The information content in implied idiosyncratic volatility and the cross‐section of stock returns: Evidence from the option markets

Current literature is inconclusive as to whether idiosyncratic risk influences future stock returns and the direction of the impact. Earlier studies are based on historical realized volatility. Implied volatilities from option prices represent the market's assessment of future risk and are likely a superior measure to historical realized volatility. Implied idiosyncratic volatilities on firms with traded options are used to examine the relationship between idiosyncratic volatility and future returns. A strong positive link was found between implied idiosyncratic risk and future returns. After considering the impact of implied idiosyncratic volatility, historical realized idiosyncratic volatility is unimportant. This performance is strongly tied to small size and high book‐to‐market equity firms. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 1013–1039, 2008     

Smiling less at LIFFE

This study investigates the structure of the implied volatility smile, using the prices of equity options traded on the LIFFE. First, the slope of the implied volatility curve is significantly negative for both individual stocks and index options, and the slope is less negative for longer‐term options. The implied volatility skew can be described by risk‐neutral skewness and kurtosis, with the former having the first‐order effect. Moreover, the implied volatility skew for individual stock options is less severe than for index options. Finally, the relationship between the real and risk‐neutral moments implied in option prices is significant. The results indicate that, for equity options traded on the LIFFE, the slope of the implied volatility skew is flatter than that on the Chicago Board of Exchange (CBOE). © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:57–81, 2008     

Price discovery in the options markets: An application of put‐call parity

This study investigates the relative rate of price discovery in Taiwan between index futures and index options, proposing a put‐call parity (PCP) approach to recover the spot index embedded in the options premiums. The PCP approach offers the benefits of reducing model risk and alleviating the burden of volatility estimation. Consistent with the trading‐cost hypothesis, a dominant tendency is found for futures and a subordinate but non‐trivial price discovery from options. The relative weight of options price discovery is sensitive to the methodology employed as the means of inferring the option‐implicit spot price. The empirical evidence suggests that the information contained in the PCP‐implied spot encompasses that provided by the Black‐Scholes‐implied spot. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:354– 375, 2008     

The impact of liquidity on option prices

This study illustrates the impact of both spot and option liquidity levels on option prices. Using implied volatility to measure the option price structure, our empirical results reveal that even after controlling for the systematic risk of Duan and Wei ( 2009 ), a clear link remains between option prices and liquidity; with a reduction (increase) in spot (option) liquidity, there is a corresponding increase in the level of the implied volatility curve. The former is consistent with the explanation on hedging costs provided by Cetin, Jarrow, Protter, and Warachka ( 2006 ), whereas the latter is consistent with the “illiquidity premium” hypothesis of Amihud and Mendelson ( 1986a ). This study also shows that the slope of the implied volatility curve can be partially explained by option liquidity. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Option happiness and liquidity: Is the dynamics of the volatility smirk affected by relative option liquidity?

This study investigates the dynamic relationship between option happiness (the steepness of the volatility smirk) and relative index option liquidity. We find that, on a daily basis, option happiness is significantly dependent on the relative liquidity between option series with different moneyness. In particular, deterioration (improvement) in liquidity of an out‐of‐the‐money put option relative to a concurrent at‐the‐money call option would lead to higher (lower) option happiness. This relationship is robust to relative option liquidity measures based on bid–ask spreads, option price impacts, and option order book imbalances. The results also show a significant maturity effect in option happiness, consistent with the notion that options are “dying smiling.” © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Expiration‐day effects on individual stocks and the overall market: Evidence from Taiwan

On expiration days of the MSCI‐TW index futures, the Taiwan spot market is associated with abnormally large volume and high index volatility, along with mild index reversal. The effects concentrate only in the last five minutes of expiration days and appear to be strengthened by the adoption a call auction closing procedure by the Taiwan Stock Exchange. Individual index stocks show high volatility and strong tendency of price reversal, with large‐ and small‐cap stocks being affected more than the medium‐sized stocks. The highest‐weighted stocks exhibit excessive volume and volatility, which is disproportionate to the impact on all other index stocks, indicating that the expiration‐day effects may have been amplified by the attempt of price manipulation using large‐cap stocks. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:920–945, 2009     

Empirical performance of alternative pricing models of currency options

This article examines the out‐of‐sample pricing performance and biases of the Heston’s stochastic volatility and modified Black‐Scholes option pricing models in valuing European currency call options written on British pound. The modified Black‐Scholes model with daily‐revised implied volatilities performs as well as the stochastic volatility model in the aggregate sample. Both models provide close and similar correspondence to actual prices for options trading near‐ or at‐the‐money. The prices generated from the stochastic volatility model are subject to fewer and weaker aggregate pricing biases than are the prices from the modified Black‐Scholes model. Thus, the stochastic volatility model may provide improved estimates of the measures of option price sensitivities to key option parameters that may lead to more effective hedging and speculative strategies using currency options. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:265–291, 2000     

