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.     

Asymmetric effects of federal funds target rate changes on S&P100 stock returns,volatilities and correlations

We study the effects of FOMC announcements of federal funds target rate decisions on individual stock returns, volatilities and correlations at the intraday level. For all three characteristics we find that the stock market responds differently to positive and negative target rate surprises. First, the average response to positive surprises (that is, bad news for stocks) is larger. Second, in case of bad news the mere occurrence of a surprise matters most, whereas for good news its magnitude is more important. These new insights are possible due to the use of high-frequency intraday data.     

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.     

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.     

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.     

Factorization of European and American option prices under complete and incomplete markets

In a standard option-pricing model, with continuous-trading and diffusion processes, this paper shows that the price of one European-style option can be factorized into two intuitive components: One robust, X₀, which is priced by arbitrage, and a second, Π₀, which depends on a risk orthogonal to the traded securities. This result implies the following: (1) In an incomplete market, these parts represent the price of a hedging portfolio, which is unique, and a premium, which depends only on the risk premiums associated with the residual risk, respectively. (2) In a complete market, it allows factoring the contribution of the different sources of risk to the final option price. For example, in a stochastic volatility model, we can quantify the impact on the option price of volatility risk relative to market risk, Π₀ and X₀, respectively. Hence, certain misspricings in option markets can be directly related to the premium, Π₀. (3) Moreover, these results extend to American securities, which have a third component – an additional early-exercise premium.     

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 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.     

Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets

We estimate a flexible affine model using an unbalanced panel containing S&P 500 and VIX index returns and option prices and analyze the contribution of VIX options to the model’s in- and out-of-sample performance. We find that they contain valuable information on the risk-neutral conditional distributions of volatility at different time horizons, which is not spanned by the S&P 500 market. This information allows enhanced estimation of the variance risk premium. We gain new insights on the term structure of the variance risk premium, present a trading strategy exploiting these insights, and show how to improve S&P 500 return forecasts.     

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.