Index Option Prices Research Articles

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.

VIX option pricing through nonaffine GARCH dynamics and semianalytical formula

AbstractThis paper develops analytical approximations for volatility index (VIX) option pricing under nonaffine generalized autoregressive conditional heteroskedasticity (GARCH) models as advocated by Christoffersen et al. We obtain the approximation formulae for pricing VIX options and then evaluate their performance with three expansions under four empirically well‐tested models. Our numerical experiments find that the weighted expansion generated by the fat‐tailed weighting kernel can significantly reduce approximation error over the Gram‐Charlier expansion; the Taylor expansion of conditional moments can lead to divergence for parameters with certain high persistence in the affine GARCH, nonlinear asymmetric GARCH, and Glosten‐Jagannathan‐Runkle GARCH models, while surviving during high persistence in the exponential GARCH.

Realized Volatility Skewness and Kurtosis Implied by Index Option Prices

Realized Volatility Skewness and Kurtosis Implied by Index Option Prices

Comprehensive study on the impact of theta decay and delta fluctuations on pricing of Indian index options

Comprehensive study on the impact of theta decay and delta fluctuations on pricing of Indian index options

Fast Filtering with Large Option Panels: Implications for Asset Pricing

Abstract The cross section of options holds great promise for identifying return distributions and risk premia, but estimating dynamic option valuation models with latent state variables is challenging when using large option panels. We propose a particle Markov Chain Monte Carlo framework with a novel filtering approach and illustrate our method by estimating index option pricing models. Estimates of variance risk premiums, variance mean reversion, and higher moments differ from the literature. We show that these differences are due to the composition of the option sample. Restricting the option sample’s maturity dimension has the strongest impact on parameter inference and option fit in these models.

Pricing Technique for European Option and Application

In financial mathematics, the pricing technique for derivatives is constantly debated. In this paper, the pricing technique of the European Option is mainly discussed, and the binomial tree (BN) model is first applied to the pricing process of European options. The previous results show that carbon credit index can be traded as an option, and BN model can correctly simulate the future price of call option constructed by consuming the carbon credit index. Secondly, the Black-Scholes (BN) model is also a crucial technique for pricing European options, and it is successfully applied to predicting the future three months' CSI 300 index option price. Finally, BN model is compared with BS model, and the result reflects that BN model can perform as well as BS model for pricing European Option When the step reaches 2000. However, the efficiency of the BN model is stable under low volatility. Under higher volatility, such as 1.5 sigmas, the required steps will increase to achieve the same accuracy level. For American options, the BN simulator of a put option is close to the actual value, but the call option simulator will fluctuate. For the stock-pricing process, both models estimate far above Monte-Carlo method. The result of this paper is to provide some clues for pricing European options with different methods.

Reconstructing volatility: Pricing of index options under rough volatility

AbstractAvellaneda et al. (2002, 2003) pioneered the pricing and hedging of index options – products highly sensitive to implied volatility and correlation assumptions – with large deviations methods, assuming local volatility dynamics for all components of the index. We present an extension applicable to non‐Markovian dynamics and in particular the case of rough volatility dynamics.

Realized Volatility Skewness and Kurtosis Implied by Index Option Prices

Realized Volatility Skewness and Kurtosis Implied by Index Option Prices

Realised Volatility Skewness and Kurtosis Implied by Index Option Prices

Realised Volatility Skewness and Kurtosis Implied by Index Option Prices

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 Ross recovery without discretization

AbstractWe propose a new continuous‐state method for empirically recovering the key objects in the Ross recovery theory which avoids discretization. The new method is based on a key bivariate orthogonal Hermite representation of the state price transition kernel, which leads to an elegant correspondence of the eigenvalue–eigenfunction system of the transition kernel and the eigenvalue–eigenvector system of the expansion coefficient matrix. Using S&P 500 index option prices, we demonstrate how our method can generate well‐behaved state price transition kernels and physical densities. Our method can also be used to compute the key objects in the Hansen and Scheinkman's factorization theory.

Market Instability, Investor Sentiment, and Probability Judgment Error in Index Option Prices

In a natural experiment with index option prices, we study how probability judgment error, and probabilistic risk attitudes, characterize investors’ sentiment about the ranking of index option attractiveness, the weight they place on each rank, and their ability to discriminate between prices. We introduce a novel behavioral process that (1) characterizes investor sentiment about tail events in index option prices over time and probability ranks, (2) provides early warning signals of market instability, and (3) crash probability estimates from a closed form expression for the time varying transition probability that a seemingly stable market state will become unstable and crash.

