The measurement of option mispricing

Different studies have examined the ability of the Black-Scholes option pricing model to estimate accurately market prices of publicly traded options and reached conflicting results. This study examines commonly used ex ante measures of option mispricing, finds that they can produce differing conclusions about option prices, and develops an alternative measure for gauging option mispricing. Empirical analysis of returns to options selected using the various mispricing measures indicates that this new measure is more likely to detect mispricing and identify options that yield excess returns before commissions.     

Risk,Mispricing, and Value Investing

We evaluate the stock return performance of a modified version of the book-to-market strategy and its implications for market efficiency. If the previously documented superior stock return of the book-to-market strategy represents mispricing, its performance should be improved by excluding fairly valued firms with extreme book-to-market ratios. To attain this, we classify stocks as value or glamour on book-to-market ratios and accounting accruals jointly. This joint classification is likely to exclude stocks with extreme book-to-market ratios due to mismeasured accounting book values reflecting limitations underlying the accounting system. Using both 12-month buy-and-hold returns and earnings announcement returns, our results show that this joint classification generates substantially higher portfolio returns in the post-portfolio-formation year than the book-to-market classification alone with no evidence of increased risk. In addition, this superior stock return performance is more pronounced among firms held primarily by small (unsophisticated) investors and followed less closely by market participants (stock price <$10). Finally, and most importantly, financial analysts are overly optimistic (pessimistic) about earnings of glamour (value) stock, and for a subset of firms identified as overvalued by our strategy, the earnings announcement raw return, as well as abnormal return, is negative. These last results are particularly important because it is hard to envision a model consistent with rational investors holding risky stocks with predictable negative raw returns for a long period of time rather than holding fT-bills and with financial analysts systematically overestimating the earnings of these stocks while underestimating earnings of stocks that outperform the stock market.     

Can mispricing explain the value premium?

Empirical research finds that stocks with low market-to-book (MTB) ratios outperform stocks with high MTB ratios. Rhodes-Kropf, Robinson, and Viswanathan separate the MTB ratio into mispricing and growth options components. We report that the mispricing component, but not the growth options component, predicts abnormal returns for up to 5 years. We also find that the mispricing component, but not the growth options component, provides incremental information relative to existing asset pricing models. Moreover, after controlling for mispricing, value no longer beats growth. Overall, our evidence is consistent with a behavioral explanation of the value premium.     

Sentiment-scaled CAPM and market mispricing

This study explores the conditional version of the capital asset pricing model on sentiment to provide a behavioural intuition behind the value premium and market mispricing. We find betas (β) and the market risk premium to vary over time across different sentiment indices and portfolios. More importantly, the state β derived from this sentiment-scaled model provides a behavioural explanation of the value premium and a set of anomalies driven by mispricing. Different from the static β–return relation that gives a flat security market line, we document upward security market lines when plotting portfolio returns against their state βs and portfolios with higher state βs earn higher returns.     

THE RELATION BETWEEN OPTION MISPRICING AND VOLUME IN THE BLACK-SCHOLES OPTION MODEL

We investigate the relation between mispricing in the Black-Scholes option pricing (BSOP) model and volume in the option market. Our results indicate heavily traded call options are priced more efficiently and have lower mispricing errors than thinly traded options. However, this relation shifts significantly on days when call option trading is high. On high-volume days, the BSOP model mispricing errors are significantly larger than mispricing errors on normal-volume days. We believe large increases in volume may reflect new and changing market information, thus making pricing less efficient in the BSOP model.     

THE EVALUATION OF TRADED OPTIONS PRICING MODELS IN AUSTRALIA

The aim of this paper is to report the results of an Australian empirical study which examined a number of testable implications of the original Black and Scholes (B-S) Option Pricing Model, and a variant of the model, that incorporates the dividends paid on the underlying security. The results do not support the notion that the B-S model prices options "correctly" within the Australian Options Market.     

Excess Returns to R&D-Intensive Firms

Recent studies indicate that both current R&D investment levels and current or recent changes in R&D investment are positively associated with subsequent excess (risk-adjusted) stock returns. The tentative explanation offered for these results is that shares of R&D-intensive firms are mispriced because investors fail to see through earnings distortions caused by conservative accounting for R&D costs. However, an alternative explanation is that conventional controls for risk do not completely capture the riskiness of R&D-intensive firms, causing measured excess returns for these firms to be biased upward. This study provides evidence useful for distinguishing between the mispricing and risk explanations for R&D-related excess returns. Overall, our empirical results suggest that the positive association between R&D investment levels and excess returns is more likely to result from failure to control adequately for risk than from mispricing. On the other hand, our results do not rule out the possibility of a second source of excess returns that are due to mispricing and that are associated with changes in the level of R&D investment.     

