Equity Options Research Articles

Optimal Market Completion through Financial Derivatives with Applications to Volatility Risk

This paper investigates the optimal choices of financial derivatives to complete a financial market in the framework of stochastic volatility (SV) models. We first introduce an efficient and accurate simulation-based method applicable to generalized diffusion models to approximate the optimal derivatives-based portfolio strategy. We build upon a double optimization approach, i.e., expected utility maximization and risk exposure minimization, already proposed in the literature, demonstrating that strangle options are the best choices for market completion within equity options. They lead to lower investors’ risk exposure for a wide range of strikes compared to the lesser flexibility of calls, puts, and strangles. Furthermore, we explore the benefit of using volatility index derivatives and conclude that they could be more convenient substitutes when short-term maturity equity options are not available.

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 .

A local volatility correction to mean-reverting stochastic volatility model for pricing derivatives

Generally, in the real market, empirical findings suggest that either local volatility (LV) or stochastic volatility (SV) models have a limit to capture the full dynamics and geometry of the implied volatilities of the given equity options. In this study, to overcome the disadvantage of such LV and SV models, we propose a special type of hybrid stochastic-local volatility (SLV∗) model in which the volatility is given by the squared logarithmic function of the underlying asset price added to a function of a fast mean-reverting process. By making use of asymptotic analysis and Mellin transform, we derive analytic pricing formulas for European derivatives with both smooth and non-smooth payoffs under the SLV∗ model. We run numerical experiments to verify the accuracy of the pricing formulas using a Monte-Carlo simulation method and to display that the proposed new model fits the geometry of the market implied volatility more closely than other models such as the Heston model, the stochastic elasticity of variance (SEV) model, the hybrid stochastic and CEV type local volatility (SVCEV) model and the multiscale stochastic volatility (MSV) model, especially for short time-to-maturity options.

Very Noisy Option Prices and Inference Regarding the Volatility Risk Premium

ABSTRACTThe stylized fact that volatility is not priced in individual equity options does not withstand scrutiny. First, we show that the average return of heavily traded deep out‐of‐the‐money call options on stocks is −116 basis points per day. Second, Fama‐MacBeth estimates of the volatility risk premium in stock options are similar to those in S&P 500 Index call options. Third, the mean return of heavily traded delta‐hedged at‐the‐money calls (puts) is −23 (−30) basis points. Fourth, the variance risk premium in stock options is negative. Our analysis highlights the importance of microstructure biases and robustness in empirical work with options.

Pricing cryptocurrency options with machine learning regression for handling market volatility

Pricing cryptocurrency options, crucial for risk management and market stabilization, presents unique challenges due to specific underlying dynamics like the inversion of the leverage effect. Classical option pricing models like Black–Scholes and Heston struggle to address these dynamics due to their set of assumptions. This study introduces machine learning models for options pricing, specifically regression-tree methods. A data-driven machine learning model can incorporate high-frequency volatility estimators into the input set to enhance pricing accuracy. By integrating these estimators, machine learning models can capture the complex dynamics of cryptocurrency markets more effectively than classical pricing approaches. The comparative analysis reveals that equity options are easier to price, clearly indicating inefficiencies in the cryptocurrency option market, which confirms the challenges in achieving accurate pricing. Our results highlight the effectiveness of machine learning models in adapting to the unique characteristics of emerging asset classes, suggesting a shift towards more data-oriented pricing methodologies

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)

Excess cash and equity option liquidity

AbstractWe examine the relation between excess corporate cash holdings and equity option market liquidity from January 3, 2005 to December 31, 2019. We show that the level of cash reserve in excess of what can be captured by firm characteristics significantly explains stock option liquidity. Trading volume and option open interest increase in companies with a higher magnitude of excess cash, whereas the bid–ask spreads of stock options decline in excess cash. Our findings confirm the theoretical prediction that excess cash improves option market liquidity as it reduces adverse selection problems caused by uncertainty in firm valuations. This relation remains more pronounced with put options, out‐of‐the‐money contracts, and short‐maturity contracts. In addition, excess cash has a stronger impact on option liquidity within firms that have a greater degree of informed trading and during high‐volatility periods in financial markets. Our results show that when uncertainty about firm prospects rises, excess cash becomes more valuable and affects option market liquidity.

