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.     

Option pricing under a stressed-beta model

Empirical studies have concluded that stochastic volatility is an important component of option prices. We introduce a regime-switching mechanism into a continuous-time Capital Asset Pricing Model which naturally induces stochastic volatility in the asset price. Under this Stressed-Beta model, the mechanism is relatively simple: the slope coefficient—which measures asset returns relative to market returns—switches between two values, depending on the market being above or below a given level. After specifying the model, we use it to price European options on the asset. Interestingly, these option prices are given explicitly as integrals with respect to known densities. We find that the model is able to produce a volatility skew, which is a prominent feature in option markets. This opens the possibility of forward-looking calibration of the slope coefficients, using option data, as illustrated in the paper.     

CALL OPTION VALUATION FOR DISCRETE NORMAL MIXTURES

In this study a mixture call option pricing model is derived to examine the impact of non-normal underlying returns densities. Observed fat-tailed and skewed distributions are assumed to be the result of independent Gaussian processes with nonstationary parameters, modeled by discrete k-component independent normal mixtures. The mixture model provides an exact solution with intuitive appeal using weighted sums of Black-Scholes (B-S) solutions. Simulating returns densities representative of equity securities, significant mispricing by B-S is found in low-priced at- and out-of-the-money near-term options. The lower the variance and the higher the leptokurtosis and positive skewness of the underlying returns, the more pronounced is this mispricing. Values of in-the-money options and options with several weeks or more to expiration are closely approximated by B-S.     

Option Mispricing around Nontrading Periods

We find that option returns are significantly lower over nontrading periods, the vast majority of which are weekends. Our evidence suggests that nontrading returns cannot be explained by risk, but rather are the result of widespread and highly persistent option mispricing driven by the incorrect treatment of stock return variance during periods of market closure. The size of the effect implies that the broad spectrum of finance research involving option prices should account for nontrading effects. Our study further suggests how alternative industry practices could improve the efficiency of option markets in a meaningful way.     

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.     

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.     

Transactions data tests of efficiency of the Chicago board options exchange

This paper performs lower boundary condition tests based on rational pricing of call options and an implied standard deviation test based on the bid/ask prices of options. These efficiency tests attempt to closely approximate conditions in the option markets to avoid the pitfalls indicated by Phillips and Smith (1980). The tests use transactions data and account for the effects of stock and option bid/ask prices, simultaneity of stock and option prices, depth of market, execution lag and transaction costs. The small and relatively infrequent profits due to market mispricing disappear in the lower boundary tests when transaction costs are taken into account. Frequent violations of the tighter boundary conditions in the implied standard deviation test are reported, but the estimated profits cannot be unambiguously attributed to option market inefficiency.     

Does Inflation Illusion Explain the Relation between REITs and Inflation?

We examine whether the observed negative relations between real estate investment trust (REIT) returns and inflation can be explained by the inflation illusion. We identify the mispricing component in REIT prices based on present value models, both linear and loglinear, and then we investigate whether inflation can explain the mispricing component. When we allow for time-varying interest rates, inflation no longer explains the REIT mispricing component. Instead, we find that behavioral factors such as consumer sentiments contribute to the mispricing of REIT prices.     

A MULTIFACTOR MODEL OF THE QUALITY OPTION IN TREASURY FUTURES CONTRACTS

The values of quality options in Treasury futures contracts are set relative to the prices of all coupon bonds in their respective deliverable sets. As a result, any model used to value the quality option should set its price relative to the set of observed bond prices. This requirement rules out the use of most simple equilibrium models that represent all bond prices in terms of a finite number of state variables. We use the two-factor Heath-Jarrow-Morton model, which permits claims to be priced relative to observable bond prices, to investigate the potential value of the quality option in Treasury bond and note futures. We show that the quality option has significantly more value in a two-factor interest rate economy than in a single-factor economy, and that ignoring it could lead to significant mispricing.     

