Option Market Data Research Articles

The wealth effect of the US net zero announcement

This study investigates the impact of announcements relating to climate change mitigation in the US on the Energy Select Sector ETF (XLE), starting with the US president's net zero emissions announcement on 22 April 2021. We use options market data, in addition to ETF market data, to disaggregate the news effect and value effect of the announcement, finding a positive news effect ($1.65 billion) but a negative value effect (−$2.02 billion). The novel approach proposed by Barraclough et al. (2013) is adopted to identify traders' perceived probability of the achievement of net zero emissions as perceived by investors, finding that investors assigned a 30.9 % probability. Given the difficult journey of the passage of the net zero bill through Congress, we also examine the investors' perceived probability of achievement of later initiatives, as well as their news and value effects. Estimation around the introduction of the Inflation Reduction Act (IRA) in Congress on 27 October 2021 shows a positive news effect ($824.61 million) and an almost analogous, negative value effect (−$2.32 billion). The news effect is a result of the signal to the market that reduces policy uncertainty and enables fossil fuel firms to plan with greater certainty the transition to clean energy and the value effect comes from the fact that some reserves may not be able to be extracted and some assets will be stranded. This study finds if the net zero emissions announcement is successfully enacted as legislation, the value of XLE would be 96.90 % of its current value while a failure to become legislation leads to a rise in the value of XLE to reach 106.90 % of its current value.

OptionNet: A multiscale residual deep learning model with confidence interval to predict option price

Option is an important financial derivative. Accurate option pricing is essential to the development of financial markets. For option pricing, existing time series models and neural networks are difficult to extract multi-scale temporal features from option data, which greatly limits their performance. To solve this problem, we propose a novel deep learning model named as MRC-LSTM-CI. It contains three modules, including Multi-scale Residual CNN module (MRC), Long Short-Term Memory neural network module (LSTM) and confidence interval output module (CI). The proposed model can effectively extract multi-scale features from real market option data, and make interval prediction to provide more information to the decision maker. In addition, the proposed model is further improved using the residual prediction strategy, where the output value is chosen as the residual value between BS theory price and actual market price. Experimental results show that our model has better prediction accuracy than other deep learning models and achieves the state-of-the-art performance.

Belief distortion near 52W high and low: Evidence from Indian equity options market

AbstractWe examine investors' behavioral biases and preferences in the options market near 52‐week high and low (52W‐H/L) using Indian options market data. We document that as the stock price approaches 52W high (low), the skewness of risk‐neutral density (RND), and out‐of‐the‐money (OTM) call volume decreases (increases), while OTM put volume increases (decreases). After crossing the 52W high (low), the skewness of RND and OTM call volume increases (decreases), while OTM put volume decreases (increases). The effects are economically large and significant. Our findings provide evidence consistent with the anchoring theory of belief distortion near 52W‐H/L. There is no evidence of preference distortion, contrary to what prospect theory predicts.

On the Class of Risk Neutral Densities under Heston’s Stochastic Volatility Model for Option Valuation

The celebrated Heston’s stochastic volatility (SV) model for the valuation of European options provides closed form solutions that are given in terms of characteristic functions. However, the numerical calibration of this five-parameter model, which is based on market option data, often remains a daunting task. In this paper, we provide a theoretical solution to the long-standing ‘open problem’ of characterizing the class of risk neutral distributions (RNDs), if any, that satisfy Heston’s SV for option valuation. We prove that the class of scale parameter distributions with mean being the forward spot price satisfies Heston’s solution. Thus, we show that any member of this class could be used for the direct risk neutral valuation of option prices under Heston’s stochastic volatility model. In fact, we also show that any RND with mean being the forward spot price that satisfies Heston’s option valuation solution must also be a member of the scale family of distributions in that mean. As particular examples, we show that under a certain re-parametrization, the one-parameter versions of the log-normal (i.e., Black–Scholes), gamma, and Weibull distributions, along with their respective inverses, are all members of this class and thus, provide explicit RNDs for direct option pricing under Heston’s SV model. We demonstrate the applicability and suitability of these explicit RNDs via exact calculations and Monte Carlo simulations, using already published index data and a calibrated Heston’s model (S&P500, ODAX), as well as an illustration based on recent option market data (AMD).

