a rise of 26.31%, whereas the Spanish risk premium had raised dramatically. By linear interpolation, implied volatilities for moneyness points needed were calculated. Then, we construct 3288 smile curves and the same quantity of distortion levels. Thousand six hundred and forty-four smiles are for both call and put option contracts, and for all summer 2011 and 2012 maturities (June, July, August and September). Next, we compare all smile curves with 1 of the 17-typical shape patterns for calls, puts, different dates, etc. Afterwards, we take the value of the distortion level calculated before and include the smile in one A–E class of distortion. We can notice that the most popular types are only two, for both calls and puts, Left Smirk (LK) rather than Reversed Right Smirk (RRK); all smiles are formed in the same way, and they are all from ‘D’ class. The changes between LK and RRK occur only on, or one day after, expiring dates, thus are jumps in distortion. Afterwards, we make a comparison with 2013 and 2014 summers' smiles which are not marred by the short-selling ban imposed by the Spanish Securities Exchange Commission in 2011 and 2012.     

Asymmetric information about volatility: How does it affect implied volatility,option prices and market liquidity?

This paper develops a model of asymmetric information in which an investor has information regarding the future volatility of the price process of an asset and trades an option on the asset. The model relates the level and curvature of the smile in implied volatilities as well as mispricing by the Black-Scholes model to net options order flows (to the market maker). It is found that an increase in net options order flows (to the market maker) increases the level of implied volatilities and results in greater mispricing by the Black-Scholes model, besides impacting the curvature of the smile. The liquidity of the option market is found to be decreasing in the amount of uncertainty about future volatility that is consistent with existing evidence. This revised version was published online in June 2006 with corrections to the Cover Date.     

The information content of option-implied information for volatility forecasting with investor sentiment

This study explores the effect of investor sentiment on the volatility forecasting power of option-implied information. We find that the risk-neutral skewness has the explanatory power regarding future volatility only during high sentiment periods. Furthermore, the implied volatility has varying volatility forecasting ability depending on the level of investor sentiment. Our findings suggest that the effectiveness of volatility forecasting models based on option-implied information varies over time with the level of investor sentiment. We confirm the important role of investor sentiment in volatility forecasting models exploiting option-implied information with strong evidence from in-sample and out-of-sample analyses. We also present improvements in the accuracy of volatility forecasts from volatility forecasting models derived by incorporating investor sentiment in these models.     

The information content of CDS implied volatility and associated trading strategies

Using the theoretical link between put options and credit default swaps (CDS) in a very general setting, we develop a robust measure of CDS implied volatility (CIV) that captures the information content of CDS markets. Specifically, we use the unit recovery claim to bridge CDS and deep out-of-the-money put options of the same firm and then back out CIV via the binomial tree. Our CIV measure strongly co-moves with the option implied volatility (OIV), with a correlation coefficient of 0.8. Based on the standardized difference between CIV and OIV, we construct CDS and option trading strategies. Without taking transaction costs into account, the long–short CDS trading strategy achieves an annualized return of 58.29% and a Sharpe ratio of 2.97, which cannot be explained by non-parametric skewness and volatility risk.     

The calm after the storm: implied volatility and future stock index returns

This article explores the predictive power of five implied volatility indices for subsequent returns on the corresponding underlying stock indices from January 2000 through October 2013. Contrary to previous research, very low volatility levels appear to be followed by significantly positive average returns over the next 20, 40 or 60 trading days. Rolling trading simulations show that positive adjusted excess returns can be achieved when long positions in the stock indices are taken on days of very low implied volatility. This may be a hint that market inefficiencies exist in some markets, especially outside the USA. The excess returns measured against a buy and hold benchmark are significant for the German and Japanese market when tested with a bootstrap methodology. The results are robust against a broad spectrum of specifications.     