Implementing Intraday Model-Free Implied Volatility for Individual Equities to Analyze the Return–Volatility Relationship

We implement the VIX methodology on intraday data of a large set of individual equity options. We thereby consider approaches based on monthly option contracts, weekly option contracts, and a cubic spline interpolation approach. Relying on 1 min, 10 min, and 60 min model-free implied volatility measures, we empirically examine the individual equity return–volatility relationship on the intraday level using quantile regressions. The results confirm a negative contemporaneous link between stock returns and volatility, which is more pronounced in the tails of the distributions. Our findings hint at behavioral biases causing the asymmetric return–volatility link rather than the leverage and volatility-feedback effects.

THE ROLE OF DIGITAL CROWDFUNDING PLATFORMS IN DEMOCRATIZING GLOBAL ENTREPRENEURSHIP

Digital platforms for crowdfunding have emerged as a breakthrough in the field of entrepreneurial finance, offering a digital channel for democratizing capital access on a worldwide level. This study demonstrates how crowdfunding platforms assist impending firms in managing worldwide finances’ intricacies while surpassing institutional and cultural obstacles through practical occurrences. This paper closely examines the social impact of these platforms as well as legislative frameworks, cultural norms, key performance indicators, and platform features. An important factor determining whether or not a crowdfunding site succeeds is its design and characteristics. The study points out that some platform features like reward tiers, equity options, and community-building tools can have an impact on investor involvement and the outcome of campaigns. Furthermore, the research showcases that crowdfunding is increasingly being used as a technique to enhance diversity and inclusion, especially among unrepre-sented business owners including females and ethnic minorities. The study finds optimal practices and typical problems in obtaining foreign finance by examining the success rates of businesses and how these platforms assist disadvantaged entrepreneurs. The results are intended to contribute to a more inclusive entrepreneurial environment by exposing tactics that business owners can use to optimize the potential of crowdfunding in various geographic areas. In essence, this paper intends to give practical information that can be used by politicians, private-public partners, and other stakeholders in business to promote an entrepreneurship environment that is fairer and more sustainable.

Decomposing Informed Trading in Equity Options

Decomposing Informed Trading in Equity Options

A Hybrid Model for Equity Option with Heston and Forward Market Model

A Hybrid Model for Equity Option with Heston and Forward Market Model

Understanding Equity Option Returns in the Chinese Market

Understanding Equity Option Returns in the Chinese Market

A Bayesian SDF for Equity Options

A Bayesian SDF for Equity Options

A Simplified Approach to the Pricing of Vulnerable Options with Two Underlying Assets in an Intensity-Based Model

In this paper, we study a simplified approach to determine the pricing formula for vulnerable options involving two correlated underlying assets. We utilize an intensity-based model to describe the credit risk associated with these vulnerable options. Without the change of measure technique, we derive pricing formulas for vulnerable options involving two underlying assets based on the probabilistic approach. We provide closed-form pricing formulas for two specific types of options: the vulnerable exchange option and the vulnerable foreign equity option. Finally, we present numerical results to demonstrate the accuracy of our formulas using the Monte-Carlo method and the effect of various parameters on the price of options.

Gender Equity in Land Distribution and Food Poverty: Evidence Using Cameroonian Data

ABSTRACT This article examines the food poverty impacts of gender equity in the distribution of land for productive activities using the most recent Cameroon household consumption survey data conducted in 2014. It employs the Blinder–Oaxaca decomposition to investigate the existence of a gender-land inequality gap and the factual and counterfactual regression analyses and Foster, Greer, and Thorbecke class of poverty measures to tease out the food poverty impacts of gender equity options in land distribution. The article’s major contribution to literature is in disintegrating the food poverty impacts of two salient policy packages—the policy package which gives each woman without land at least one hectare of land to exploit for productive activities relative to that which gives women the same rights to own land as their male counterparts. The results indicated that policy efforts to ensure a female head without land has at least a piece of land for productive purposes (referred to as equity-within) are more potent in alleviating food poverty compared to those that promote gender equality in the distribution (referred to as equity-between) of land for productive purposes. These results have implications for policy measures to enhance women’s roles as agricultural producers, especially with respect to ownership of land for productive use.

