Pinning in the S&P 500 futures

We show that Standard & Poor's (S&P) 500 futures are pulled toward the at-the-money strike price on days when serial options on the S&P 500 futures expire (pinning) and are pushed away from the cost-of-carry adjusted at-the-money strike price right before the expiration of options on the S&P 500 index (anti-cross-pinning). These effects are driven by the interplay of market makers' rebalancing of delta hedges due to the time decay of those hedges as well as in response to reselling (and early exercise) of in-the-money options by individual investors. The associated shift in notional futures value is at least $115 million per expiration day.     

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.     

A comprehensive long-term analysis of S&P 500 index additions and deletions

We investigate the long-term effects of S&P 500 index additions and deletions on a sample of stocks from 1962 to 2003 and find a significant long-term price increase for both added and deleted stocks, with deleted stocks outperforming added stocks. The long-term price increase for added stocks can be attributed to increases in institutional ownership, liquidity, and analyst coverage, and a decrease in the shadow cost in the long-term. However, while deletion has no significant effect on analyst coverage and shadow cost, we find a rebound in the institutional ownership and liquidity of deleted stocks. The difference in the long-term price increase of added and deleted stocks can be explained by analyst coverage and operating performance.     

The jump component of S&P 500 volatility and the VIX index

Much research has investigated the differences between option implied volatilities and econometric model-based forecasts. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing of past volatility to generate forecasts. Implied volatility has the potential to reflect information that a model-based forecast could not. This paper considers two issues relating to the informational content of the S&P 500 VIX implied volatility index. First, whether it subsumes information on how historical jump activity contributed to the price volatility, followed by whether the VIX reflects any incremental information pertaining to future jump activity relative to model-based forecasts. It is found that the VIX index both subsumes information relating to past jump contributions to total volatility and reflects incremental information pertaining to future jump activity. This issue has not been examined previously and expands our understanding of how option markets form their volatility forecasts.     

VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation

This study integrates CBOE VIX Term Structure and VIX futures to simplify VIX option pricing in multifactor models. Exponential and hump volatility functions with one- to three-factor models of the VIX evolution are used to examine their pricing for VIX options across strikes and maturities. The results show that using exponential volatility functions presents an effective choice as pricing models for VIX calls, whereas hump volatility functions provide efficient out-of-sample valuation for most VIX puts, in particular with deep in-the-money and deep out-of-the-money. Pricing errors for calls can be further reduced with a two-factor model.     

An FFT-network for Lévy option pricing

This paper develops a simple network approach to American exotic option valuation under Lévy processes using the fast Fourier transform (FFT). The forward shooting grid (FSG) technique of the lattice approach is then generalized to expand the FFT-network to accommodate path-dependent variables. This network pricing approach is applicable to all Lévy processes for which the characteristic function is readily available. In other words, the log-value of the underlying asset can follow finite-activity or infinite-activity Lévy processes. With the powerful computation of FFT, the proposed network has a negligible additional computational burden compared to the binomial tree approach. The early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach. Numerical examples using American-style barrier, lookback, and Asian options demonstrate that the FFT-network is accurate and efficient.     

Hedging the black swan: Conditional heteroskedasticity and tail dependence in S&P500 and VIX

The recent financial crisis has accentuated the fact that extreme outcomes have been overlooked and not dealt with adequately. While extreme value theories have existed for a long time, the multivariate variant is difficult to handle in the financial markets due to the prevalent heteroskedasticity embedded in most financial time series, and the complex extremal dependence that cannot be conveniently captured by a single structure. Moreover, most of the existing approaches are based on a limiting argument in which all variables become large at the same rate. In this paper, we show how the conditional approach of Heffernan and Tawn (2004) can be implemented to model extremal dependence between financial time series. We use a hedging example based on VIX futures to demonstrate the flexibility and superiority of the conditional approach against the conventional OLS regression approach.     

