Index Option Prices Research Articles

The Information Content of Option Prices: Evidence from S&P 500 Index Options

This study addresses the question as to whether the option prices have useful predictive information on the direction of stock markets by investigating a forecasting power of volatility curvatures and skewness premiums implicit in S&P 500 index option prices traded in Chicago Board Options Exchange. We begin by estimating implied volatility functions and risk neutral price densities every minute based on non-parametric method and then calculate volatility curvature and skewness premium using them. The rationale is that high volatility curvature or high skewness premium often leads to strong bullish sentiment among market participants. We found that the rate of return on the signal following trading strategy was significantly higher than that on the intraday buy-and-hold strategy, which indicates that the S&P500 index option prices have a strong forecasting power on the direction of stock index market. Another major finding is that the information contents of S&P 500 index option prices disappear within one minute, and so one minute-delayed signal following trading strategy would not lead to any excess return compared to a simple buy-and-hold strategy.

Pricing VIX options in a stochastic vol‐of‐vol model

This paper proposes and makes a study of a new model for volatility index option pricing. Factors such as mean‐reversion, jumps, and stochastic volatility are taken into consideration. In particular, the positive volatility skew is addressed by the jump and the stochastic volatility of volatility. Daily calibration is used to check whether the model fits market prices and generates positive volatility skews. Overall, the results show that the mean‐reverting logarithmic jump and stochastic volatility model (called MRLRJSV in the paper) serves as the best model in all the required aspects. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamic Linkages between Implied Volatility Indices of Developed and Emerging Financial Markets: An Econometric Approach

Since 2008, the financial systems around the world have been hit by a series of financial crisis from burst housing bubbles and crippling unemployment to unsustainable debt levels and volatile financial markets. An important measure to assess the market expectation of the future volatility of underlying asset is the implied volatility index (IVI). The main objective of the article is to examine the IVI linkages between developed financial markets (US, UK and Japan) and emerging financial markets (BRIC—Brazil, Russia, India and China) and to conclude about the degree of integration between these markets. The data consist of daily closing prices of stock index options between April 2010 and March 2013. The methodology involves the augmented Dickey–Fuller (ADF) test, unit root test, vector autoregressive (VAR) modelling and variance decomposition. The results of the study suggest that the US IVI has substantial impact over the variations of other IVIs, thus raising the possibility of it constituting a usable risk factor for investors internationally.

Option-Based Estimation of the Price of Co-Skewness and Co-Kurtosis Risk

We show that the prices of risk for factors that are nonlinear in the market return are readily obtained using index option prices. The price of co-skewness risk corresponds to the market variance risk premium, and the price of co-kurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An out-of-sample analysis of factor models with co-skewness and co-kurtosis risk indicates that the new estimates of the price of risk improve the models' performance.

Pricing competitiveness of jump-diffusion option pricing models: evidence from recent financial upheavals

Purpose – The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which can meet the requirements of option traders and practitioners during tumultuous periods in the future. Design/methodology/approach – Envisioning the fact, the all option-pricing models normally does wrong valuation relative to market. For estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset return data, we have used the nonlinear least-square method. As an approach, we analyzed model prices by dividing the option data into 15 moneyness-maturity groups – depending on the time to maturity and strike price. The prices are compared analytically by continuously updating the parameters of two models using cross-sectional option data on daily basis. Estimated parameters then used to figure out the forecasting performance of models with corresponding BS and market – for pricing day-ahead option prices and implied volatility. Findings – The outcomes of the paper reveal that the jump-diffusion models are a better substitute of classical BS, thus improving the pricing bias significantly. But compared to jump-diffusion model of Merton’s, the model of Bates’ can be applied more uniquely to find out the pricing of three popularly traded categories: deep-out-of-the-money, out-of-the-money and at-the-money of Nifty index options. Practical implications – The outcome of this research work reveals that the jumps are important components of pricing dynamics of Nifty index options. Incorporation of jump-diffusion process into option pricing of Nifty index options leads to a higher pricing effectiveness, reduces the pricing bias and gives values closer to the market. As the models have been tested in extreme conditions to determine the dominant effectuality, the outcome of this paper helps traders in keeping the investment protected under normal conditions. Originality/value – The specific period chosen for this study is very unique; it canvasses the extreme up and down limits (jumps) of the Indian capital market and provides the most apt situation for testifying the pricing competitiveness of the models in question. To testify the robustness of models, they have been put into a practical implication of complete cycle of financial frame.

