Charles Cao

Inequality Constraints in the Univariate GARCH Model

To keep the conditional variances generated by the GARCH (p, q) model nonnegative, Bollerslev imposed nonnegativity constraints on the parameters of the process. We show that these constraints can be substantially weakened and so should not be imposed in estimation. We also provide empirical examples illustrating the importance of relaxing these constraints.

Informational Content of Option Volume Prior to Takeovers

This paper examines the information embedded in both the stock and option markets prior to takeover announcements. During normal periods, buyer-seller initiated stock volume imbalances are significant predictors of next-day stock returns and option volume imbalances are uninformative. However, prior to takeover announcements, call volume imbalances are strongly positively related to next-day stock returns. Cross-sectional analysis shows that those takeover targets with the largest pre-announcement call-imbalance increases experience the highest announcement-day returns. The largest increase in buyer-initiated trading activity is in short-term out-of-the-money calls that subsequently experience the largest returns. Collectively, these findings are consistent with the hypothesis that, in the presence of pending extreme informational events, the options market plays an important role in price discovery.

Pricing and hedging long-term options

Recent empirical studies find that once an option pricing model has incorporated stochastic volatility, allowing interest rates to be stochastic does not improve pricing or hedging any further while adding random jumps to the modeling framework only helps the pricing of extremely short-term options but not the hedging performance. Given that only options of relatively short terms are used in existing studies, this paper addresses two related questions: Do long-term options contain different information than short-term options? If so, can long-term options better differentiate among alternative models? Our inquiry starts by first demonstrating analytically that differences among alternative models usually do not surface when applied to short term options, but do so when applied to long-term contracts. For instance, within a wide parameter range, the Arrow-Debreu state price densities implicit in different stochastic-volatility models coincide almost everywhere at the short horizon, but diverge at the long horizon. Using regular options (of less than a year to expiration) and LEAPS, both written on the S&P 500 index, we find that short- and long-term contracts indeed contain different information and impose distinct hurdles on any candidate option pricing model. While the data suggest that it is not as important to model stochastic interest rates or random jumps (beyond stochastic volatility) for pricing LEAPS, incorporating stochastic interest rates can nonetheless enhance hedging performance in certain cases involving long-term contracts.

The information content of an open limit‐order book

Lehmann, Mark Lipson, Chris Muscarella, Gideon Saar, Chester Spatt, Avanidhar Subrahmanyam, Robert Webb (the Editor), an anonymous referee, and seminar participants at Penn State, Rutgers, George Washington Universities, the Western Finance Association Meetings, the NBER-JFM Microstructure Conference, the American Finance Association Meetings, and the 15th Annual Asia Pacific Futures Research Symposium for their helpful comments. The authors are grateful to the Australian Stock Exchange and the Securities Industry Research Centre Asia-Pacific for providing the data used in this study. The authors also thank Morgan Stanley for providing the equity market microstructure research grant for this study.

Decimalization and competition among stock markets: Evidence from the Toronto Stock Exchange cross-listed securities

We study the impact of Toronto Stock Exchange (TSE) decimalization on the competition for order flow. For TSE stocks cross-listed on the NYSE/AMEX, spreads decrease by 27% on the TSE and do not change on the NYSE/AMEX. For TSE stocks cross-listed on Nasdaq, spreads decline by 16% and 8% on the TSE and Nasdaq, respectively. However, order flow does not migrate from U.S. markets to the TSE. Our results indicate that the savings in TSE transaction costs do not o⁄set the benefits of trading on the NYSE/AMEX, and that Nasdaq dealers might not operate as eƒciently as perfect competition warrants. ( 1998 Elsevier Science B.V. All rights reserved.

