Option Returns Research Articles

Stock Return Autocorrelations and Expected Option Returns

We show that the return autocorrelation of underlying stock is an important determinant of expected equity option returns. Using an extended Black-Scholes model incorporating the presence of stock return autocorrelation, we demonstrate that expected returns of both call and put options are increasing in the return autocorrelation coefficient of the underlying stock. Consistent with this insight, we find strong empirical support in the cross-section of average returns of equity options. Our paper highlights the necessity to control for stock return autocorrelation when studying option return predictability. This paper was accepted by Agostino Capponi, finance. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03071 .

The risk and return of equity and credit index options

We develop a structural credit risk model, which allows us to price equity/credit indices and their options through the asset dynamics of index constituents. We estimate the model via MLE and find that equity and credit index option prices are well explained out-of-sample. Contrary to recent empirical findings, the two option markets are not inconsistently priced through the lens of our model. Returns on both options, while extreme, do not indicate any evidence of mispricing. Our analysis suggests that jointly addressing the pricing of various instruments requires properly attributing three different sources of systematic risk: asset, variance, and jump risks.

Asymmetry and the Cross-section of Option Returns

We propose a novel measure of upside asymmetry based on probability density function that utilizes information from the distribution of option returns. Our analysis of U.S. option data reveals a positive cross-sectional relationship between the upside asymmetry (RML) and subsequent option returns. This relationship cannot be explained by stock or option characteristics studied in previous literature and do not reverse in the following months. Additionally, the relationship is stronger among firms with higher costs of arbitrage. RML robustly predicts future realized and implied volatilities after controlling for historical volatility and lagged implied volatility.

Option trading volume and the cross-section of option returns

This paper examines a novel pattern of option return predictability. Specifically, we find option trading volume negatively and significantly predicts the cross-section of delta-hedged option returns. Our portfolio strategies of option trading volume yield significant returns in options across different moneyness and time to maturity. Furthermore, the evidence shows that market capitalization and idiosyncratic volatility are able to explain the predictability of option trading volume on option returns. Our results are robust to alternative measures of option returns and option subsamples.

The asymmetry in day and night option returns: Evidence from an emerging market

AbstractDelta‐hedged option selling strategies typically yield positive returns, owing to the volatility risk premium embedded in the option price. Recent research based on S&P 500 options has found a day–night asymmetry in option returns. We find a similar disparity in the returns for short Nifty option strategies. Positive and significant overnight option returns are accompanied by negative intraday returns. The day–night asymmetry is robust across option categories and subsamples but weaker on days with significant jumps in the underlying. We confirm that the variance risk premium earned by option sellers is mainly a reward for overnight risk.

Asymmetry in option implied volatility and yield: Evidence from China's ETF options market ,

This paper analyzes the changes in implied volatility and positive/negative returns of options using data from the China 50 ETF options and the CSI 300 ETF options. We employs quantile regression and least squares methods to explore the asymmetry between volatility and returns in the Chinese options market under different market capacities and time periods. The study reveals significant volatility-return asymmetry in both the China 50 ETF and the CSI 300 ETF markets, indicating that negative returns have a stronger impact on implied volatility changes than positive returns during the same period. Additionally, in both markets, the lagged changes in implied volatility are found to be an important determinant of current implied volatility changes. Differences in the underlying assets covered by the options and investor structures may influence the mechanisms of implied volatility changes and the asymmetry between volatility and returns. Furthermore, since the outbreak of the pandemic, investors' sensitivity and caution toward market information may weaken the asymmetry between volatility and returns.

EXPRESS: A Suite of Metrics to Understand Return on Investments in Customers

When making customer investments under resource constraints, approaches based upon next period accounting profit fail to consider the long-term. As we show, marketers’ suggested solutions often omit retention spend from the customer investment, understating the required committed marketing spend. Unfortunately, the logical outcome is a focus on the wrong (high retention cost) customers. Marketers may even try to acquire customers as long-term investments, then refuse to invest in their retention. We develop a suite of metrics to consider investments in customers, including customer return on investment (CROI), acquisition return on investment (AROI), retention return on investment (RROI), and option return on investment (OROI). Using the suite can help marketers calculate meaningful ROIs, even when they cannot clearly differentiate between acquisition and retention marketing spend. Our key contributions show how to assess the value of customer investments and treat customer acquisition as gaining an option to spend on retention. We outline the connection between the metrics, detail when each are appropriate, and show how to apply the suite of metrics to a variety of simulated datasets.