Performance of a Balanced Portfolio With Active Covered-Call Strategies

This study investigates the performance of local and global investments with and without covered call option strategies over the period from January 2000 to December 2015. The Covered Call Strategy (CCS) is a common return enhancing strategy used in portfolio management. The strategy consists of simultaneously holding a long position in an asset and writing call options on that asset. The local investment are on the top twenty stocks from Australian market while the global investment is an international balanced portfolio. For covered call strategies, market option data from Australian Stock Exchange is used. The results show that under some constraints, using covered call strategies in general improves the risk-adjusted returns.

The Generalized Gamma Distribution as a Useful RND under Heston’s Stochastic Volatility Model

We present the Generalized Gamma (GG) distribution as a possible risk neutral distribution (RND) for modeling European options prices under Heston’s stochastic volatility (SV) model. We demonstrate that under a particular reparametrization, this distribution, which is a member of the scale-parameter family of distributions with the mean being the forward spot price, satisfies Heston’s solution and hence could be used for the direct risk-neutral valuation of the option price under Heston’s SV model. Indeed, this distribution is especially useful in situations in which the spot’s price follows a negatively skewed distribution for which Black–Scholes-based (i.e., the log-normal distribution) modeling is largely inapt. We illustrate the applicability of the GG distribution as an RND by modeling market option data on three large market-index exchange-traded funds (ETF), namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long-term US Treasury bonds). As of the writing of this paper (August 2021), the option chain of each of the three market-index ETFs shows a pronounced skew of their volatility ‘smile’, which indicates a likely distortion in the Black–Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion in the volatility ‘smile’ appears not to exist in the TLT option data. We provide a thorough modeling of the option data we have on each ETF (with the 15 October 2021 expiration) based on the GG distribution and compare it to the option pricing and RND modeling obtained directly from a well-calibrated Heston’s SV model (both theoretically and also empirically, using Monte Carlo simulations of the spot’s price). All three market-index ETFs exhibited negatively skewed distributions, which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black–Scholes modeling in such instances, which involves negatively skewed distribution, is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. Similarly, the closely related Inverse Generalized Gamma distribution (IGG) is also proposed as a possible RND for Heston’s SV model in situations involving positively skewed distribution. In all, utilizing the Generalized Gamma distributions as possible RNDs for direct option valuations under the Heston’s SV is seen as particularly useful to the retail traders who do not have the numerical tools or the know-how to fine-calibrate this SV model.

On the utility maximization of the discrepancy between a perceived and market implied risk neutral distribution

A method is developed to determine the portfolio that maximizes the expected utility of an agent that trades the difference between a perceived future price distribution of an asset and the associated market implied risk neutral density. Exact results to construct and price such a portfolio are presented under the assumption that the underlying asset price evolves according to a geometric Brownian motion. Integer programming optimization techniques are applied to the general case where one first calibrates the asset price risk neutral density directly from option market data using Gatheral’s SVI parameterization. Several numerical examples approximating the optimal payoff function with liquid securities are given.

Improved Dividend Estimation from Intraday Quotes.

Liquid financial markets, such as the options market of the S&P 500 index, create vast amounts of data every day, i.e., so-called intraday data. However, this highly granular data is often reduced to single-time when used to estimate financial quantities. This under-utilization of the data may reduce the quality of the estimates. In this paper, we study the impacts on estimation quality when using intraday data to estimate dividends. The methodology is based on earlier linear regression (ordinary least squares) estimates, which have been adapted to intraday data. Further, the method is also generalized in two aspects. First, the dividends are expressed as present values of future dividends rather than dividend yields. Second, to account for heteroscedasticity, the estimation methodology was formulated as a weighted least squares, where the weights are determined from the market data. This method is compared with a traditional method on out-of-sample S&P 500 European options market data. The results show that estimations based on intraday data have, with statistical significance, a higher quality than the corresponding single-times estimates. Additionally, the two generalizations of the methodology are shown to improve the estimation quality further.