Pricing Credit Default Swaps with Option-Implied Volatility

Using the industry benchmark CreditGrades model to analyze credit default swap (CDS) spreads across a large number of companies during the 2007–09 credit crisis, the authors demonstrate that the performance of the model can be significantly improved by calibrating it with option-implied volatility rather than with historical volatility. Moreover, the advantage of using option-implied volatility is greater among companies with more volatile CDS spreads, more actively traded options, and lower credit ratings. Structural credit risk models are important tools in relative value trading strategies because they use equity market information to price such credit-risky securities as corporate bonds and credit default swaps (CDSs). One of the most important inputs for such models is equity volatility, which can be estimated from either historical returns or equity option prices. We examined the relative performance of historical versus option-implied volatility in CDS pricing through the lens of an industry benchmark model called CreditGrades, which was jointly developed by the RiskMetrics Group, J.P. Morgan, Goldman Sachs, and Deutsche Bank in 2002. Using CDS and options market data on 332 companies over January 2007–October 2009 (which encompasses the recent credit crisis), we found that option-implied volatility generally dominates historical volatility in both in-sample and out-of-sample pricing performance. This finding is robust to the horizon of the historical volatility estimator and the initial burn-in period for calibrating the CreditGrades model. It also remains qualitatively unchanged during the earlier and less chaotic sample period of 2001–2004. Perhaps more interestingly, we identified significant cross-sectional variations in such relative performance. For instance, option-implied volatility provides much more added value in terms of improved CDS pricing performance when the company in question has a lower credit rating, a more volatile CDS spread, and larger options-trading volume. Our interpretation is that these characteristics are associated with a higher signal-to-noise ratio of options market information. Our findings are important to market participants who need to monitor their credit risk exposures constantly. The improvement in pricing performance is likely to result in fewer false trading signals and superior profitability for capital structure arbitrageurs. On a more fundamental level, our findings suggest that having forward-looking inputs from the market could be as important as having the right model for pricing credit risk.

Share repurchase tender offers and bid-ask spreads

Abstract This paper examines the impact of share repurchase tender offers on the market microstructure. We find that there is a temporary reduction in the bid–ask spread, and a temporary increase in volume and quotation depth during the offer period. Our evidence suggests that the bid–ask spread is asymmetric during the offer period with the bid-side spread smaller than the ask-side spread. The temporary reduction in the spread around offers is consistent with the competing-market-maker hypothesis which predicts that the intensified competition for the market maker raises bid prices and narrows the spread asymmetrically during the offer period.

Liquidity risk and institutional ownership

Institutional ownership affects the sensitivity of stock returns to changes in market liquidity (liquidity risk). Overall, institutional ownership lowers the liquidity risk of stocks. However, different types of institutions affect liquidity risk in opposite ways. Stocks held by hedge funds, especially levered hedge funds, as marginal investors are more sensitive to changes in market liquidity than comparable stocks held by other types of institutions or by individuals. In contrast, stocks held by banks are less sensitive to changes in aggregate liquidity. These findings are robust to alternative specifications that control for institutional preferences for different stock characteristics and risk.

Option Pricing and Hedging Performance Under Stochastic Volatility and Stochastic Interest Rates

Recent studies have extended the Black–Scholes model to incorporate either stochastic interest rates or stochastic volatility. But, there is not yet any comprehensive empirical study demonstrating whether and by how much each generalized feature will improve option pricing and hedging performance. This paper fills this gap by first developing an implementable option model in closed-form that admits both stochastic volatility and stochastic interest rates and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Based on the model, both delta-neutral and single-instrument minimum-variance hedging strategies are derived analytically. Using S&P 500 option prices, we then compare the pricing and hedging performance of this model with that of three existing ones that respectively allow for (i) constant volatility and constant interest rates (the Black–Scholes), (ii) constant volatility but stochastic interest rates, and (iii) stochastic volatility but constant interest rates. Overall, incorporating stochastic volatility and stochastic interest rates produces the best performance in pricing and hedging, with the remaining pricing and hedging errors no longer systematically related to contract features. The second performer in the horse-race is the stochastic volatility model, followed by the stochastic interest rates model and then by the Black–Scholes.

The Role of Hedge Funds in the Security Price Formation Process

Using comprehensive quarterly data on hedge fund stock holdings, we study the role of hedge funds in the process of stock price formation. We find that hedge funds tend to hold undervalued stocks, and that both hedge fund ownership and their trades are positively related to the degree of stock mispricing. A portfolio consisting of undervalued stocks with high hedge fund ownership generates a risk-adjusted return of 0.40% per month (or, 4.8% annually), and the profit stands even after transaction costs. Hedge fund ownership and trades also precede the dissipation of stock mispricing. In contrast, these patterns are either nonexistent or much weaker for other types of institutional investors. Taken together, our results suggest that hedge funds exploit and help correct mispricing, but the process is not instantaneous.