Considering momentum spillover effects via graph neural network in option pricing

AbstractTraditional options pricing relies on underlying asset volatility and contract properties. However, asset volatility is affected by the “lead–lag effects,” known as the “momentum spillover effect.” To address this, we propose a proxy measuring correlated options' influence based on maturity date. Findings indicate that 1‐day‐lagged proxy indicators positively impact option returns. Furthermore, to capture the dynamic effects of correlated options, we introduce a deep graph neural network‐based model (GNN‐MS). Empirical results on Shanghai Stock Exchange 50 exchange‐traded fund options reveal GNN‐MS significantly outperforms classics, enhancing root‐mean‐square error by at least 8.81%. This study provides novel insights into option pricing considering momentum spillover effects.

Modeling Conditional Factor Risk Premia Implied by Index Option Returns

ABSTRACTWe propose a novel factor model for option returns. Option exposures are estimated nonparametrically, and factor risk premia can vary nonlinearly with states. The model is estimated using regressions with minimal assumptions on factor and option return dynamics. We estimate the model using index options to characterize the conditional risk premia for factors of interest, such as the market return, market variance, tail and intermediary risk factors, higher moments, and the VIX term structure slope. Together, market return and variance explain more than 90% of option return variation. Unconditionally, the magnitude of the variance risk premium is plausible. It displays pronounced time variation, spikes during crises, and always has the expected sign.

Contingent Claims and Hedging of Credit Risk with Equity Options

Abstract Using contingent-claims valuation, we introduce novel hedge ratios for credit exposures using put options. Option hedge ratios are generally in line with the empirical sensitivities of credit spread changes to put option returns and, relative to stock hedge ratios, produce further reductions in volatility for a portfolio of North American firms. We show that option hedge ratios capture option-specific credit exposure related to the VIX index and the default spread, which is unaccounted for by Merton’s (1974) equity hedge ratios alone. Combining stocks and put options for credit risk hedging can be done effectively using the volatility smirk. (JEL E43, E44, G10)

A Study on Futures and Options in Derivative

Examining the processes that influence risk and return profiles for market players, this research probes the complicated world of futures and options markets. This study takes a holistic view of the topic, delving into market behavior studies, quantitative models, and historical data to provide a detailed picture of how financial market options and futures work. Part one of the research delves into the theory of futures and options, explaining how these derivative products work. It delves into the ways these monetary instruments help hedgers manage risk, investors make speculative bets, and arbitrageurs use them strategically. Futures and options are both distinguished from one another in the research, with the study elaborating on the specific features and consequences of each. In the future, the study will examine the volatility patterns and risk-adjusted returns of several asset classes' futures and options markets. The research intends to find patterns and outliers that have affected the risk-reward environment for market players by looking at case studies and past market occurrences. Option pricing models and their use in analyzing market expectations and implied volatility are further explored in the paper. The study investigates the effect of market mood on option pricing and uses empirical analysis to assess how well option pricing models capture market dynamics.

The Impact of the Russo-Ukrainian War on the Risk and Return of TAIEX

Abstract This study examines the impact of the Russia-Ukraine war (RUW) on the dynamic of TAIEX options' risk-return profile. Since the outbreak of the war on February 24, 2022, global economic sanctions have disrupted the world economy. Soaring energy and food prices and supply shortages have suppressed global economic growth, leading to rising inflation. Financial markets have reacted to the shocks caused by this war, thus intensifying the volatility of options markets. This study utilizes Hsu's (2013) option return models to investigate the impacts of how the war influences the TAIEX options' risk-return profile, including PDFs, profitability, and expected returns. The contributions of this paper are two-fold: It is the first paper on the (RUW) on the options markets; additionally, we demonstrate theoretically and empirically that the normality assumption of simple arithmetic returns is acceptable, making the Hsu's (2013) option return models more robust. The results indicate that the war has significantly affected and altered the PDFs of option returns, expected option returns, and volatility after the war. However, both theoretically and empirically shows that, despite the challenges posed by the war, put options trading during this period has been profitable. Keywords: Russo-Ukrainian War, TAIEX options, Option return model, Risk/Return Profile.

Expected Index Option Return: What Can We Learn From Macro and Anomalies ?

Expected Index Option Return: What Can We Learn From Macro and Anomalies ?