Jump risk,stock returns,and slope of implied volatility smile

In the presence of jump risk, expected stock return is a function of the average jump size, which can be proxied by the slope of option implied volatility smile. This implies a negative predictive relation between the slope of implied volatility smile and stock return. For more than four thousand stocks ranked by slope during 1996–2005, the difference between the risk-adjusted average returns of the lowest and highest quintile portfolios is 1.9% per month. Although both the systematic and idiosyncratic components of slope are priced, the idiosyncratic component dominates the systematic component in explaining the return predictability of slope. The findings are robust after controlling for stock characteristics such as size, book-to-market, leverage, volatility, skewness, and volume. Furthermore, the results cannot be explained by alternative measures of steepness of implied volatility smile in previous studies.     

The relationship between implied and realized volatility: evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

FX volatility forecasts and the informational content of market data for volatility

The paper examines the medium-term forecasting ability of several alternative models of currency volatility. The data period covers more than eight years of daily observations, January 1991 to March 1999, for the spot exchange rate, 1- and 3-month volatility of the DEM/JPY, GBP/DEM, GBP/USD, USD/CHF, USD/DEM and USD/JPY. Comparing with the results of ‘pure’ time series models, the reported work investigates whether market implied volatility data can add value in terms of medium-term forecasting accuracy. This is done using data directly available from the marketplace in order to avoid the potential biases arising from ‘backing out’ volatility from a specific option pricing model. On the basis of the over 34 000 out-of-sample forecasts produced, evidence tends to indicate that, although no single volatility model emerges as an overall winner in terms of forecasting accuracy, the ‘mixed’ models incorporating market data for currency volatility perform best most of the time.     

An empirical comparison of continuous-time models of implied volatility indices

We explore the ability of alternative popular continuous-time diffusion and jump-diffusion processes to capture the dynamics of implied volatility indices over time. The performance of the various models is assessed under both econometric and financial metrics. To this end, data are employed from major European and American implied volatility indices and the rapidly growing CBOE volatility futures market. We find that the addition of jumps is necessary to capture the evolution of implied volatility indices under both metrics. Mean reversion is of second-order importance though. The results are consistent across the various metrics, markets, and construction methodologies.     

The information content of implied skewness and kurtosis changes prior to earnings announcements for stock and option returns

We use option prices to examine whether changes in stock return skewness and kurtosis preceding earnings announcements provide information about subsequent stock and option returns. We demonstrate that changes in jump risk premiums can lead to changes in implied skewness and kurtosis and are also associated with the mean and variability of the stock price response to the earnings announcement. We find that changes in both moments have strong predictive power for future stock returns, even after controlling for implied volatility. Additionally, changes in both moments predict call returns, while put return predictability is primarily linked to changes in skewness.     

Accounting quality,information risk and the term structure of implied volatility around earnings announcements

We examine the association between accounting quality, which is used as a proxy for firm information risk, and the behavior of the term structure of implied option volatility around earnings announcements. By employing a large sample of US firms having options traded on their equity during 1996–2010, we find that lower (higher) accounting quality is significantly associated with stronger (weaker) changes in the steepness of the term structure of implied volatility curve around quarterly earnings announcements. This finding (which is robust to controls for business-stemming uncertainty regarding future firm performance) is consistent with a stronger differential of short vs. long-term uncertainty for higher information risk firms, indicating greater uncertainty on the future economic performance of poorer vs. stronger accounting quality firms. We also establish the trading implications of these findings by demonstrating a (profitable in-sample) self-financed option trading strategy that is based on the quality of the accounting information released on earnings announcement days.     

The information content of implied volatilities and model-free volatility expectations: Evidence from options written on individual stocks

We measure the volatility information content of stock options for individual firms using option prices for 149 US firms and the S&P 100 index. We use ARCH and regression models to compare volatility forecasts defined by historical stock returns, at-the-money implied volatilities and model-free volatility expectations for every firm. For 1-day-ahead estimation, a historical ARCH model outperforms both of the volatility estimates extracted from option prices for 36% of the firms, but the option forecasts are nearly always more informative for those firms that have the more actively traded options. When the prediction horizon extends until the expiry date of the options, the option forecasts are more informative than the historical volatility for 85% of the firms. However, at-the-money implied volatilities generally outperform the model-free volatility expectations.     