Mark-to-Market Credit Index Option Pricing and Credit Volatility Index

Credit index options cannot be priced as simple vanilla options. In this paper we derive the pricing formula using both replication method and linear annuity mapping. We develop a model-free process to calculate a VIX-like credit volatility index based on observable credit index options market. We imply all model parameters from market traded data.

The role of the variance premium in Jump-GARCH option pricing models

Abstract We develop a discrete-time option pricing model incorporating a variance-dependent pricing kernel of Christoffersen et al. (2013) under an economic framework allowing for dynamic volatility and jump intensity. Based on the model, we examine the role of the variance premium and jump risk premium in explaining S&P 500 index option prices and returns. According to the results, the variance premium is equally important as the jump risk premium in explaining the empirical option data. Whereas the incorporation of the jump risk premium improves the model fit on option prices, the incorporation of the variance premium improves the fit on option returns. In particular, the variance premium can explain both 1-month holding period returns of 2-month maturity straddles, which are significantly negative, and call returns, which decrease according to moneyness. The model incorporating the jump risk premium only has a limitation in explaining the above two stylized returns. The outperformance of the model incorporating the variance premium on option returns stems from its ability to capture the wedge between physical and risk-neutral volatilities.

Influence of individual investor sentiment on Taiwan option prices during 2007-2010 financial crisis

Purpose – This paper investigates changes in risk-neutral distribution derived from Taiwan stockindex options under different market conditions. The purpose of this paper is to explore whether individual investor sentiment significantly influences the Taiwan option prices. Design/methodology/approach – The authors adopt the optimization method to estimate the risk-neutral distribution from the Taiwan stock index options and use the t-test to examine the difference in risk-neutral skewness, kurtosis, and confidence interval between the pre-crisis and crisis periods. This paper tests the impact of individual investor sentiment on risk-neutral skewness and confidence interval in two sub-periods. Findings – The authors find that errors in individual investors’ expectations significantly influence the Taiwan stock index option prices. Research limitations/implications – The data concerning the sentiment of speculative institutional investors are incomplete for the Taiwan option market. Therefore, this paper focusses on the analysis of individual investor sentiment. Further research can study the impact of institutional investor sentiment in emerging markets. Social implications – The previous literature has suggested that option prices reflect information before the information is revealed in stock prices. Therefore, an important implication is to analyze the information quality revealed in option prices by studying whether the changes in option prices are due to investor sentiment or non-sentiment-related components. Originality/value – Most of the studies in the literature have focussed on the US option market, and their applicability may vary across different microstructures. This paper shows that the influence of individual investor sentiment in an emerging market is different from that in the US market.

An Investigation of Box‐Spread Strategy and Arbitrage Efficiency on Indian Index Options Market

The aim of the present study is to examine the internal market efficiency of the Indian index options by testing S and P CNX Nifty index options using box-spread arbitrage strategy. Daily closing prices of index options from April 01, 2008 to March 31, 2012 are used to identify the mispricing and arbitrage opportunities with the model-free box-spread approach. The result of the sensitivity analysis of violations with respect to time to maturity and moneyness demonstrates that the majority of violations in options contract are deceptive, as the liquidity is expected to be very low in such contracts. Further, the proportion of exploitable violations severely falls after considering the transaction costs, as most of the profits were wiped out and showing negative profits. Thus, although the Indian index options market shows traces of inefficiency, in totality it is suggested that the Indian index options market is efficient as majority of violations are un-exploitable after incorporating transaction costs.

The Financial Crisis and the Behavior of S&P 500 Index Option Prices

Stronger volatility skew and smile effects accompanied by a risk-neutral distribution that is closer to the Normal seem unconventional at first thought. But that is what we find during the financial crisis, with the unconventionally high risk-neutral volatility level playing a major role. Additionally, the term structure of implied volatility became inverted (negatively sloped) during the crisis, driven by the inversion of the term structure of risk-neutral volatility and by the rise in the shorter term unconditional volatility. The term structures of risk-neutral skewness and kurtosis appear relatively flat with only negligible change during the crisis. The scale and its term structure rather than the shape factors of the unconditional risk neutral distribution to maturity thus appear more important for the structure of crisis time option prices.