Option Pricing Practices Based on the B-S-M Model in Carbon Markets

Carbon trading refers to the buying and selling of carbon emission allowances, stimulating businesses to adopt low-carbon development strategies through price signals. By allocating limited emission allowances to emitters, the carbon market encourages the reduction of carbon emissions to achieve emission reduction targets. Market participants can compensate for emissions exceeding their own quotas by trading carbon emission allowances, thus minimizing the cost of emission reductions. The Chinese carbon market has a large trading volume and numerous development opportunities, but currently, the carbon financial market is not fully open. In comparison to Western countries, China lacks carbon emission derivatives such as futures, options, and swap contracts. The risk and return of carbon emission allowance options are estimated and managed using the B-S-M option pricing model. This paper utilizes data from the Shenzhen Carbon Emission Allowance Exchange as a sample to conduct option pricing practices for carbon emission allowances using the B-S-M model. The aim is to promote research and development in the carbon emission allowance market and contribute to the achievement of emission reduction goals.

Is Firm-Level Political Risk Priced in the Equity Option Market?

Abstract We find a negative relation between firm-level political risk and future delta-hedged equity option returns. A quasi-natural experiment based on Brexit corroborates this finding since after the referendum there is a decrease in the option returns of the positive-Brexit exposure firms. The predictability is driven by the jump risk component of political uncertainty, is more pronounced in periods of high intermediary constraints, and is stronger among high-demand pressure options but weaker among politically active firms. Finally, consistent with a risk-based explanation, investors of options on politically risky firms are compensated with high returns when major unexpected political shocks happen. (JEL G13, G18)

Option Momentum

ABSTRACTThis paper investigates the performance of option investments across different stocks by computing monthly returns on at‐the‐money straddles on individual equities. We find that options with high historical returns continue to significantly outperform options with low historical returns over horizons ranging from 6 to 36 months. This phenomenon is robust to including out‐of‐the‐money options or delta‐hedging the returns. Unlike stock momentum, option return continuation is not followed by long‐run reversal. Significant returns remain after factor risk adjustment and after controlling for implied volatility and other characteristics. Across stocks, trading costs are unrelated to the magnitude of momentum profits.

Default Risk and Option Returns

This paper studies the effects of default risk on expected equity option returns. In the cross-section, expected delta-hedged equity option returns have a negative relation with default risk measured by credit ratings or default probability. In the time series, credit rating downgrades (upgrades) lead to a decrease (increase) in the firm’s delta-hedged option return. Our results are consistent with a stylized capital structure model in which the negative relation between option returns and default risk is driven by firm leverage and asset volatility. This paper was accepted by Lukas Schmid, finance. Funding: A. Vasquez thanks the Asociación Mexicana de Cultura A.C. for financial support. Supplemental Material: The online appendix and data are available at https://doi.org/10.1287/mnsc.2023.4796 .

Option Return Predictability with Machine Learning and Big Data

Abstract Drawing upon more than 12 million observations over the period from 1996 to 2020, we find that allowing for nonlinearities significantly increases the out-of-sample performance of option and stock characteristics in predicting future option returns. The nonlinear machine learning models generate statistically and economically sizable profits in the long-short portfolios of equity options even after accounting for transaction costs. Although option-based characteristics are the most important standalone predictors, stock-based measures offer substantial incremental predictive power when considered alongside option-based characteristics. Finally, we provide compelling evidence that option return predictability is driven by informational frictions and option mispricing. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Limits of Arbitrage and Primary Risk-Taking in Derivative Securities

Abstract Classic option pricing theory values a derivative contract via dynamic delta hedging and treating the contract as redundant relative to the underlying security. Dynamic delta hedging proves highly effective in practice, but the remaining risk is still large because of the practical limits of arbitrage. Derivatives can play primary roles in risk allocation. This paper quantifies the percentage variance reduction of delta hedging on U.S. stock options, proposes a top-down return attribution framework to identify the remaining risk sources of the delta-hedged option investment, and constructs a statistical return factor model to explain the variations of the delta-hedged option returns. (JEL C13, C51, G12, G13)

Firm Growth Potential and Option Returns

This paper shows that firm growth potential – representing a firm's yet-unexercised growth opportunities – is associated with option overpricing and low future delta-hedged option returns. We provide an explanation of this phenomenon based on the idea that retail investors exert buying pressure and tend to overpay for the call options of growth-oriented firms because they overestimate the potential profits arising from the return skewness of the underlying stocks. We further show that the effect is stronger among stocks that are more likely to exhibit high skewness, are more prone to limits-to-arbitrage and are more exposed to informational frictions.