Investor sentiment and value and growth stock index options

The paper examines the relationship between both individual and institutional investor sentiment measures and the risk-neutral skewness (RNS) of seven stock index options comprising either growth or value stocks. It provides novel evidence that growth index option prices are affected by sentiment measures. The regression results indicate a significantly positive relationship between sentiment measures and the RNS estimated from four growth index options and a negative relationship with two value index options. The results are economically significant since an associated long–short trading strategy yields high abnormal returns with a Sharpe ratio of up to 1.1 and zero exposure to systematic risk. These high abnormal returns provide evidence of a value premium type anomaly in the index options markets.     

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.     

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.     

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.     

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.     

The Price of Correlation Risk: Evidence from Equity Options

We study whether exposure to marketwide correlation shocks affects expected option returns, using data on S&P100 index options, options on all components, and stock returns. We find evidence of priced correlation risk based on prices of index and individual variance risk. A trading strategy exploiting priced correlation risk generates a high alpha and is attractive for CRRA investors without frictions. Correlation risk exposure explains the cross-section of index and individual option returns well. The correlation risk premium cannot be exploited with realistic trading frictions, providing a limits-to-arbitrage interpretation of our finding of a high price of correlation risk.     

A NO-ARBITRAGE MARTINGALE ANALYSIS FOR JUMP-DIFFUSION VALUATION

This study presents a jump-diffusion valuation framework using the no-arbitrage martingale approach. Equilibrium conditions needed to support a jump-diffusion pricing standard process are derived. The results are a generalized jump-diffusion security market line and its corresponding equilibrium valuation relation that prices both jump and diffusion risk. To value options, a fundamental formula is derived that includes existing jump-diffusion option valuation formulas as special cases. 1 find Merton's (1976a) assumption of diversifiable jump risk to be consistent with no-arbitrage only when the aggregate consumption flow does not jump. Simulation shows that Merton's formula undervalues/overvalues options on hedging/cyclical assets. When the jump arrival frequency is larger, the mispricing is larger/smaller for in-the-money/out-of-the-money options.     

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.     

Option prices and stock market momentum: evidence from China

Option prices tend to be correlated to past stock market returns due to market imperfections. We unprecedentedly examine this issue on the SSE 50 ETF option in the Chinese derivatives market. To measure the price pressure in the options market, we construct an implied volatility spread based on pairs of the SSE 50 ETF option with identical expiration dates and strike prices. By regressing the implied volatility spread on past stock returns, we find that past stock returns exert a strong influence on the pricing of index options. Specifically, we find that SSE 50 ETF calls are significantly overvalued relative to SSE 50 ETF puts after stock price increases and the reverse is also true after the stock price decreases. Moreover, we validate the momentum effects in the underlying stock market to be responsible for the price pressure. These findings are both economically and statistically significant and have important implications.     

Stock price clustering on option expiration dates

This paper presents striking evidence that option trading changes the prices of underlying stocks. In particular, we show that on expiration dates the closing prices of stocks with listed options cluster at option strike prices. On each expiration date, the returns of optionable stocks are altered by an average of at least 16.5 basis points, which translates into aggregate market capitalization shifts on the order of $9 billion. We provide evidence that hedge rebalancing by option market makers and stock price manipulation by firm proprietary traders contribute to the clustering.     

Binomial Option Pricing Biases and Inconsistent Implied Volatilities

We evaluate the binomial option pricing methodology (OPM) by examining simulated portfolio strategies. A key aspect of our study involves sampling from the empirical distribution of observed equity returns. Using a Monte Carlo simulation, we generate equity prices under known volatility and return parameters. We price American–style put options on the equity and evaluate the risk–adjusted performance of various strategies that require writing put options with different maturities and moneyness characteristics. The performance of these strategies is compared to an alternative strategy of investing in the underlying equity. The relative performance of the strategies allows us to identify biases in the binomial OPM leading to the well–known volatility smile . By adjusting option prices so as to rule out dominated option strategies in a mean–variance context, we are able to reduce the pricing errors of the OPM with respect to option prices obtained from the LIFFE. Our results suggest that a simple recalibration of inputs may improve binomial OPM performance.