Rationality of Option Prices Relative to Underlying Asset Prices in Taiwan

This study explores whether Taiwan stock index option (TXO) prices vary rationally with underlying asset prices, using an intraday sample covering January 1, 2009 through June 30, 2009. This study focuses on two violations: the call (put) price and its underlying asset moving in the opposite (same) direction, and the absolute change in the option price exceeding that in the underlying asset. Overall, these violations in this study are extremely significant relative to the findings of Bakshi et al. [5]. This inconsistent result probably results from the market mechanism, namely that the TXO market is emerging and order-driven rather than developed and quote-driven. Despite this, both the impractical assumption of one-dimensional diffusion model and the market microstructure can significantly affect the rational movement of TXO options with their underlying assets.

Risk-Adjusted Option-Implied Moments

Option-implied moments, like implied volatility, contain useful information about an underlying asset's return distribution but are derived under the risk-neutral probability measure. This paper provides a direct way of converting risk-neutral moments into the corresponding physical moments, which are required for many applications. The main result is a representation of physical moments in terms of observed option prices and a representative investor's preferences. As an empirical application of this result, we provide implied estimates of the representative stock market investor's disappointment aversion using S&P 500 index option prices. We find that disappointment aversion has a procyclical pattern. It is high in times of high index levels and declines when the index falls. We confirm the view that investors with high risk aversion and disappointment aversion leave the stock market during times of turbulence and reenter it after a period of high returns.

Noisy Chaos in a Large System of Decision‐Makers with Heterogeneous Beliefs with Application to Index Option Prices

Decision‐makers (DMs) often exhibit preference reversal and phase transitions in their states of confidence. We show how those behaviors induce chaos in a large system of DMs with heterogeneous beliefs. We construct a behavioral matrix operator [from a DM's probability weighting function (PWF)] that characterizes a projective mapping of confidence in dual psychological spaces. Moreover, we prove that in a seemingly stable system of DMs, the empirical Lyapunov exponent process for the noisy orbit of DM deterministic PWFs admits tail event chaos controlled by risk attitude factors. We use reported results from rank‐dependent Standard & Poor's 500 index option prices and Chicago Board Options Exchange Volatility Index to illustrate our theory. Data show phase transitions in the state of DM confidence over time as PWFs change from skew S‐shape to inverted S‐shape. Our model identifies an instability criterion function for the distribution of critical values of risk attitude factors over a convex set of probabilities bounded from above by the fixed‐point probability for PWFs. In particular, we use the criterion function to estimate critical values for risk attitude factors in index option price data that predict market crash based on the orientation of the PWF implied by option data. Copyright © 2014 John Wiley & Sons, Ltd.

A Nonparametric Approach to Pricing Options Learning Networks

For practitioners of equity markets, option pricing is a major challenge during high volatility periods and Black-Scholes formula for option pricing is not the proper tool for very deep out-of-the-money options. The Black-Scholes pricing errors are larger in the deeper out-of-the money options relative to the near the-money options, and it's mispricing worsens with increased volatility. Experts opinion is that the Black-Scholes model is not the proper pricing tool in high volatility situations especially for very deep out-of-the-money options. They also argue that prior to the 1987 crash, volatilities were symmetric around zero moneyness, with in-the-money and out-of-the money having higher implied volatilities than at-the-money options. However, after the crash, the call option implied volatilities were decreasing monotonically as the call went deeper into out-of-the-money, while the put option implied volatilities were decreasing monotonically as the put went deeper into in-the-money. Since these findings cannot be explained by the Black-Scholes model and its variations, researchers searched for improved option pricing models. Feedforward networks provide more accurate pricing estimates for the deeper out-of-the money options and handles pricing during high volatility with considerably lower errors for out-of-the-money call and put options. This could be invaluable information for practitioners as option pricing is a major challenge during high volatility periods. In this article a nonparametric method for estimating S&P 100 index option prices using artificial neural networks is presented. To show the value of artificial neural network pricing formulas, Black-Scholes option prices are compared with the network prices against market prices. To illustrate the practical relevance of the network pricing approach, it is applied to the pricing of S&P 100 index options from April 4, 2014 to April 9, 2014. On the five days data while Black-Scholes formula prices have a mean $10.17 error for puts, and $1.98 for calls, while neural network’s error is less than $5 for puts, and $1 for calls.

