Stock Index Options Research Articles

Data-driven hedging of stock index options via deep learning

We develop deep learning models to learn the hedge ratio for S&P500 index options from options data. We compare different combinations of features and show that with sufficient training data, a feedforward neural network model with time to maturity, the Black-Scholes delta and market sentiment as inputs performs the best in the out-of-sample test under daily hedging. This model significantly outperforms delta hedging and a data-driven hedging model. Our results also demonstrate the importance of market sentiment for hedging.

Pricing research on CSI 300 stock index options based on B-S model and GARCH model

The development of the financial market has always been accompanied by a variety of risks, and with the continuous improvement of the financial market and the increase of investor demand, the society's demand for risk avoidance tools is also increasing, and CSI 300 stock index options as a new type of financial derivatives can largely make up for the vacancy of China's options market, in risk control and price discovery can play a huge role. Therefore, it is very important to study its functions and predict the price. This paper uses the option pricing model B-S model as the pricing basis and combines the GARCH model to analyze the volatility of the CSI 300 Index yield, so as to complete the construction of the pricing model and predict the future trend of option prices and analyze the effectiveness of model pricing. Finally, according to the empirical results, some suggestions are provided on the accurate pricing of options, so as to promote the healthy development of the options market.

Performance Persistence and the Implied Volatility Smile. Evidence from the Nasdaq OMX Copenhagen 25 Stock Index Options

Performance Persistence and the Implied Volatility Smile. Evidence from the Nasdaq OMX Copenhagen 25 Stock Index Options

Joint Arbitrage Conditions for Stock Index Options and Volatility Index Options

Joint Arbitrage Conditions for Stock Index Options and Volatility Index Options

A Study on the Applicability of Black-Scholes Option Pricing Model in Chinese Stock Index Option Market

Compared with the developed countries, Chinese stock index option market developed late and accumulated less historical data. At the same time, it has the characteristics that many developed countries' stock option markets do not have. Black-Scholes Model is an important model in the field of option pricing. It is not enough for a financial model to be reasonable in theory, but it needs to be tested by the actual market. Therefore, based on the main transaction data of the CSI 300 stock index option contracts from 2010 to 2020, this paper analyzes the compliance of the CSI 300 stock index option market to the basic assumptions of the B-S option pricing model, the main parameters of the CSI 300 stock index options in the B-S option pricing model, and the fitting degree of the B-S model's prediction and actual prices. The result shows that there is a certain deviation between the pricing conclusions of the B-S model and the actual option prices. This paper analyzes the reasons for the deviation from many aspects, and puts forward the corresponding improvement strategies that the users of the model should adopt, so as to improve the applicability of the B-S option pricing model in Chinese stock index option market.

The pricing of China stock index options based on monetary policy uncertainty

In the field of option pricing, scholars have been exploring the constant settings of volatility and interest rate ever since the Black-Scholes model was put forward. This research introduces a floating interest rate into the local volatility model, analyzes the model’s pricing effects, and compares them from the aspects of an in-sample pricing error and out-of-sample pricing error respectively using data of CSI (China Securities Index) SH-SZ (Shanghai-Shenzhen) 300 stock index options. The empirical results show that the Surface Stochastic Volatility Inspire model is better than the Stochastic Volatility Inspire model.

Empirical Option Pricing Models

This article provides an overview of empirical options research, with primary emphasis on research into systematic stochastic volatility and jump risks relevant for pricing stock index options. It reviews evidence from time series analysis, option prices, and option price evolution regarding those risks and discusses required compensation.

The application of the improved option parity arbitrage model in SSE 50ETF option

The SSE 50ETF option is China's first stock index option product launched in 2015. For a number of reasons, the options market can sometimes create arbitrage opportunities. Based on the theory of option parity arbitrage and taking into account the transaction costs, this paper explores effective options arbitrage strategies and practices them. Based on the theory of option parity arbitrage and taking into account the transaction costs, this paper establishes an effective option arbitrage strategy model and puts it into practice. The results show that there are indeed arbitrage opportunities in the market that exceed the risk-free rate of return, but there are not many such opportunities, and there is not much arbitrage space under many opportunities. This is not only the embodiment of high market efficiency, but also the result of taking various transaction costs into full consideration in this paper to ensure the effectiveness of arbitrage.

How Risky Are the Options? A Comparison with the Underlying Stock Using MaxVaR as a Risk Measure

This paper investigates the risk exposure for options and proposes MaxVaR as an alternative risk measure which captures the risk better than Value-at-Risk especially. While VaR is a measure of end-of-horizon risk, MaxVaR captures the interim risk exposure of a position or a portfolio. MaxVaR is a more stringent risk measure as it assesses the risk during the risk horizon. For a 30-day maturity option, we find that MaxVaR can be 40% higher than VaR at a 5% significance level. It highlights the importance of MaxVaR as a risk measure and shows that the risk is vastly underestimated when VaR is used as the measure for risk. The sensitivity of MaxVaR with respect to option characteristics like moneyness, time to maturity and risk horizons at different significance levels are observed. Further, interestingly enough we find that the MaxVar to VaR ratio is higher for stocks than the options and we can surmise that stock returns are more volatile than options. For robustness, the study is carried out under different distributional assumptions on residuals and for different stock index options.