A NEW LOOK AT SHORT‐TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS

We analyze the behavior of the implied volatility smile for options close to expiry in the exponential Lévy class of asset price models with jumps. We introduce a new renormalization of the strike variable with the property that the implied volatility converges to a nonconstant limiting shape, which is a function of both the diffusion component of the process and the jump activity (Blumenthal–Getoor) index of the jump component. Our limiting implied volatility formula relates the jump activity of the underlying asset price process to the short‐end of the implied volatility surface and sheds new light on the difference between finite and infinite variation jumps from the viewpoint of option prices: in the latter, the wings of the limiting smile are determined by the jump activity indices of the positive and negative jumps, whereas in the former, the wings have a constant model‐independent slope. This result gives a theoretical justification for the preference of the infinite variation Lévy models over the finite variation ones in the calibration based on short‐maturity option prices.     

Who knows more about future currency volatility?

We use four currency pairs from October 1, 2001 to September 29, 2006 to compare the predictive power of the implied volatility derived from currency option prices that are traded on the Philadelphia Stock Exchange (PHLX), Chicago Mercantile Exchange (CME), and over‐the‐counter market (OTC). Among the competing implied volatility forecasts, OTC‐implied volatility subsumes the information content of PHLX‐ and CME‐implied volatility. Consistent with extant studies our result also shows that the implied volatility provides more information about future volatility–regardless of whether it is from the OTC, PHLX, or CME markets–than time series based volatility. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:270–295, 2009     

Options on bond futures: Isolating the risk premium

The introduction of unspanned sources of risk (and frictions) implies that option prices include a risk premium. Prima facie evidence of the existence of risk premia in option prices is contained in the implied volatility smile patterns reported in the literature. This article isolates the risk premium (defined as the simple difference between estimated and observed option prices) on options on U.K. Gilts, German Bunds, and U.S. Treasury bond futures using models that include price jumps and stochastic volatility. This study finds that single and multi‐factor stochastic volatility models with jumps may explain the empirical regularities observed in bond futures. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:169–215, 2003     

A non‐lattice pricing model of American options under stochastic volatility

In this article, an analytical approach to American option pricing under stochastic volatility is provided. Under stochastic volatility, the American option value can be computed as the sum of a corresponding European option price and an early exercise premium. By considering the analytical property of the optimal exercise boundary, the formula allows for recursive computation of the American option value. Simulation results show that a nonlattice method performs better than the lattice‐based interpolation methods. The stochastic volatility model is also empirically tested using S&P 500 futures options intraday transactions data. Incorporating stochastic volatility is shown to improve pricing, hedging, and profitability in actual trading. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:417–448, 2006     

Black‐Scholes‐Merton revisited under stochastic dividend yields

European options are priced in a framework à la Black‐Scholes‐Merton, which is extended to incorporate stochastic dividend yield under a stochastic mean–reverting market price of risk. Explicit formulas are obtained for call and put prices and their Greek parameters. Some well‐known properties of the Black‐Scholes‐Merton formula fail to hold in this setting. For example, the delta of the call can be negative and even greater than one in absolute terms. Moreover, call prices can be a decreasing function of the underlying volatility although the latter is constant. Finally, and most importantly, option prices highly depend on the features of the market price of risk, which does not need to be specified at all in the standard Black‐Scholes‐Merton setting. The results are simulated in order to assess the economic impact of assuming that the dividend yield is deterministic when it is actually stochastic, as well as to assess the economic importance of the features of the market price of risk. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:703–732, 2006     

Show me the money: Option moneyness concentration and future stock returns

Informed traders often use options that are not in-the-money due to higher potential gains for a smaller upfront cost. Thus, trading activity by option moneyness should be a gauge of informed option trading. We construct a dollar volume-weighted average moneyness measure to capture option trading activity at different moneyness levels. Stock returns increase with this measure, suggesting more trading activity in options with higher leverage predicts future stock returns. Our results hold cross-sectionally and at the portfolio level yielding a Fama–French five-factor α of 12% per year for all stocks and 33% per year for high implied volatility stocks.     

Complete Models with Stochastic Volatility

The paper proposes an original class of models for the continuous-time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log-price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference-independent options prices.
We find a partial differential equation for the price of a European call option. Smiles and skews are found in the resulting plots of implied volatility.     