Differences in Trading and Pricing Between Stock and Index Options

We find that the demand for stock options that increases exposure to the underlying is positively related to the individual investor sentiments and past market returns, whereas the demand for index options is invariant to these factors. These differences in trading patterns are also reflected in the differences in the composition of traders with different types of options—options on stocks are actively traded by individual investors, whereas trades in index options are more often motivated by the hedging demand of sophisticated investors. Consistent with a demand-based view of option pricing, the individual investor sentiments and past market returns are related to time-series variations in the slope of the implied volatility smile of stock options, but they have little impact on the prices of index options. The pricing impact is more pronounced in options with a higher concentration of unsophisticated investors and those with higher delta hedging costs. Our results provide evidence that factors not related to fundamentals also impact security prices. This paper was accepted by Brad Barber, finance.

A framework for robust measurement of implied correlation

In this paper we consider the problem of deriving correlation estimates from observed option data. An implied correlation estimate arises when we match the observed index option price with a corresponding model price. The underlying model assumes that stock prices can be described using a lognormal distribution, while a Gaussian copula describes the dependence structure. Within this multivariate stock price model, the index option price is not given in a closed form and has to be approximated. Different methods exist and each choice leads to another implied correlation estimate.We show that the traditional approach for determining implied correlations is a member of our more general framework. It turns out that the traditional implied correlation underestimates the real correlation. This error is more pronounced when some stock volatilities are large compared to the other volatility levels. We propose a new approach to measure implied correlation which does not have this drawback. However, our numerical illustrations show that determining implied correlations with the traditional approach may be justified for strike prices which are close to the at-the-money strike price.We also show that implied correlation estimates can be used to define an index, called the Implied Correlation Index (ICX), which reflects the market’s perception about future (short-term) co-movement between stock prices. Using a volatility index together with the ICX gives an accurate description of the current level of market fear.

Partial Moment Volatility Indices

Forward‐looking partial moment volatility indices are developed using state‐pricing, called the bear index (BEX) and bull index (BUX). Using S&P 500 index (SPX) option prices, we find that BEX and BUX provide superior forecasts for the lower and upper partial moments of future market realised volatility, respectively. We examine the relation between SPX returns and changes in BEX and BUX at the daily level. Results are consistent with the volatility feedback hypothesis. Further, we show that BEX may be more suitable as the ‘investor fear gauge’ than VIX.

Practical Applications of Trading Volatility: At What Cost?

Exchange-traded products (ETPs) linked to VIX short-term futures indices are popular among retail investors, even though they consistently lose money over time. Don’t be fooled by their popularity. These VIX ETPs are simply not good buy-and-hold investments. This is the advice of Robert E. Whaley, author of Trading Volatility: At What Cost? and creator of the CBOE Market Volatility Index (VIX). Launched in 1993, VIX is a key measure of market expectations of near-term volatility expressed by Standard & Poor’s 500 stock index option prices. It has become the market’s most closely watched “fear index.” In this Practical Applications report, Whaley tells us why these VIX-linked ETPs are not appropriate for long-term investment. He identifies inverse opportunities and alternatives for investors who do want to buy and hold VIX ETPs. Whaley is the Valere Blair Potter Professor of Management and Director of the Financial Markets Research Center at the Owen Graduate School of Management, Vanderbilt University. His Journal of Portfolio Management article has gained attention in the broader media. Barron’s recently featured it in VIX Creator: Volatility ETPs ‘Virtually Guaranteed to Lose Money.’

Pricing Index Options in a Multivariate Black & Scholes Model

The price of an index option depends on the distributions of the marginals and the dependence structure. In this paper we assume that the stocks composing the index can be described by a multivariate Black & Scholes model, which is the most straightforward extension of the one-dimensional Black & Scholes model. In this multivariate stock price model, vanilla option prices can be determined in closed form, but the price of an index option as well as the cdf of the index cannot be determined analytical. In this paper, we use the theory of comonotonicity to derive approximate index option prices which can be determined using the Black & Scholes formula. Furthermore, we show that the approximate index option curve can be interpreted as an index option curve of a modified, synthetic, index and the cdf of this synthetic index is given in closed form.

Option Returns in Emerging European Markets and the Impact of the 2008 Crisis

This study examines the risk premia embedded in index option prices using a sample of emerging exchanges in the European Union which have been more heavily affected by the financial crisis of 2008. In contrast to the commonly reported overpriced puts puzzle in the US market, writing puts in developing European exchanges was found to offer statistically insignificant returns after accounting for risk. However, investors were willing to pay a substantial premium for insurance against volatility risk, especially during the crisis. Insurance against negative skewness also commanded a high premium before the crisis, with these premia eliminated once markets began to depreciate post 2008. The returns of profitable option-selling strategies cannot be explained in an obvious way as compensation for risk across a wide set of risk factors.