Methods and Analysis of Collar Strategies

An equity portfolio with a collar strategy consists of a long position in the underlying index together with long put options for insurance and short call options to mitigate the cost of insurance or enhance the return. Using the S&P/ASX 200 index, this study investigates the performances of fourteen collar strategies and for comparison two protective put strategies. We consider two simulations: one with traded option market data and the other utilizing Black-Scholes option prices. The investigation period is 2008−2016 and we consider three sub-periods representing different market conditions. The active collar strategies considered follow those introduced by Szado & Schneeweis (2010a). As a summary of our results, the best performing strategies are a protective put and a zero-cost collar.

Learning sequential option hedging models from market data

Following a direct data-driven approach, we propose a robust encoder-decoder Gated Recurrent Unit (GRU), GRU δ , for optimal discrete option hedging. The proposed GRU δ utilizes the Black-Scholes model as a pre-trained model and incorporates sequential information and feature selection. Using the S&P 500 index European option market data, we demonstrate that the weekly and monthly hedging performance of the proposed GRU δ significantly surpasses that of the data-driven minimum variance (MV) method, the regularized kernel data-driven model, and the SABR-Bartlett method. In addition, the daily hedging performance of the proposed GRU δ also surpasses that of MV methods based on parametric models, the kernel method, and SABR-Bartlett method.

Delta-hedged gains of SSE 50 ETF options

ABSTRACT Using Chinese option market data, we construct a delta-neutral strategy for Shanghai Stock Exchange (SSE) 50ETF options and investigate the statistical properties of the strategy gains. The empirical results show that the delta-hedged gains are significantly negative, indicating that to hedge the volatility risk, the option buyer needs to pay a volatility risk premium to the option seller.

Forecasting value at risk and conditional value at risk using option market data

AbstractWe forecast monthly value at risk (VaR) and conditional value at risk (CVaR) using option market data and four different econometric techniques. Independent from the econometric approach used, all models produce quick to estimate forward‐looking risk measures that do not depend from the amount of historical data used and that, through the implied moments of options, better reflect the ever‐changing market scenario. All proposed option‐based approaches outperform or are equally good to different “traditional” forecasts that use historical returns as input. The extensive robustness of our results shows that the real driver of the better forecasts is the use of option market data as inputs for the analysis, more than the type of econometric approach implemented.

On the RND under Heston's Stochastic Volatility Model

We consider Heston's (1993) stochastic volatility model for valuation of European options to which (semi) closed form solutions are available and are given in terms of characteristic functions. We prove that the class of scale-parameter distributions with mean being the forward spot price satisfies Heston's solution. Thus, we show that any member of this class could be used for the direct risk-neutral valuation of the option price under Heston's SV model. In fact, we also show that any RND with mean being the forward spot price that satisfies Hestons' option valuation solution, must be a member of a scale-family of distributions in that mean. As particular examples, we show that one-parameter versions of the {\it Log-Normal, Inverse-Gaussian, Gamma, Weibull} and the {\it Inverse-Weibull} distributions are all members of this class and thus provide explicit risk-neutral densities (RND) for Heston's pricing model. We demonstrate, via exact calculations and Monte-Carlo simulations, the applicability and suitability of these explicit RNDs using already published Index data with a calibrated Heston model (S&P500, Bakshi, Cao and Chen (1997), and ODAX, Mrazek and Pospisil (2017)), as well as current option market data (AMD).

Investor Sentiment Index and Option Price Volatility Based on MIDAS Model: Evidence from China

The paper selects the transaction data of the option market and network data from June 1, 2015 to February 2, 2018. The principal component analysis is adopted to construct investor sentiment index. The OLS and MIDAS model are employed to study the influence of investor sentiment index on the option implied volatility in Shanghai Stock Exchange 50ETF. The empirical results show that the MIDAS model with more high-frequency information has stronger interpretation ability than the same frequency model. Investor sentiment index based on traditional indicators has a negative effect on the option implied volatility while the excessive attention of investors on the Internet would exert positive pressure on the option market. The conclusion can well explain the inherent mechanism of investor sentiment affecting option implied volatility. Therefore, it is of great practical significance to study the influence of investor sentiment on the option price volatility in China