Correlated implied volatility with jump and cross section of stock returns

I derive the option‐implied volatility allowing for nonzero correlation between price jump and diffusive risk to examine the information content of implied diffusive, jump risks and their implied covariance in the cross‐sectional variation of future returns. This study documents a strong predictive power of realized volatility and correlated implied volatility spread (RV ? IV_C) in the cross section of stock returns. The difference of realized volatility with the implied diffusive volatility (RV ? σ_C), jump risk (RV ? γ_C) and covariance (RV ? ICov) can forecast future returns. These RV ? σ_C and RV ? γ_C anomalies are robustly persistent even after controlling for market, size, book‐to‐market value, momentum and liquidity factors.     

The information content of the term structure of risk-neutral skewness

We seek to reconcile the debate about the price effect of risk-neutral skewness (RNS) on stocks. We document positive predictability from short-term skewness, consistent with informed-trading demand, and negative predictability from long-term skewness, consistent with skewness preference. A term spread on RNS captures different information from long- and short-term contracts, resulting in stronger predictability. The quintile portfolio with the lowest spread outperforms that with highest spread by 14.64% annually. The term structure of RNS predicts earnings surprises and price crashes. We extract the slope factor from RNS term structure, estimate its risk premium, and explore its relation with several macroeconomic variables.     

Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging

In this paper, we analyze properties of multinomial lattices that model general stochastic dynamics of the underlying stock by taking into account any given cumulants (or moments). First, we provide a parameterization of multinomial lattices, and demonstrate that mean, variance, skewness, and kurtosis of the underlying may be matched using five branches. Then, we investigate the convergence of the multinomial lattice when the basic time period approaches zero, and prove that the limiting process of the multinomial lattice that matches annualized mean, variance, skewness and kurtosis is given by a compound Poisson process. Finally, we illustrate the effect of higher order moments in the underlying asset process on the price of derivative securities through numerical experiments using the multinomial lattice, and provide a comparison with jump-diffusion models.     

The asymmetric relationship between returns and implied volatility: Evidence from global stock markets

We investigate the asymmetric relationship between returns and implied volatility for 20 developed and emerging international markets. In particular we examine how the sign and size of return innovations affect the expectations of daily changes in volatility. Our empirical findings indicate that the conditional contemporaneous return-volatility relationship varies not only based on the sign of the expected returns but also upon their magnitude, according to recent results from the behavioral finance literature. We find evidence of an asymmetric and reverse return-volatility relationship in many advanced, Asian, Latin-American, European and South African markets. We show that the US market displays the highest reaction to price falls, Asian markets present the lowest sensitivity to volatility expectations, while the Euro area is characterized by a homogeneous response both in terms of direction and impact. These results may be safely attributed to cultural and societal characteristics. An extensive quantile regression analysis demonstrates that the detected asymmetric pattern varies particularly across the extreme distribution tails i.e., in the highest/lowest quantile ranges. Indeed, the classical feedback and leverage hypotheses appear not plausible, whilst behavioral theories emerge as the new paradigm in real-world applications.     

投资者情绪、期权隐含信息与股市波动率预测——基于上证50ETF期权的经验研究

在异质自回归模型(HAR-RV)中引入中国上证50ETF期权隐含信息和投资者情绪,本文分别对中国股票市场未来日、周和月波动率进行预测。研究发现,期权隐含信息和投资者情绪能够提高HAR-RV模型对股票市场未来波动率的预测效果。投资者情绪对未来波动率的影响存在两种机制:在情绪高涨期间,月已实现波动率与未来波动率正相关,说明以个人投资者占主体所引起的价格信息机制,在中国股票市场交易中占主导作用;风险中性偏度与未来波动率负相关,说明以个人投资者占主体所引起的噪声交易机制占主导作用。