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Stocks with large increases in call (put) implied volatilities over the previous month tend to have high (low) future returns. Sorting stocks ranked into decile portfolios by past call implied volatilities produces spreads in average returns of approximately 1% per month, and the return differences persist up to six months. The cross section of stock returns also predicts option implied volatilities, with stocks with high past returns tending to have call and put option contracts that exhibit increases in implied volatility over the next month, but with decreasing realized volatility. These predictability patterns are consistent with rational models of informed trading.

This paper examines expected option returns in the context of mainstream asset-pricing theory. Under mild assumptions, expected call returns exceed those of the underlying security and increase with the strike price. Likewise, expected put returns are below the risk-free rate and increase with the strike price. S&P index option returns consistently exhibit these characteristics. Under stronger assumptions, expected option returns vary linearly with option betas. However, zero-beta, at-the-money straddle positions produce average losses of approximately three percent per week. This suggests that some additional factor, such as systematic stochastic volatility, is priced in option returns.

Recent evidence shows that option volatility skews and volatility spreads between call and put options predict equity returns. This study investigates whether such predictive ability is driven by option traders' information advantage.We examine the predictive ability of volatility skews and volatility spreads around significant information events including earnings announcements, other firm-specific information events, and events that trigger significant market reactions. Consistent with option traders having an information advantage relative to equity traders before information events, we find that the option measures immediately before these events have higher predictive ability for short-term event returns than they do in a more dated window or before a randomly selected pseudo-event. We also find that option measures have predictive ability after information events. However, this predictive ability holds only for unscheduled corporate announcements, which suggests that, relative to equity traders, option traders have superior ability to process less anticipated information.

Informed traders may prefer the options market to the stock market for reasons including the leverage effect, transaction costs, restrictions on short sale. Many studies try to predict future returns of stocks using informed traders' behavior in the options market. In this study, we examine whether the trading volume ratios of single stock options have the predictive power for future returns of the underlying stock. By analyzing the stock price responses to the “preliminary announcement of performance” of 36 underlying stocks on the Korea Exchange from November 2014 to March 2021 and the trading volume of options written on those stocks, we investigate the relation between the option ratios, which are the call option volume to put option volume ratio (C/P ratio) and the option volume to stock volume ratio (O/S ratio), and the future returns of the underlying stock. We also examine which ratio is better in predicting the future returns. The authors found that both option ratios showed the statistically significant predictability about future returns of the underlying stock and that the return predictability of the O/S ratio is more robust than that of the C/P ratio. This study shows that indicators generated in the options market can be used to predict future underlying stock returns. Further, the findings of this study contributed to a dearth of literature pertaining to single stock options. The results suggest that the single stock options market is efficient and influences the price discovery in the stock market.

U.S. exchange-traded stock options are exercisable before expiration. While put options should frequently be exercised early to earn interest, they are not. In this paper, we derive an early exercise decision rule and then examine actual exercise behavior during the period January 1996 through September 2008. We find that more than 3.96 million puts that should have been exercised early remain unexercised, representing over 3.7% of all outstanding puts. We also find that failure to exercise cost put option holders $1.9 billion in forgone interest income and that this interest is systematically captured by market makers and proprietary firms.

Brownian motion and normal distribution have been widely used in the Black–Scholes option–pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called \"volatility smile\" in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jump–diffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of option–pricing problems, including call and put options, interest rate derivatives, and path–dependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.

This article presents a simple yet powerful new approach for approximating the value of American options by simulation. The key to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation. This makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniques cannot be used. We illustrate this technique with several realistic examples including valuing an option when the underlying asset follows a jump-diffusion process and valuing an American swaption in a 20-factor string model of the term structure.

We develop a simple robust link between deep out-of-the-money American put options on a company's stock and a credit insurance contract on the company's bond. We assume that the stock price stays above a barrier B before default but drops below a lower barrier A after default, thus generating a default corridor [A, B] that the stock price can never enter. Given the presence of this default corridor, a spread between two co-terminal American put options struck within the corridor replicates a pure credit contract, paying off when and only when default occurs prior to the option expiry.

Previous research concludes that options are mispriced based on the high average returns, CAPM alphas, and Sharpé ratios of various put selling strategies. One criticism of these conclusions is that these benchmarks are ill suited to handle the extreme statistical nature of option returns generated by nonlinear payoffs. We propose an alternative way to evaluate the statistical significance of option returns by comparing historical statistics to those generated by option pricing models. The most puzzling finding in the existing literature, the large returns to writing out-of-the-money puts, is not inconsistent (i.e.,is statistically insignificant) relative to the Black-Scholes model or the Heston stochastic volatility model due to the extreme sampling uncertainty associated with put returns. This sampling problem can largely be alleviated by analyzing market-neutral portfolios such as straddles or deltahedged returns. The returns on these portfolios can be explained by jump risk premiums and estimation risk.

In this paper, an implicit scheme is proposed to solve a parabolic variational inequality arising from the American put options. The discretization leads to a class of discrete elliptic variational inequalities. Well-posedness, including existence, uniqueness, comparison principle, and stability of the discrete elliptic variational inequality is established. A simple and efficient algorithm to solve the implicit discretized variational inequality is discovered. The novelty here is an explicit formula for the optimal exercise boundary. An improved algorithm is also presented to eliminate the singularity near the time to expiry. Numerical examples are carried out to show the accuracy and efficiency of the proposed algorithms.