The Generalized Gamma Distribution as a Useful RND Under Heston’s Stochastic Volatility Model

Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Heston's (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in which the spot's price follows a negatively skewed distribution and hence, Black-Scholes based (i.e. the log-normal distribution) modeling is largely inapt. We apply the GG distribution as RND to modeling current market option data on three large market-index ETFs, namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long term US Treasury bonds). The current option chain of each of the three market-index ETFs shows of a pronounced skew of their volatility `smile' which indicates a likely distortion in the Black-Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion appears not to exist in the TLT option data. We provide a thorough modeling of the available option data we have on each ETF (with the October 15, 2021 expiration) based on the GG distribution and compared it to the option pricing and RND modeling obtained directly from a well-calibrated Heston's (1993) SV model (both theoretically and empirically, using Monte-Carlo simulations of the spot's price). All three market-index ETFs exhibit negatively skewed distributions which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black-Scholes modeling in such instances which involve negatively skewed distribution is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. In contrast, for the TLT ETF, which exhibits no such distortion to the volatility `smile', the three pricing models (i.e. Heston's, Black-Scholes and Generalized Gamma) appear to yield similar results.

OPTION PRICING IN MARKETS WITH INFORMED TRADERS

The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete markets, where we consider traders with information on the stock price direction and stock return mean. The Black–Scholes–Merton option pricing theory is extended for markets with informed traders, where price processes are following continuous-diffusions. By doing so, the discontinuity puzzle in option pricing is resolved. Using market option data, we estimate the implied surface of the probability for a stock upturn, the implied mean stock return surface, and implied trader information intensity surface.

Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model

Empirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility. This paper introduces a two-factor stochastic volatility jump-diffusion model in which two variance processes with jumps drive the underlying stock price and then considers the valuation on European style option. We derive a semianalytical formula for European vanilla option and develop a fast and accurate numerical algorithm for the computation of the option prices using the fast Fourier transform (FFT) technique. We compare the volatility smile and probability density of the proposed model with those of alternative models, including the normal jump diffusion model and single-factor stochastic volatility model with jumps, respectively. Finally, we provide some sensitivity analysis of the model parameters to the options and several calibration tests using option market data. Numerical examples show that the proposed model has more flexibility to capture the implied volatility term structure and is suitable for empirical work in practice.

Forecasting Value at Risk and Conditional Value at Risk using Option Market Data

We forecast monthly Value at Risk (VaR) and Conditional Value at Risk (CVaR) using option market data and four different econometric techniques. Independently from the econometric approach used, all models produce quick to estimate forward-looking risk measures that do not depend from the amount of historical data used and that, through the implied moments of options, better reflect the ever-changing market scenario. All proposed option-based approaches outperform or are equally good to different “traditional” forecasts that use historical returns as input. The extensive robustness of our results shows that the real driver of the better forecasts is the use of option market data as inputs for the analysis, more than the type of econometric approach implemented.

Option market trading activity and the estimation of the pricing kernel: A Bayesian approach

We propose a nonparametric Bayesian approach for the estimation of the pricing kernel. Historical stock returns and option market data are combined through the Dirichlet Process (DP) to construct an option-adjusted physical measure. The precision parameter of the DP process is calibrated to the amount of trading activity in deep-out-of-the-money options. We use the option-adjusted physical measure to construct an option-adjusted pricing kernel. An empirical investigation on the S&P 500 Index from 2002 to 2015 shows that the option-adjusted pricing kernel is consistently monotonically decreasing, regardless of the level of volatility, thus providing an explanation to the well known U-shaped pricing kernel puzzle.

S&P 500 Index, an Option-Implied Risk Analysis

The forward-looking nature of option market data allows one to derive economically-based and model-free risk measures. This article proposes an extensive analysis of the performances of option-implied VaR and CVaR, and compare them with classical risk measures for the S&P500 Index. Delivering good results both at short and long time horizons, the proposed option-implied risk metrics emerge as a convenient alternative to the existing risk measures.