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Abstract:
We examine the forecast quality of Chicago Board Options Exchange (CBOE) implied volatility indexes based on the Standard and Poor's 100 and Nasdaq 100 stock indexes. We find that the forecast quality of CBOE implied volatilities for the S&P 100 (VIX) has significantly improved in recent years, and implied volatilities for the Nasdaq 100 (VXN) provide even higher quality forecasts of future realized volatility. CBOE implied volatilities appear to contain significant forecast errors in the period 1988-94, but we find no indication of significant forecast errors in the period 1995-2002.

options, implied volatility, volatility forecasting

Abstract:
The academic literature generally concludes that the Black-Scholes model overstates the value of employee stock options (ESOs). In particular, because ESOs cannot be traded, employee risk aversion often elicits premature exercise. As a result, the ESO is less valuable than a traded option. An important factor affecting ESO values has been overlooked in reaching this conclusion. This is the implicit repricing provision in ESOs, whereby the ESO exercise price resets to a lower level if the stock price falls.

We develop a new valuation model for pricing ESOs. Our valuation model incorporates explicit repricing rules. Simulations based on various repricing rules suggest that the Black-Scholes model typically understates ESO value. Without a repricing provision, the Black-Scholes model will overstate ESO value, because risk aversion still has a significant effect on ESO value.

Abstract:
Hallerbach (2004) derives an approximation formula to compute a Black-Scholes implied volatility. This formula is equivalent to equation (7) in Corrado and Miller (1996a), with the substitution of a geometric average of stock and strike prices in place of an arithmetic average. Ceteris paribus the same numerical values are obtained. Although useful in a pedagogic setting, even with tweaking neither formula has the robustness typically required for commercial or research applications.

Options, implied volatility, implied standard deviation

Abstract:
The generalized lambda distribution is proposed as a useful model for security price distributions. Originally used to generate random variables with varied skewness and kurtosis values in Monte Carlo simulations, proposed financial applications include estimation of state price densities from option prices and VaR simulations based on a multivariate version of the generalized lambda distribution.

Option pricing, Monte Carlo simulations, Generalized lambda

Abstract:
Derman and Taleb (The Issusions of Dynamic Hedging, 2005) uncover a seeming anomaly in option pricing theory which suggests that static hedging based on put-call parity provides sufficient theoretical support to justify risk-neutral option pricing. From this they suggest that dynamic hedging as a theoretical basis for the celebrated option pricing model of Black and Scholes (1973) and Merton (1973), while correct, is redundant [see also Haug and Taleb (Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula, 2009)]. This paper examines the anomaly and finds that put-call parity does not provide a basis for risk-neutral option pricing.

option pricing, put-call parity, dynamic hedging, static hedging, Black-Scholes-Merton

Abstract:
Originally developed as a statistical tool for empirical research in accounting and finance, event studies have since migrated to other disciplines as well, including economics, history, law, management, marketing, and political science. Despite the elegant simplicity of a standard event study, variations in methodology and their relative merits continue to attract attention in the literature. This paper reviews some of the fundamental topics in short-term event study methodology, with an attempt to add new perspectives to some pressing topics.

Event studies, Abnormal returns, Nonparametric statistical tests

Abstract:
We investigate the effectiveness of several well-known parametric and nonparametric event study test statistics with security price data from the major Asia-Pacific security markets. Extensive Monte Carlo simulation experiments with actual daily security returns data reveal that the parametric test statistics are prone to misspecification with Asia-Pacific returns data. Two nonparametric tests, a rank test [Corrado and Zivney (1993)] and a sign test [Cowan (1992)] performed the best overall with market model excess returns computed using an equal weight index.

Asia-Pacific stock markets, event study methods, Monte Carlo simulations

Abstract:
Geared Equity Investments (GEI) are an over-the-counter product offered by Macquarie Bank, Ltd. to high-income investors in Australia and New Zealand as a managed-risk investment in local shares with a significant tax-shield benefit. Upon issuance, a geared equity contract has three stakeholders: 1) the investor, 2) the issuer, and 3) the tax authority. We measure the value of these contracts to each stakeholder and assess their support for investor tax arbitrage. Our main conclusion is that the tax-shield benefit of a GEI contract supports investor tax arbitrage in certain cases, but that most of the tax shield flows through to the issuer and the credit markets.

