Pricing American options with stochastic volatility: Evidence from S&P 500 futures options

This article is the first attempt to test empirically a numerical solution to price American options under stochastic volatility. The model allows for a mean‐reverting stochastic‐volatility process with non‐zero risk premium for the volatility risk and correlation with the underlying process. A general solution of risk‐neutral probabilities and price movements is derived, which avoids the common negative‐probability problem in numerical‐option pricing with stochastic volatility. The empirical test shows clear evidence supporting the occurrence of stochastic volatility. The stochastic‐volatility model outperforms the constant‐volatility model by producing smaller bias and better goodness of fit in both the in‐sample and out‐of‐sample test. It not only eliminates systematic moneyness bias produced by the constant‐volatility model, but also has better prediction power. In addition, both models perform well in the dynamic intraday hedging test. However, the constant‐volatility model seems to have a slightly better hedging effectiveness. The profitability test shows that the stochastic volatility is able to capture statistically significant profits while the constant volatility model produces losses. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:625–659, 2000     

The information content of the S&P 500 index and VIX options on the dynamics of the S&P 500 index

Given that both S&P 500 index and VIX options essentially contain information about the future dynamics of the S&P 500 index, in this study, we set out to empirically investigate the informational roles played by these two option markets with regard to the prediction of returns, volatility, and density in the S&P 500 index. Our results reveal that the information content implied from these two option markets is not identical. In addition to the information extracted from the S&P 500 index options, all of the predictions for the S&P 500 index are significantly improved by the information recovered from the VIX options. Our findings are robust to various measures of realized volatility and methods of density evaluation. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Dynamic Dependence Between Liquidity and the S&P 500 Index Futures‐Cash Basis

Roll, Schwartz, and Subrahmanyam (2007) investigate the linear relationship between stock market liquidity and index futures‐cash basis. We extend their work and examine nonlinear relationship between the two variables of interests, in particular, tail dependence. We find that the tail dependence is asymmetric and varies significantly over times. The lower tail dependence between changes in (il) liquidity measured by bid–ask spread of S&P 500 index and changes in absolute value of S&P 500 index futures‐cash basis is almost zero and the upper tail dependence is positive and significantly different from zero. The results suggest that an increase in liquidity is not always associated with a decrease in basis. However, a reduction in liquidity is significantly associated with an increase in basis. At the extreme situation, the link between changes in basis and changes in liquidity can break down. Arbitrage profits cannot be realized and hedging becomes less effective. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:327‐342, 2013     

Is volatility risk priced in the securities market? Evidence from S&P 500 index options

The authors examine whether volatility risk is a priced risk factor in securities returns. Zero‐beta at‐the‐money straddle returns of the S&P 500 index are used to measure volatility risk. It is demonstrated that volatility risk captures time variation in the stochastic discount factor. The results suggest that straddle returns are important conditioning variables in asset pricing, and investors use straddle returns when forming their expectations about securities returns. One interesting finding is that different classes of firms react differently to volatility risk. For example, small firms and value firms have negative and significant volatility coefficients, whereas big firms and growth firms have positive and significant volatility coefficients during high‐volatility periods, indicating that investors see these latter firms as hedges against volatile states of the economy. Overall, these findings have important implications for portfolio formation, risk management, and hedging strategies. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:617–642, 2007     

Optimal No‐Arbitrage Bounds on S&P 500 Index Options and the Volatility Smile

This article shows that the volatility smile is not necessarily inconsistent with the Black–Scholes analysis. Specifically, when transaction costs are present, the absence of arbitrage opportunities does not dictate that there exists a unique price for an option. Rather, there exists a range of prices within which the option's price may fall and still be consistent with the Black–Scholes arbitrage pricing argument. This article uses a linear program (LP) cast in a binomial framework to determine the smallest possible range of prices for Standard & Poor's 500 Index options that are consistent with no arbitrage in the presence of transaction costs. The LP method employs dynamic trading in the underlying and risk‐free assets as well as fixed positions in other options that trade on the same underlying security. One‐way transaction‐cost levels on the index, inclusive of the bid–ask spread, would have to be below six basis points for deviations from Black–Scholes pricing to present an arbitrage opportunity. Monte Carlo simulations are employed to assess the hedging error induced with a 12‐period binomial model to approximate a continuous‐time geometric Brownian motion. Once the risk caused by the hedging error is accounted for, transaction costs have to be well below three basis points for the arbitrage opportunity to be profitable two times out of five. This analysis indicates that market prices that deviate from those given by a constant‐volatility option model, such as the Black–Scholes model, can be consistent with the absence of arbitrage in the presence of transaction costs. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1151–1179, 2001     

Has the introduction of S&P 500 ETF options led to improvements in price discovery of SPDRs?