Generalized parameter functions for option pricing

We extend the benchmark nonlinear deterministic volatility regression functions of Dumas et al. (1998) to provide a semi-parametric method where an enhancement of the implied parameter values is used in the parametric option pricing models. Besides volatility, skewness and kurtosis of the asset return distribution can also be enhanced. Empirical results, using closing prices of the S&P 500 index call options (in one day ahead out-of-sample pricing tests), strongly support our method that compares favorably with a model that admits stochastic volatility and random jumps. Moreover, it is found to be superior in various robustness tests. Our semi-parametric approach is an effective remedy to the curse of dimensionality presented in nonparametric estimation and its main advantage is that it delivers theoretically consistent option prices and hedging parameters. The economic significance of the approach is tested in terms of hedging, where the evaluation and estimation loss functions are aligned.     

Explaining Monday Returns

The Monday effect is reexamined using two stock indexes and a sample of 452 individual stocks that trade on the London Stock Exchange. The results based on conventional test methods reveal a negative average return on Monday. Extending the analysis to examine the effects of various possible influences simultaneously, the average Monday return becomes positive and does not differ significantly from the average returns of most other days of the week. Fortnight, ex‐dividend day, account period, (bad) news flow, trading activity, and bid‐ask spread effects are all controlled for. The results broadly support the trading time hypothesis.     

O/S: The relative trading activity in options and stock

Relatively little is known about the trading volume in derivatives relative to the volume in underlying stocks. We study the time-series properties and the determinants of the options/stock trading volume ratio (O/S) using a comprehensive cross-section and time-series of data on equities and their listed options. O/S is related to many intuitive determinants such as delta and trading costs, and it also varies with institutional holdings, analyst following, and analyst forecast dispersion. O/S is higher around earnings announcements, suggesting increased trading in the options market. Further, post-announcement absolute returns are positively related to pre-announcement O/S, which suggests that at least part of the pre-announcement options trading is informed.     

The divergence of liquidity commonality in the cross-section of stocks

This paper demonstrates that the cross-sectional variation of liquidity commonality has increased over the period 1963–2005. The divergence of systematic liquidity can be explained by patterns in institutional ownership over the sample period. We document that our findings are associated with similar patterns in systematic risk. Our analysis also indicates that the ability to diversify systematic risk and aggregate liquidity shocks by holding large-cap stocks has declined. The evidence suggests that the fragility of the US equity market to unanticipated events has increased over the past few decades.     

Cross-section of option returns and volatility

We study the cross-section of stock option returns by sorting stocks on the difference between historical realized volatility and at-the-money implied volatility. We find that a zero-cost trading strategy that is long (short) in the portfolio with a large positive (negative) difference between these two volatility measures produces an economically and statistically significant average monthly return. The results are robust to different market conditions, to stock risks-characteristics, to various industry groupings, to option liquidity characteristics, and are not explained by usual risk factor models.     

Volatility dynamics for the S&P 500: Further evidence from non-affine,multi-factor jump diffusions

We apply Markov chain Monte Carlo methods to time series data on S&P 500 index returns, and to its option prices via a term structure of VIX indices, to estimate 18 different affine and non-affine stochastic volatility models with one or two variance factors, and where jumps are allowed in both the price and the instantaneous volatility. The in-sample fit to the VIX term structure shows that the second (stochastic long-term volatility) factor is required to fit the VIX term structure. Out-of-sample tests on the fit to individual option prices, as well as in-sample tests, show that the inclusion of jumps is less important than allowing for non-affine dynamics. The estimation and testing periods together cover more than 21 years of daily data.     

Stock and option market divergence in the presence of noisy information

We examine market behavior of the stock and option markets upon the arrival of noisy information in the form of CNBC’s Mad Money recommendations. If stock and option markets are not equally efficient, they should respond differently to noisy information, with the less efficient market more susceptible to noise. We find that the stock market is less efficient than the option market. The abnormal difference between option-implied and actual stock returns is negative and significant upon exposure to noisy information. This difference may yield an economically significant monthly trading profit of up to 5%. We conclude that the stock market is more susceptible to noisy information than the option market and is therefore less efficient.     

The S&P500 index effect reconsidered: Evidence from overnight and intraday stock price performance and volume

This study focuses on S&P500 inclusions and deletions, examining the impact of potential overnight price adjustment after the announcement of an S&P500 index change. We find evidence of a significant overnight price change that diminishes the returns available to speculators although there are still profits available from the first day after announcement until a few days after the actual event. More importantly, observing the tick-by-tick stock price performance and volume effects on the key days during the event window for the first time, we find evidence of consistent trading patterns during trading hours. A separate analysis of NASDAQ and NYSE listed stocks allows for a detailed examination of the price and volume effect at an intra-day level. We find that index funds appear to cluster their rebalancing activities near to and after the close on the event date, suggesting that they are more concerned with tracking error than profit.     