Option valuation, Tax shield, Geared equity investments

Abstract:
Option professionals routinely tweak the Black-Scholes option pricing model using a volatility smile. Using algebraic analysis and Monte Carlo simulation experiments, we compare the hedging performance of the tweaked Black-Scholes option pricing model with a stochastic volatility model in a stochastic volatility setting. We find that the tweaked Black-Scholes model almost perfectly mimics the stochastic volatility model representing the true stochastic process. This suggests why volatility smiles are widely used by options professionals to calibrate option trading and hedging strategies. These results also have implications for empirical tests of option pricing models.

options, hedging, Black-Scholes

Abstract:
The exact joint distribution of the maximum and minimum of a multinomial distribution of n balls in m urns is compactly represented as a product of stochastic matrices. This representation does not require equal urn probabilities, is invariant to urn order, and permits rapid calculation of exact probabilities. The exact distribution of the multinomial range is also derived. An application to the September effect in stock returns is presented.

Dirichlet multinomial, Multinomial maximum minimum range, Multinomial outliers and inliers, September effect, Stochastic matrix

Abstract:
We examine the effect of options trading volume on the stock price response to earnings announcements over the period 1996–2007. Contrary to prior studies, we find no significant difference in the immediate stock price response to earnings information announcements between firms with listed options and firms without listed options. However, within the sample of firms with listed options, we find that higher options trading volume reduces the immediate stock price response to earnings announcements. This is consistent with evidence that the stock prices of high options trading volume firms have anticipated and pre-empted some earnings information in the pre-announcement period. We also find that abnormal options trading volume around earnings announcements hastens the stock price adjustment to earnings news. We present evidence that post-earnings announcement drift is lower for stocks of firms with high abnormal options trading volume around earnings announcements.

Options, Trading Volume, Earnings Announcement, Stock Price

Abstract:
We examine the effect of options trading volume on the stock price response to earnings announcements over the period 1996–2007. Contrary to prior studies, we find no significant difference in the immediate stock price response to earnings information announcements between firms with listed options and firms without listed options. However, within the sample of firms with listed options, we find that higher options trading volume reduces the immediate stock price response to earnings announcements. This is consistent with evidence that the stock prices of high options trading volume firms have anticipated and pre-empted some earnings information in the pre-announcement period. We also find that abnormal options trading volume around earnings announcements hastens the stock price adjustment to earnings news. We present evidence that post-earnings announcement drift is lower for stocks of firms with high abnormal options trading volume around earnings announcements.

Options, Trading Volume, Earnings Announcement, Stock Price

Abstract:
The exact distribution of the maximum and minimum frequencies of Multinomial/Dirichlett and Multivariate Hypergeometric distributions of n balls in m urns is compactly represented as a product of stochastic matrices. This representation does not require equal urn probabilities, is invariant to urn order, and permits rapid calculation of exact probabilities. The exact distribution of the range is also obtained. These algorithms satisfy a long-standing need for routines to compute exact Multinomial/Dirichlett and Multivariate Hypergeometric maximum, minimum, and range probabilities in statistical computation libraries and software packages.

Dirichlet multinomial, Multivariate hypergeometric, Multinomial maximum, minimum, range, Multinomial outliers, inliers, Stochastic matrix

Abstract:
A hidden martingale restriction is developed for option pricing models based on Gram-Charlier expansions of the normal density function. The restriction is hidden behind a reduction in parameter space for the Gram-Charlier expansion coefficients. The resulting restriction is invisible in the option price.

Option prices, martingale restriction, skewness, kurtosis, Gram-Charlier density expansions

Abstract:
We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003, using the proportional reward-to-risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and realized excess returns. In contrast, when risk is measured by option-implied volatility, we find a positive and significant relation between expected and realized excess returns in the 1994-1998 sub-period. In the 1999-2003 sub-period, the option-implied volatility risk measure yields a positive, but statistically insignificant, risk-return relation. We attribute this performance difference to the fact that, in the 1994-1998 sub-period, return volatility was lower and the average return was much higher than in the 1999-2003 sub-period, thereby increasing the signal-to-noise ratio in the latter sub-period.

Asset pricing, security returns

Abstract:
The Black-Scholes option pricing model is used to value a wide range of option contracts. It often prices deep in- the-money and deep out-of-the-money options inconsistently, a phenomenon we refer to as a volatility "skew" or "smile." This article applies an extension of the Black-Scholes model developed by Jarrow and Rudd to an investigation of S&P 500 index option prices. Non-normal skewness and kurtosis in option-implied distributions of index returns are found to contribute significantly to the phenomenon of volatility skews.