Predictability of OTC Option Volatility for Future Stock Volatility

This study explores the information content of the implied volatility inferred from stock index options in the over-the-counter (OTC) market, which has rarely been studied in the literature. Using OTC calls, puts, and straddles on the KOSPI 200 index, we find that implied volatility generally outperforms historical volatility in predicting future realized volatility, although it is not an unbiased estimator. The results are more apparent for options with shorter maturity. However, while implied volatility has strong predictability during normal periods, historical volatility is superior to implied volatility during a period of crisis due to the liquidity contraction of the OTC options market. This finding suggests that the OTC options market can play a role in conveying important information to predict future volatility.

The Impact of Heterogeneous Unconventional Monetary Policies on Market Uncertainty

This article analyzes the impact of the unconventional monetary policies (UMPs) of four major central banks (the Fed, ECB, BoE and BOJ) on market uncertainty. We exploit the heterogeneity of different UMP actions to disentangle their influence on reducing the ex ante perception of extreme events (tail risks) using the information contained in risk-neutral densities from the most liquid stock index options. The empirical findings show that the announcement of UMPs reduces the risk-neutral probability of extreme events across various horizons and thresholds, supporting the hypothesis of the risk-taking channel. The most effective measures are the forward guidance and liquidity actions, rather than asset purchases. Interestingly, foreign UMP actions also prove to be significant variables affecting domestic tail risks, mainly at longer horizons. These results reveal an original cross-border effect of foreign UMPs on domestic tail risks. Finally, the dynamics of the UMPs are captured by a structural model that confirms a transitory impact of UMPs on market tail risk perceptions.

Application of Diffusion Models in the Analysis of Financial Markets: Evidence on Exchange Traded Funds in Europe

Exchange traded funds (ETFs) are financial innovations that may be considered as a part of the index financial instruments category, together with stock index derivatives. The aim of this paper is to explore the trajectories and formulates predictions regarding the spread of ETFs on the financial markets in six European countries. It demonstrates ETFs’ development trajectories with regard to stock index futures and options that may be considered as their substitutes, e.g., in risk management. In this paper, we use mathematical models of the diffusion of innovation that allow unveiling the evolutionary patterns of turnover of ETFs; the time span of the analysis is 2004–2015, i.e., the period of dynamic changes on the European ETF markets. Such an approach has so far rarely been applied in this field of research. Our findings indicate that the development of ETF markets has been strongest in Italy and France and weaker in the other countries, especially Poland and Hungary. The results highlight significant differences among European countries and prove that diffusion has not taken place in all the cases; there are also considerable differences in the predicted development paths.

The shale revolution and shifting crude dynamics

SummaryOil price fluctuates in response to both demand and supply shocks. This paper proposes a new methodology that allows for timely identification of the shifting contribution from the two types of shock through a joint analysis of crude futures options and stock index options. Historical analysis shows that crude oil price movements are dominated by supply shocks from 2004 to 2008, but demand shocks have become much more dominant since then. The large demand shock following the 2008 financial crisis contributes to the start of this dynamics shift, whereas the subsequent shale revolution has fundamentally altered the crude supply behavior.

Partial Moments for Quadratic Forms in Non-Gaussian Random Vectors: A Parametric Approach

Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression for the cdf exists, and one resorts to numerical methods. Traditionally the problem is analyzed under the assumption of joint Gaussianity; the algorithm that is usually employed is that of Imhof (1961). The present manuscript generalizes this result to the case of multivariate generalized hyperbolic random vectors. This flexible distribution nests, among others, the multivariate t, Laplace, and variance gamma distributions. An expression for the first partial moment is also obtained, which plays a vital role in financial risk management. The proof involves a generalization of the classic inversion formula due to Gil-Pelaez (1951). Two numerical applications are considered: first, the finite-sample distribution of the two stage least squares estimator of a structural parameter. Second, the Value at Risk and expected shortfall of a quadratic portfolio with heavy-tailed risk factors. An empirical application is examined, in which a portfolio of Dow Jones Industrial Index stock options is optimized with respect to its expected shortfall. The results demonstrate the benefits of the analytical expression.

Nonlinear Relationships between Oil Prices and Implied Volatilities: Providing More Valuable Information

This paper investigates the linear/nonlinear long-run and short-run dynamic relationships between oil prices and two implied volatilities, oil price volatility index (OVX) and stock index options volatility index (VIX), representing panic gauges. The results show that there is a long-run equilibrium relationship between oil prices and OVX (VIX) using the linear autoregressive distributed lag (ARDL)-bounds test. Likewise, while using the nonlinear autoregressive distributed lag (NARDL)-bounds test, not only does a long-run equilibrium relationship exist, but also the rising OVX (VIX) has a greater negative influence on oil prices than the declining OVX (VIX), thus indicating that a long-run, asymmetric cointegration exists between the variables. Furthermore, OVX (VIX) oil prices have a linear Granger causality, while for the nonlinear Granger causality test, oil prices have a bidirectional relation with OVX (VIX). In addition, we find that once major international political and economic events occur, structural changes in oil prices change the behavior of oil prices, and thus panic indices, thereby switching from a linear relationship to a nonlinear one. The empirical results of this study provide market participants with more valuable information.

