Patrick J. Dennis

Risk-Neutral Skewness: Evidence from Stock Options

We investigate the relative importance of various factors in explaining the volatility skew observed in the prices of stock options traded on the Chicago Board Options Exchange. The skewness of the risk-neutral density implied by individual stock option prices tends to be more negative for stocks that have larger betas, suggesting that market risk is important in pricing individual stock options. Also, implied skewness tends to be more negative in periods of high market volatility, and when the risk-neutral density for index options is more negatively skewed. Other firm-specific factors, including firm size and trading volume a so help explain cross-sectional variation in skewness. However, we find no robust relationship between skewness and the firms leverage. Nor do we find evidence that skewness is related to the put/call ratio, which may be viewed as a proxy for trading pressure or market sentiment. Overall, firm-specific factors seem to be more important than systematic factors in explaining the variation in the skew for individual firms.

Stock Returns, Implied Volatility Innovations, and the Asymmetric Volatility Phenomenon

We study the dynamic relation between daily stock returns and daily innovations in optionderived implied volatilities. By simultaneously analyzing innovations in index- and firmlevel implied volatilities, we distinguish between innovations in systematic and idiosyncratic volatility in an effort to better understand the asymmetric volatility phenomenon. Our results indicate that the relation between stock returns and innovations in systematic volatility (idiosyncratic volatility) is substantially negative (near zero). These results suggest that asymmetric volatility is primarily attributed to systematic market-wide factors rather than aggregated firm-level effects. We also present evidence that supports our assumption that innovations in implied volatility are good proxies for innovations in expected stock volatility.

The Effect Of Stock Splits On Liquidity And Excess Returns: Evidence From Shareholder Ownership Composition

We examine the influence of firm ownership composition on both the abnormal returns at the announcement of a stock split and liquidity changes following a stock split. We find three results. First, the largest post-split increase in institutional ownership occurs for firms that had low institutional ownership before the split. Second, changes in liquidity are negatively related to the level of institutional ownership before the split. Last, the abnormal return following a split is negatively related to the level of institutional ownership before the split. These findings are important as they shed new light on the source of stock split announcement returns. 2003 The Southern Finance Association and the Southwestern Finance Association.

Stock Splits and Liquidity: The Case of the Nasdaq‐100 Index Tracking Stock

In an attempt to disentangle the signaling effect from the liquidity effect of stock splits, I examine the liquidity changes following the two-for-one split of the Nasdaq-100 Index Tracking Stock. Since there can be no signaling with an index stock split, any difference between pre- and postsplit trading may be driven by liquidity but not signaling effects. I find that though the postsplit relative bid-ask spread is higher and daily turnover is unchanged, the frequency, share volume, and dollar-volume of small trades all increased after the split, indicating that the split improved liquidity for small trade-sizes. Copyright 2003 by the Eastern Finance Association.

Valuing Multiple Employee Stock Options Issued by the Same Company

Stock options issued to employees has become a significant component of total compensation in many firms. Although option pricing technology has evolved remarkably over the years, valuing employee stock options (ESOs) still presents numerous challenges, and there is no model that is generally accepted in practice. Simply treating ESOs as if they were plain vanilla (American) stock options fails to take proper account of a number of their particular features. Along with vesting rules and the uncertainty they entail, these features include the fact that the equity of existing stockholders will be diluted when the ESOs are exercised. In that sense they resemble warrants rather than traded option contracts. Also, the fact that ESOs are issued on a regular basis means there are typically a number of outstanding ESOs with differing maturities and strike prices, which introduces interaction among them in valuation and in optimal exercise strategy. In this article, Dennis and Rendleman present a lattice technique to value ESOs that takes account of the effects of dilution and optimal exercise for a firm that has a diverse set of ESOs outstanding. Their approach increases computational efficiency substantially over the standard solution technique for a lattice model, but realistic problems still can become intractable as the number of time steps and options grows. Fortunately, the results indicate that in most cases, the effect of dilution and interaction among exercise decisions is present but relatively small.