This study sets out to investigate trading in Standard and Poor's Depository Receipt Trust Series I (SPDR) options and the impact on the price‐discovery process of SPDRs. The empirical results reveal a significant rise in liquidity within the SPDR market following the introduction of SPDR options. Furthermore, the results also show that the introduction of SPDR options has led to a significant improvement in the information share of SPDRs, and that the contribution of SPDRs to price discovery has become very close to that of E‐mini index futures. These findings imply that developments in the derivatives market can lead to improvements in market quality, including the level of liquidity and price discovery of the underlying securities. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:683–711, 2012     

Pricing and hedging S&P 500 index options with Hermite polynomial approximation: empirical tests of Madan and Milne's model

The universal use of the Black and Scholes option pricing model to value a wide range of option contracts partly accounts for the almost systematic use of Gaussian distributions in finance. Empirical studies, however, suggest that there is an information content beyond the second moment of the distribution that must be taken into consideration.This article applies a Hermite polynomial-based model developed by Madan and Milne (1994) to an investigation of S&P 500 index option prices from the CBOE when the distribution of the underlying index is unknown. The model enables us to incorporate the non-normal skewness and kurtosis effects empirically observed in option-implied distributions of index returns. Out-of-sample tests confirm that the model outperforms Black and Scholes in terms of pricing and hedging. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 735–758, 1999     

Is investor misreaction economically significant? Evidence from short‐ and long‐term S&P 500 index options

Several recent studies present evidence of investor misreaction in the options market. Although the interpretation of their results is still controversial, the important question of economic significance has not been fully addressed. Here this gap is addressed by formulating regression‐based tests to identify misreaction and its duration and constructing trading strategies to exploit the empirical patterns of misreaction. Regular S&P 500 index options and long‐dated S&P 500 LEAPS are used to find an underreaction that on average dissipates over the course of 3 trading days and an increasing misreaction that peaks after four consecutive daily variance shocks of the same sign. Option trading strategies based on these findings produce economically significant abnormal returns in the range of 1–3% per day. However, they are not profitable in the presence of transaction costs. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:717–752, 2005     

Measuring and forecasting S&P 500 index‐futures volatility using high‐frequency data

In the 24‐hr foreign exchange market, Andersen and Bollerslev measure and forecast volatility using intraday returns rather than daily returns. Trading in equity markets only occurs during part of the day, and volatility during nontrading hours may differ from the volatility during trading hours. This paper compares various measures and forecasts of volatility in equity markets. In the absence of overnight trading it is shown that the daily volatility is best measured by the sum of intraday squared 5‐min returns, excluding the overnight return. In the absence of overnight trading, the best daily forecast of volatility is produced by modeling overnight volatility differently from intraday volatility. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:497–518, 2002     

Early exercise of American put options: Investor rationality on the Swedish equity options market

Using Swedish equity option data, this study investigates how well the actual exercise behavior of American put options corresponds to the early exercise rules. The optimal exercise strategy is established in two ways. First, the critical exercise price, above which a put option should be exercised early, is computed and compared to the actual exercise price. Second, the exercise value of the option is compared to its market bid price. The results show that most early exercise decisions conform to rational exercise behavior, even though a large number of failures to exercise are found. Most of the faulty exercises can also be discarded after a sensitivity analysis, although several failures to exercise are considered irrational, even after taking transaction costs into account. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:167–188, 2000     

Indian equity options: Smile,risk premiums,and efficiency

We study the pricing of equity options in India which is one of the world's largest options markets. Our findings are supportive of market efficiency: A parsimonious smile-adjusted Black model fits option prices well, and the implied volatility (IV) has incremental predictive power for future volatility. However, the risk premium embedded in IV for Single Stock Options appears to be higher than in other markets. The study suggests that even a very liquid market with substantial participation of global institutional investors can have structural features that lead to systematic departures from the behavior of a fully rational market while being “microefficient.”