Predictable Dynamics in the Implied Volatility Surface Based on Weighted Least Squares: Evidence from Soybean Meal Futures Options in China

ABSTRACT This article examines the dynamics and predictability of the implied volatility surface derived from weighed trading volume. We study the Chinese soybean meal futures options market. By assigning larger weights to options with higher trading volume, we find more precise fittings on the implied volatility surface. Our estimation method outperforms traditional methods in terms of the dynamics and predictability of the implied volatility surface, both in the sample and out of the sample. We also document that soybean futures options exhibit implied volatility smirk that is different from those in the stock index options. In addition, we find that the implied volatility term structure shows an inverted U-shape during the period of high implied volatility.

Portfolio Optimization with Higher-order Stochastic Dominance Constraints

Optimal portfolio choice is investigated for investors with various types of higher-order risk aversion. Finite systems of convex inequalities are introduced to evaluate the efficiency of a given benchmark, and for constructing enhanced portfolios which dominate the benchmark for all higher-order risk averters. An analysis of equity industry rotation strategies shows that accounting for skewness love and kurtosis aversion increases long positions in recent winner industries which feature more favorable skewness and kurtosis than the market index. An analysis of equity stock index options combinations shows that accounting for higher-order risk aversion leads to buying of underpriced option series in addition to the standard solution of writing of overpriced options. In both applications, optimization with higher-order risk constraints appears leads to superior out-of-sample performance compared with simpler strategies based on heuristic rules, single utility functions and limiting portfolio variance.

Stock Index Options Pricing under Jump Patterns Driven by Market States

ABSTRACTThis article reports that both jump amplitudes and arrival rates are related to the economic states in the DJX and the SPX markets. It then proposes a jump-diffusion process model with modulated frequency and amplitude (JD-MF-MA) to depict these patterns. Using this model, we also derive a closed-form formula for the European index option through the characteristic function pricing approach. The empirical results show that the model with modulated jumps not only captures the characteristics of returns but also improves pricing performance. Overall, the modulated jump should be the default modeling choice for derivatives pricing models.

Expiration day effects on European trading volumes

This study investigates the effect of periodic events, such as the stock index futures and options expiration days and the Morgan Stanley Capital International (MSCI) quarterly index reviews, on the trading volume in the pan-European equity markets. The motivation of this study stems from anecdotal evidence of increased trading volume in the equity markets during the run-up to the index options and futures expiration days and MSCI rebalances. This study investigates this phenomenon in more detail and analyses the trading volumes of seven European stock indices and the MSCI International Pan-Euro Price Index. The analysis features a multi-step ahead volume forecast, which is important for practitioners in order to plan multi-day trades while looking to minimise the market impact. The results confirm higher trading activity on the futures and options expiration days, as well as on the MSCI rebalance day. We report a clear futures and options expiration day effect, which accounts for the Friday effect in terms of larger trading volumes. The MSCI rebalance trading volume is significantly different from the volume of the adjacent months with no MSCI reviews, but they cannot explain the end-of-month effect entirely.

Pricing of stochastic volatility stock index option based on Feynman path integral

<sec>Under the background that stock index options urgently need launching in China, the research on stock option pricing model has important theoretical and practical significance. In the traditional B-S-M model it is assumed that the volatility remains unchanged, which differs tremendously from the market’s reality. When the market fluctuates drastically, it is difficult to realize the risk management function of stock index options. Although in the Heston model, as one of the traditional stochastic volatility option pricing models, the correlation risk between the volatility and underlying price is taken into consideration, its pricing accuracy is still to be improved. From the quantum finance perspective, in this paper we use the Feynman path integral method to explore a more practical stock index option pricing model.</sec><sec>In this paper, we construct a Feynman path integral pricing model of stock index options with stochastic volatility by taking Hang Seng index option as the research object and Heston model as the control group. It is found that the Feynman path integral pricing model is significantly superior to the Heston model either at different strike prices on the same expiration date or at different expiration dates for the same strike price. The stock index option pricing model constructed in this paper can give the numerical solution of Feynman's pricing kernel, and directly realizes the forecast of stock index option price. The pricing accuracy is significantly improved compared with the pricing accuracy given by the Heston model through using the characteristic function method.</sec><sec>The remarkable advantages of Feynman path integral stock index option pricing model are as follows. Firstly, the path integral has advantages in solving multivariate problems: the Feynman pricing kernel represents all the information about pricing and can be easily expanded from one-dimensional to multidimensional case, so the change of closing price of stock index and volatility of underlying index can be taken into account simultaneously. Secondly, based on the relationship between the Feynman path generation principle and the law of large number, the mean values of pricing kernel obtained by MATLAB not only optimizes the calculation process, but also significantly improves the pricing accuracy. Feynman path integral is the main method in quantum finance, and the research in this paper will provide reference for its further application in the pricing of financial derivatives.</sec>