Pricing Options on an Asset with Bernoulli Jump-Diffusion Returns

The price movements of certain assets can be modeled by stochastic processes that combine continuous diffusion with discrete jumps. This paper compares values of options on assets with no jumps, jumps of fixed size, and jumps drawn from a lognormal distribution. It is shown that not only the magnitude but also the direction of the mispricing of the Black-Scholes model relative to jump models can vary with the distribution family of the jump component. This paper also discusses a methodology for the numerical valuation, via a backward induction algorithm, of American options on a jump-diffusion asset whose early exercise may be profitable. These cannot, in general, be accurately priced using analytic models. The procedure has the further advantage of being easily adaptable to nonanalytic, empirical distributions of period returns and to nonstationarity in the underlying diffusion process.     

Overconfidence, Arbitrage, and Equilibrium Asset Pricing

This paper offers a model in which asset prices reflect both covariance risk and misperceptions of firms' prospects, and in which arbitrageurs trade against mispricing. In equilibrium, expected returns are linearly related to both risk and mispricing measures (e.g., fundamental/price ratios). With many securities, mispricing of idiosyncratic value components diminishes but systematic mispricing does not. The theory offers untested empirical implications about volume, volatility, fundamental/price ratios, and mean returns, and is consistent with several empirical findings. These include the ability of fundamental/price ratios and market value to forecast returns, and the domination of beta by these variables in some studies.     

m-Double Poisson Lévy markets

We develop novel mispricing of markets under asymmetric information and jumps for informed and uninformed investors, called m-Double Poisson markets, driven by independent Double Poisson processes. In the special case m?=?1, called the Double Poisson pure-jump Lévy market, both types of investors hold the same optimal portfolio and expected utility, and hence, the informed investor has no utility advantage over the uninformed. For the general market, instantaneous centralized moments of returns are used to compute optimal portfolios and utilities. The mean, variance, skewness and kurtosis of instantaneous returns are reported using jump amplitudes and frequencies.     

Option pricing in a lognormal securities market with discrete trading

This paper derives a call option valuation equation assuming discrete trading in securities markets where the underlying asset and market returns are bivariate lognormally distributed and investors have increasing, concave utility functions exhibiting skewness preference. Since the valuation does not require the continouus time riskfree hedging of Black and Scholes, nor the discrete time riskfree hedging of Cox, Ross and Rubinstein, market effects are introduced into the option valuation relation. The new option valuation seems to correct for the systematic mispricing of well-in and well-out of the money options by the Black and Scholes option pricing formula.     

Recovering risk aversion from option prices and realized returns

A relationship exists between aggregate risk-neutral and subjectiveprobability distributions and risk aversion functions. We empiricallyderive risk aversion functions implied by options prices andrealized returns on the S&P500 index simultaneously. Theserisk aversion functions dramatically change shapes around the1987 crash: Precrash, they are positive and decreasing in wealthand largely consistent with standard assumptions made in economictheory. Postcrash, they are partially negative and partiallyincreasing and irreconcilable with those assumptions. Mispricingin the option market is the most likely cause. Simulated tradingstrategies exploiting this mispricing show excess returns, evenafter accounting for the possibility of further crashes, transactioncosts, and hedges against the downside risk.     

Financial contagion and asset pricing

Asset market interconnectedness can give rise to significant contagion risks during periods of financial crises that extend beyond the risks associated with changes in volatilities and correlations. These channels include the transmission of shocks operating through changes in the higher order comoments of asset returns, including changes in coskewness arising from changes in the interaction between volatility and average returns across asset markets. These additional contagion channels have nontrivial implications for the pricing of options through changes in the payoff probability structure and more generally, in the management of financial risks. The effects of incorrectly pricing risk has proved to be significant during many financial crises, including the subprime crisis from mid 2007 to mid 2008, the Great Recession beginning 2008 and the European debt crisis from 2010. Using an exchange options model, the effects of changes in the comoments of asset returns across asset markets are investigated with special emphasis given to understanding the effects on hedging risk during financial crises. The results reveal that by not correctly pricing the risks arising from higher order moments during financial crises, there is significant mispricing of options, while hedged portfolios during noncrisis periods become exposed to price movements in times of crises.     

