Mean-reversion properties of implied volatilities

In this paper, we present a new stylized fact for options whose underlying asset is a stock index. Extracting implied volatility time series from call and put options on the Deutscher Aktien index (DAX) and financial times stock exchange index (FTSE), we show that the persistence of these volatilities depends on the moneyness of the options used for its computation. Using a functional autoregressive model, we show that this effect is statistically significant. Surprisingly, we show that the diffusion-based stochastic volatility models are not consistent with this stylized fact. Finally, we argue that adding jumps to a diffusion-based volatility model help recovering this volatility pattern. This suggests that the persistence of implied volatilities can be related to the tails of the underlying volatility process: this corroborates the intuition that the liquidity of the options across moneynesses introduces an additional risk factor to the one usually considered.     

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 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     

Implied Volatility of Interest Rate Options: An Empirical Investigation of the Market Model

We analyze the empirical properties of the volatilityimplied in options on the 13-week US Treasury bill rate. These options havenot been studied previously. It is shown that a European style put optionon the interest rate is equivalent to a call option on a zero-coupon bond.We apply the LIBOR market model and conduct a battery of validity tests tocompare three different volatility specifications: contact, affine, and exponentialvolatility. It appears that the additional parameter in the affine and theexponential volatility function is not justified. Overall, the LIBOR marketmodel fares well in describing these options.     

Asymmetric Volatility and Trading Activity in Index Futures Options

We examine the impact of option trading activity on implied volatility changes to returns in the index futures option market. Controlling for option moneyness, delta‐to‐option‐premium ratio, and liquidity, we find that net buying pressure, profit‐maximization behavior, and liquidity are interrelated and affect asymmetric responses of implied volatilities to returns. Implied volatilities of options with more liquidity, a higher exercise price, and a higher delta‐to‐option‐premium ratio have the most profound asymmetric response.     

A Non-Parametric Option Pricing Model: Theory and Empirical Evidence

In this paper, we propose an empirically-based, non-parametric option pricing model to evaluate S&P 500 index options. Given the fact that the model is derived under the real measure, an equilibrium asset pricing model, instead of no-arbitrage, must be assumed. Using the histogram of past S&P 500 index returns, we find that most of the volatility smile documented in the literature disappears.     

Forecasting implied volatility in foreign exchange markets: a functional time series approach

We utilise novel functional time series (FTS) techniques to characterise and forecast implied volatility in foreign exchange markets. In particular, we examine the daily implied volatility curves of FX options, namely; Euro/United States Dollar, Euro/British Pound, and Euro/Japanese Yen. The FTS model is shown to produce both realistic and plausible implied volatility shapes that closely match empirical data during the volatile 2006–2013 period. Furthermore, the FTS model significantly outperforms implied volatility forecasts produced by traditionally employed parametric models. The evaluation is performed under both in-sample and out-of-sample testing frameworks with our findings shown to be robust across various currencies, moneyness segments, contract maturities, forecasting horizons, and out-of-sample window lengths. The economic significance of the results is highlighted through the implementation of a simple trading strategy.     

The relation between implied and realised volatility in the Danish option and equity markets

We show that the conclusions to be drawn concerning the informational efficiency of illiquid options markets depend critically on whether one carefully recognises and appropriately deals with the econometrics of the errors‐in‐variables problem. This paper examines the information content of options on the Danish KFX share index. We consider the relation between the volatility implied in an option's price and the subsequently realised index return volatility. Since these options are traded infrequently and in low volumes, the errors‐in‐variables problem is potentially large. We address the problem directly using instrumental variables techniques. We find that when measurement errors are controlled for, call option prices even in this very illiquid market contain information about future realised volatility over and above the information contained in historical volatility.     

Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data

This paper empirically examines the performance of Black-Scholes and Garch-M call option pricing models using call options data for British Pounds, Swiss Francs and Japanese Yen. The daily exchange rates exhibit an overwhelming presence of volatility clustering, suggesting that a richer model with ARCH/GARCH effects might have a better fit with actual prices. We perform dominant tests and calculate average percent mean squared errors of model prices. Our findings indicate that the Black-Scholes model outperforms the GARCH models. An implication of this result is that participants in the currency call options market do not seem to price volatility clusters in the underlying process.     

Determining the implied volatility for American options using the QAM

This paper describes an efficient numerical procedure which may be used to determine implied volatilities for American options using the quadratic approximation method. Simulation results are presented. The procedure usually converges in five or six iterations with extreme accuracy under a wide variety of option market conditions. A comparison of American implied volatilities with European model implied volatilities indicates that significant differences may arise. This suggests that reliance on European model volatilities estimates may lead to significant pricing errors.     