The interrelation of price volatility and trading volume of currency options

This article examines the interrelations between future volatility of the U.S. dollar/British pound exchange rate and trading volume of currency options for the British pound. The future volatility of the exchange rate is approximated alternatively by implied volatility and by IGARCH volatility. The results suggest the presence of strong contemporaneous positive feedbacks between the exchange rate volatility and the trading volume of call and put options. Previous option volumes have significant predictive power with respect to the expected future volatility of the dollar/pound exchange rate. Similarly, lagged volatilities jointly have significant predictive power for option volume. Although option volume (volatility) responds somewhat differently to individual volatility (volume) terms under the two volatility measures, the overall volume‐volatility relations are broadly similar between the implied and IGARCH volatilities. The results generally support the hypothesis that the information‐based trading explains more of the trading volume in currency options on the U.S. dollar/British pound exchange rate than hedging. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:681–700, 2003     

What moves the tail? The determinants of the option‐implied probability density function of the DAX index

In this article a study of the option‐implied probability density function (PDF) of German stock returns is presented. The use of option prices allows for the quantification of the risk‐neutral probability of large movements in the DAX index. Using daily data for the period from December 1995 to May 2002, the mixture of log‐normals specification with a constant maturity of 49 days is estimated. The time series behavior of the option‐implied PDF during episodes of market turbulence is discussed at the outset. The main purpose of the study is to consider the relationship of summary measures of the option‐implied PDF to macroeconomic news, information from the U.S. stock market, and risk premia. The results suggest the existence of a significant spillover from the U.S. stock market. Returns and the volatility of U.S. stock prices have a strong effect on changes in the lower DAX tail probability, but also on the higher moments of the option‐implied PDF. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:515–536, 2005     

Why Doesn't the Black‐‐Scholes Model Fit Japanese Warrants and Convertible Bonds?

In this paper, we investigate the systematic departures of traded prices of Japanese equity warrants and convertible bonds from their theoretical Black–Scholes values. We briefly consider transactions costs and the dilution adjustment as potential explanations of the discrepancy. However, our major focus is on shifts in volatility of the prices of the underlying stocks as a function of the stock price changes; such shifts are not taken into account in the Black–Scholes values. We assume that the pseudo‐probability distributions of prices of stocks of cross‐sections of companies which are roughly similar in size are identical. This simple assumption, which can be generalized, enables us to infer the implied probability distribution and binomial tree for stock price changes using the Derman and Kani (1994), Rubinstein (1994) and Shimko (1993) approach. The cross‐section of warrant prices implies an inverse volatility smile and a positively skewed probability density for stock prices. Rubinstein's identifying assumptions generate an implied binomial tree in which the relative size of up‐steps and down‐steps, and thus volatility, changes systematically as stock prices change. We briefly consider potential explanations for the implied behaviour, and for the difference in the smile pattern between index options and the warrants and convertibles.     

Option pricing under fast‐varying long‐memory stochastic volatility

Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long‐range correlation properties in order to capture such a situation, and we consider European option pricing. This means that the volatility process is neither a Markov process nor a martingale. However, by exploiting the fact that the price process is still a semimartingale and accordingly using the martingale method, we can obtain an analytical expression for the option price in the regime where the volatility process is fast mean reverting. The volatility process is modeled as a smooth and bounded function of a fractional Ornstein–Uhlenbeck process. We give the expression for the implied volatility, which has a fractional term structure.     

Stock return dynamics,option volume,and the information content of implied volatility

This article reports new empirical results on the information content of implied volatility, with respect to modeling and forecasting the volatility of individual firm returns. The 50 firms with the highest option volume on the Chicago Board Options Exchange between 1988 and 1995 are examined. First, the results indicate that the ability of implied volatility to subsume all relevant information about conditional variance depends on option trading volume. For the most active options in the sample, implied volatility reliably outperforms GARCH and subsumes all information in return shocks beyond the first lag. For these active options, implied volatility performs substantially better than indicated by the prior results of Lamoureux and Lastrapes ( 1993 ), despite significant methodological improvements in the time‐series volatility models in this study including the use of high‐frequency intraday return shocks. For the lower option‐volume firms in the sample, the performance of implied volatility deteriorates relative to time‐series volatility models. Finally, compared to a time‐series approach, the implied volatility of equity index options provides reliable incremental information about future firm‐level volatility. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:615–646, 2003     

An explicitly solvable multi‐scale stochastic volatility model: Option pricing and calibration problems

We introduce an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model. The model describes the dynamics of an asset price and of its two stochastic variances using a system of three Ito stochastic differential equations. The two stochastic variances vary on two distinct time scales and can be regarded as auxiliary variables introduced to model the dynamics of the asset price. Under some assumptions, the transition probability density function of the stochastic process solution of the model is represented as a one‐dimensional integral of an explicitly known integrand. In this sense the model is explicitly solvable. We consider the risk‐neutral measure associated with the proposed multiscale stochastic volatility model and derive formulae to price European vanilla options (call and put) in the multiscale stochastic volatility model considered. We use the thus‐obtained option price formulae to study the calibration problem, that is to study the values of the model parameters, the correlation coefficients of the Wiener processes defining the model, and the initial stochastic variances implied by the “observed” option prices using both synthetic and real data. In the analysis of real data, we use the S&P 500 index and to the prices of the corresponding options in the year 2005. The web site http://www.econ.univpm.it/recchioni/finance/w7 contains some auxiliary material including some animations that helps the understanding of this article. A more general reference to the work of the authors and their coauthors in mathematical finance is the web site http://www.econ.univpm.it/recchioni/finance . © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:862–893, 2009