Skew Brownian Motion and Pricing European Options

Abstract

The volatility smile and systematic mispricing of the Black–Scholes option pricing model are the typical motivation for examining stochastic processes other than geometric Brownian motion to describe the underlying stock price. In this paper a new stochastic process is presented, which is a special case of the skew-Brownian motion of Itô and McKean. The process in question is the sum of a standard Brownian motion and an independent reflecting Brownian motion that is similar in construction to the stochastic representation of a skew-normal random variable. This stochastic process is taken in its exponential form to price European options. The derived option price nests the Black–Scholes equation as a special case and is flexible enough to accommodate stochastic volatility as well as stochastic skewness.     

Return predictability and the real option value of segments

Theory suggests that firm value should include the value of real options; that is, firms have the option to expand more profitable businesses and liquidate less profitable businesses. In a diversified firm, each segment has its own real options. Applying real options theory to a diversified firm at the firm level neglects the value of segment-level options. If investors overlook segment-level options, mispricing will occur. Using data from 1981 to 2013, we find that a hedge portfolio buying diversified firms in the highest decile of the estimated real option value of segments (RVS) and selling those in the lowest RVS decile earns a significant 0.79% size-adjusted monthly return. The hedge returns are more significant for firms whose growth opportunities mainly lie in the more profitable segments. We also find that the predictive power of RVS is stronger for firms with high growth, lower analyst coverage, and stronger corporate governance. Further investigation links improved operating performance to the exercise of segment-level real options.     

系统性定价偏误:中国A股盈余公告后的价格漂移研究

行为金融学的研究表明,投资者情绪引起的定价偏误在各支股票之间具有相关性,从而构成市场上的系统性定价偏误。基于2003年6月至2009年6月中国A股月度交易数据,本文考察了系统性定价偏误与盈余公告后漂移(PEAD)之间的关系。研究结果显示,中国股票市场上的PEAD现象可能由系统性定价偏误引致,因此,将捕捉系统性定价偏误的偏误定价因子引入定价模型能够提升模型对于PEAD的解释力。经过对定价模型调整,季度盈余公告后6个月买人持有异常收益在经济及统计意义上不显著。这一方面表明中国股票市场上存在由投资者情绪造成的系统性定价偏误,另一方面也为盈余公告后漂移的产生原因提供了新的解释。     

Reading the smile: the message conveyed by methods which infer risk neutral densities

In this study we compare the quality and information content of risk neutral densities obtained by various methods. We consider a non-parametric method based on a mixture of log–normal densities, the semi-parametric ones based on an Hermite approximation or based on an Edgeworth expansion, the parametric approach of Malz which assumes a jump-diffusion for the underlying process, and Heston's approach assuming a stochastic volatility model. We apply those models on FF/DM exchange rate options for two dates. Models differ when important news hits the market (here anticipated elections). The non-parametric model provides a good fit to options prices but is unable to provide as much information about market participants expectations than the jump-diffusion model.     

Hedging efficiency in the Greek options market before and after the financial crisis of 2008

This study examines the hedging effectiveness of the emerging Greek options market before and after the financial crisis of 2008. We test the hypothesis of market efficiency by analyzing violations of FTSE/ASE-20 index option returns with respect to standard option theory, estimating option risk-premia, and testing the statistical significance of the returns to delta and delta–vega neutral straddles. Our empirical results suggest that, despite a certain level of mispricing, the Athens Derivatives Exchange maintained a relative level of efficiency before 2008. However, the economic crisis has had a significant impact on the Greek options market, as evidenced by more pronounced violations of theoretical predictions observed in option returns and risk-premia. These findings have direct implications for the risk management of international portfolios, since the feasibility and effectiveness of hedging exposure in Greek investments is found to have declined precisely when it is needed the most.     

Firm Valuation,Earnings Expectations,and the Exchange-Rate Exposure Effect

Consistent with previous research, we fail to find a significant correlation between the abnormal returns of our sample firms with international activities and changes in the dollar. We investigate the possibility that this failure is due to mispricing. Lagged changes in the dollar are a significant variable in explaining current abnormal returns of our sample firms, suggesting that mispricing does occur. A simple trading strategy based upon these results generates significant abnormal returns. Corroborating evidence from returns around earnings announcements as well as errors in analysts' forecasts of earnings is also provided.     

Does option trading convey stock price information?

After executing option orders, options market makers turn to the stock market to hedge away the underlying stock exposure. As a result, the stock exposure imbalance in option transactions translates into an imbalance in stock transactions. This paper decomposes the total stock order imbalance into an imbalance induced by option transactions and an imbalance independent of options. The analysis shows that the option-induced imbalance significantly predicts future stock returns in the cross section controlling for the past stock and options returns, but the imbalance independent of options has only a transitory price impact. Further investigation suggests that options order flow contains important information about the underlying stock value.