Intraday technical analysis of individual stocks on the Tokyo Stock Exchange

This paper conducts an intraday technical analysis of individual stocks listed on the Nikkei 225. In addition to the price-based technical rules popularly examined in the literature, we uniquely propose and statistically investigate technical rules that utilize information regarding (1) the order-flow imbalance and (2) the order-book imbalance. Technical analysis using the imbalance-based trading rules is motivated by the evidence presented first in this paper that short-term returns can be predicted from the information regarding the order-flow and order-book imbalances for more than half of Nikkei 225-listed stocks. However, we demonstrate that no strategies, including limit order trading where trading signals are derived from the order-book imbalance, beat the buy-and-hold strategy within our sample. The results imply that past prices and demand/supply imbalances do not contribute to profiting in intraday trading and that non-execution and picking-off risks are too large for limit order trading to be profitable in our sample.     

The delivery option in credit default swaps

Under standard assumptions the reduced-form credit risk model is not capable of accurately pricing the two fundamental credit risk instruments – bonds and credit default swaps (CDS) – simultaneously. Using a data set of euro-denominated corporate bonds and CDS our paper quantifies this mispricing by calibrating such a model to bond data, and subsequently using it to price CDS, resulting in model CDS spreads up to 50% lower on average than observed in the market. An extended model is presented which includes the delivery option implicit in CDS contracts emerging since a basket of bonds is deliverable in default. By using a constant recovery rate standard models assume equal recoveries for all bonds and hence zero value for the delivery option. Contradicting this common assumption, case studies of Chapter 11 filings presented in the paper show that corporate bonds do not necessarily trade at equal levels following default. Our extension models the implied expected recovery rate of the cheapest-to-deliver bond and, applied to data, largely eliminates the mispricing. Calibrated recovery values lie between 8% and 47% for different obligors, exhibiting strong variation among rating classes and industries. A cross-sectional analysis reveals that the implied recovery parameter depends on proxies for the delivery option, primarily the number of available bonds and bond pricing errors. No evidence is found for a direct influence of the bid-ask spread, notional amount, coupon, or rating used as proxies for bond market liquidity.     

Common risk factors in bank stocks

This paper provides evidence on the risk factors that are priced in bank equities. Alternative empirical models with precedent in the nonfinancial asset pricing literature are tested, including the single-factor CAPM, three-factor Fama–French model, and ICAPM. Our empirical results indicate that an unconditional two-factor ICAPM model that includes the stock market excess return and shocks to the slope of the yield curve is useful in explaining the cross-section of bank stock returns. However, we find no evidence that firm specific factors such as size and book-to-market ratios are priced in bank stock returns. These results have a number of important implications for the estimation of the banks’ cost of capital as well as regulatory initiatives to utilize market discipline to evaluate bank risk under Basel II.     

Credit default swap spreads and variance risk premia

We find that the firm-level variance risk premium has a prominent explanatory power for credit spreads in the presence of market- and firm-level control variables established in the existing literature. Such predictability complements that of the leading state variable—the leverage ratio—and strengthens significantly with a lower firm credit rating, longer credit contract maturity, and model-free implied variance. We provide further evidence that (1) the variance risk premium has a cleaner systematic component than implied variance or expected variance, (2) the cross-section of firms’ variance risk premia capture systematic variance risk in a stronger way than firms’ equity returns in capturing market return risk, and (3) a structural model with stochastic volatility can reproduce the predictability pattern of variance risk premia for credit spreads.     

Noise, equity prices, and hedging: A new approach

The existence of noise trading in equity markets has possible economic implications for arbitrage, and asset pricing. In terms of pricing, noise trading can lead to excess volatility which has been shown to influence the value of options and futures. Furthermore, option research shows that modeling volatility leads to improved hedging performance. To this end, we derive a general hedging model for equity index futures in the presence of noise trading. Our analysis shows how the level and dynamics of noise trading should influence a hedger's behavior. Finally, we empirically test our model using the NASDAQ-100 index futures and FTSE 100 index futures over the period of January 1998 to May 2003.