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)

Options in Derivative Market: A Study on Working and Trends in Option Contracts

Indian derivative market is very vast market. Many assets,securities, products and services are offered in derivative market to the various traders and investors. In India derivative products are offered by both BSE (Bombay stock exchange) and NSE (national stock exchange). Derivatives are classified into two parts Commodity derivatives and financial derivatives. Commodity derivatives are dealt in commodities like soybean, turmeric, oats corns. Financial derivatives include securities, bonds, treasure, foreign exchange, stock index etc. All financial derivatives are performed with the help of futures; options .this paper manly concentrates option contracts. NSE and BSE are also dealt in futures and options. This paper only considers the trends and working of option contracts in BSE. Option contracts are a right to buy or sell security on or before expiry of period at a predetermined price which is called strike price. Options are not an obligation. Call option and put option are two basic positions which are used by trader to manage the risk of buying and selling of underlying asset or security. This paper shows the working and trends of options as indexed options and equity options in BSE.

Assessing the Impact of Credit Risk on Equity Options via Information Contents and Compound Options

This work aims to develop a measure of how much credit risk is priced into equity options. Such a measure appears particularly appealing when applied to a portfolio of equity options, as it allows for the factoring in of firm-specific default dynamics, thus producing a comparable statistic across different equities. As a matter of fact, comparing options written on different equities based on their moneyness does offer much guidance in understanding which option offers a better hedging against default. Our newly-introduced measure aims to fulfil this gap: it allows us to rank options written on different names based on the amount of default risk they carry, incorporating firm-specific characteristics such as leverage and asset risk. After having computed this measure using data from the US market, several empirical tests confirm the economic intuition of puts being more sensitive to changes in the default risk as well as a good integration of the CDS and option markets. We further document cross-sectional sectorial differences based on the industry the companies operate in. Moreover, we show that this newly-introduced measure displays forecasting power in explaining future changes in the skew of long-term maturity options.

Leveraging prices from credit and equity option markets for portfolio risk management

AbstractThis study presents a firm‐specific methodology for extracting implied default intensities and recovery rates jointly from unit recovery claim prices—backed by out‐of‐the‐money put options—and credit default swap premiums, therefore providing time‐varying and market‐consistent views of credit risk at the individual level. We apply the procedure to about 400 firms spanning different sectors of the US economy between 2003 and 2019. The main determinants of default intensities and recovery rates are analyzed with statistical and machine learning methods linking default risk and credit losses to market, sector, and individual variables. Consistent with the literature, we find that individual volatility, leverage, and corporate bond market determinants are key factors explaining the implied default intensities and recovery rates. Then, we apply the framework in the context of credit risk management in applications, like, market‐consistent credit value‐at‐risk calculation and stress testing.

Robustness and sensitivity analyses of rough Volterra stochastic volatility models

In this paper, we analyze the robustness and sensitivity of various continuous-time rough Volterra stochastic volatility models in relation to the process of market calibration. Model robustness is examined from two perspectives: the sensitivity of option price estimates and the sensitivity of parameter estimates to changes in the option data structure. The following sensitivity analysis consists of statistical tests to determine whether a given studied model is sensitive to changes in the option data structure based on the distribution of parameter estimates. Empirical study is performed on a data set consisting of Apple Inc. equity options traded on four different days in April and May 2015. In particular, the results for RFSV, rBergomi and alpha RFSV models are provided and compared to the results for Heston, Bates, and AFSVJD models.