Option implied volatilities and the cost of issuing equity

The structure of a firm-commitment Seasoned Equity Offering (SEO) resembles a put-option underwritten by an investment bank syndicate (Smith, 1977). Employing implied volatilities from issuers’ stock options as a direct forward-looking measure, this paper examines the impact of expected price risk around SEO issue dates on the direct cost of issuing equity. Using a comprehensive sample of 1208 SEOs between 1996 and 2009, we find issuers with higher option implied volatilities raise less external equity capital and pay higher investment bank fees in the stock market, ceteris paribus. The effect of implied volatility on the investment bank fees is stronger for larger issuers with lower pre-SEO abnormal realized stock volatilities, and for SEOs with higher expected price pressures around issue dates. These relationships are robust to adjustments for correlations among control variables, sample selection bias and also simultaneous determination of offer size and SEO fees.     

Modelling the Implied Volatility of Options on Long Gilt Futures

This paper investigates the properties of implied volatility series calculated from options on Treasury bond futures, traded on LIFFE. We demonstrate that the use of near-maturity at the money options to calculate implied volatilities causes less mis-pricing and is therefore superior to, a weighted average measure encompassing all relevant options. We demonstrate that, whilst a set of macroeconomic variables has some predictive power for implied volatilities, we are not able to earn excess returns by trading on the basis of these predictions once we allow for typical investor transactions costs.     

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.

Option pricing with random volatilities in complete markets

This article presents the theory of option pricing with random volatilities in complete markets. As such, it makes two contributions. First, the newly developed martingale measure technique is used to synthesize results dating from Merton (1973) through Eisenberg, (1985, 1987). This synthesis illustrates how Merton's formula, the CEV formula, and the Black-Scholes formula are special cases of the random volatility model derived herein. The impossibility of obtaining a self-financing trading strategy to duplicate an option in incomplete markets is demonstrated. This omission is important because option pricing models are often used for risk management, which requires the construction of synthetic options.Second, we derive a new formula, which is easy to interpret and easy to program, for pricing options given a random volatility. This formula (for a European call option) is seen to be a weighted average of Black-Scholes values, and is consistent with recent empirical studies finding evidence of mean-reversion in volatilities.Helpful comments from an anonymous referee are greatly appreciated.     

Stock Price Distributions and News: Evidence from Index Options

We estimate the shape of the distribution of stock prices using data from options on the underlying asset, and test whether this distribution is distorted in a systematic manner each time a particular news event occurs. In particular we look at the response of the FTSE100 index to market wide announcements of key macroeconomic indicators and policy variables. We show that the whole distribution of stock prices can be distorted on an event day. The shift in distributional shape happens whether the event is characterized as an announcement occurrence or as a measured surprise. We find that larger surprises have proportionately greater impact, and that higher moments are more sensitive to events however characterised.     

The information content of implied volatility, skewness and kurtosis: empirical evidence from long-term CAC 40 options

Implied standard deviation is widely believed to be the best available forecast of the volatility of returns over the remaining contract life (Jorion, 1995 ). In this paper, we take this result two steps further to the higher moments of the distribution (skewness and kurtosis) based on a Gram–Charlier series expansion of the normal distribution (Corrado and Su, 1996 ) using long-term CAC 40 option prices contract, named PXL. First, we found that implied first moments contain a substantial amount of information for future moments of CAC 40 returns although this amount decreases with respect to the moment's order. Secondly, we found that the different shapes of the volatility smile are consistent with different distribution of the underlying returns. Based on these results, we also observed that including other implied moments significantly improves the out-of-sample pricing performance of the Black–Scholes, (1973) model.     

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.     

A semiparametric factor model for implied volatility surface dynamics

We propose a semiparametric factor model, which approximatesthe implied volatility surface (IVS) in a finite dimensionalfunction space. Unlike standard principal component approachestypically used to reduce complexity, our approach is tailoredto the degenerated design of IVS data. In particular, we onlyfit in the local neighborhood of the design points by exploitingthe expiry effect present in option data. Using DAX index optiondata, we estimate the nonparametric components and a low-dimensionaltime series of latent factors. The modeling approach is completedby studying vector autoregressive models fitted to the latentfactors.     

Expectations Hypothesis of the Term Structure of Implied Volatility: Evidence from Foreign Currency and Stock Index Options

Using a stochastic volatility option pricing model, we showthat the implied volatilities of at-the-money options are notnecessarily unbiased and that the fixed interval time-seriescan produce misleading results. Our results do not support theexpectations hypothesis: long-term volatilities rise relativeto short-term volatilities, but the increases are not matchedas predicted by the expectations hypothesis. In addition, anincrease in the current long-term volatility relative to thecurrent short-term volatility is followed by a subsequent decline.The results are similar for both foreign currency and the S&P500 stock index options.