Pricing of Index Options in Incomplete Markets

We characterize a set of risk-neutral measures associated with a comprehensive class of risk averse investors. From this set, we show how to construct option price bounds and recover the implied gamma: a parameter uniquely identifying the marginal investor pricing a given option. Empirically, we find that S&P 500 option prices are reconciled by heterogeneous marginal investors who differ in their assessment of tail risk. This heterogeneity is time-varying, decreases during financial crises, and provides novel insights into the skew patterns of index options. The recovered investors' preferences related to compensation for downside risk help predict future market returns.

Pricing of index options in incomplete markets

We characterize a set of risk-neutral measures associated with a comprehensive class of risk averse investors. From this set, we show how to construct option price bounds and recover the implied γ: a parameter uniquely identifying the marginal investor pricing a given option. Empirically, we find that S&P 500 option prices are reconciled by heterogeneous marginal investors who differ in their assessment of tail risk. This heterogeneity is time-varying, decreases during financial crises, and provides novel insights into the skew patterns of index options. The recovered investors’ preferences related to compensation for downside risk help predict future market returns.

Price discovery in the volatility index option market: A univariate GARCH approach

In this paper, the GARCH option pricing model is applied to the Standard and Poor’s 500 (S&P500) Volatility Index (VIX) option pricing. The purpose is to determine whether the GARCH option pricing model can be used for price discovery in the volatility index option market. The different GARCH models are fitted to VIX futures returns. The pricing performance is tested by comparing the option prices implied by the models to market option prices. The results show that the symmetric GARCH model with skewed Student-t errors is the best performing model, and that the GARCH option pricing model provides reasonable price discovery when applied to the VIX.

Pricing and Hedging Options on Assets with Options on Related Assets

The question addressed is the pricing of options on the CBOE Skew Index. The option pricing theory developed partially hedges risk by taking positions in the market for options on a related asset. The option is then priced at the cost of this hedge. The theory is applied to pricing Volatility Index (VIX) options hedged by the SPDR S&P 500 ETF Trust (SPY) options and pricing options on JPMorgan hedged by Financial Select Sector SPDR (XLF) options. The approach is then applied to illustrate the pricing of CBOE Skew Index options with a hedge in the market for SPY options. The Skew Index smile is then seen to imply the VIX and SKEW of the Skew Index itself. The pricing of VIX options with SPY as the related asset has the Gaussian copula underpricing options while the t-copula significantly overprices them. The multivariate bilateral gamma models are closer to market. The premia of cross-asset hedge prices over the market price are observed to fall with moneyness and maturity and rise with the level of the VIX. TOPICS:Derivatives, options, exchange-traded funds and applications, quantitative methods, statistical methods, performance measurement Key Findings ▪ Time series data on physical returns may be used to obtain market relevant option prices provided market-relevant hedging costs are incorporated. ▪ Options on the CBOE Skew Index are priced at the cost of an SPY option hedge portfolio. ▪ Residual risk pricing technologies may be applied more widely with market calibrated parameters if desired.

On the Autocorrelation of the Stock Market*

Abstract I introduce an index of market return autocorrelation based on the prices of index options and of forward-start index options and implement it at a six-month horizon. The results suggest that the autocorrelation of the S&P 500 index was close to zero before the subprime crisis but was negative in its aftermath, attaining values around –20% to –30%. I speculate that this may reflect market perceptions about the likely reaction, via quantitative easing, of policymakers to future market moves.

Market Instability, Investor Sentiment, and Probability Judgment Error in Index Option Prices

How do financial markets switch from states of optimism to pessimism and vice versa? Given that a financial market is currently stable, what is the probability that it will become unstable and crash? We answer those questions in the context of a natural experiment with risk sources of probability judgment error, i.e. source functions, implied by index option prices. Source functions reflect investors (option traders) sentiments about the ranking of index options' attractiveness and the weight they place on each rank. We introduce a novel behavioural process (hereinafter BELLE), constructed from noise in investors probability judgment, that (1) characterizes investor sentiment about tail events in index option prices over time and probability ranks, (2) provides early warning signals of market instability, and (3) crash probability estimates from a closed form expression for the time varying transition probability that a seemingly stable market state will become unstable and crash. The model makes the fatalistic prediction that over time investor sentiment about index option prices characterize market transition from stable to unstable states and crash almost surely.

Option-Based Estimation of the Price of Coskewness and Cokurtosis Risk

AbstractWe show that the prices of risk for factors that are nonlinear in the market return can be obtained using index option prices. The price of coskewness risk corresponds to the market variance risk premium, and the price of cokurtosis 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 analysis of factor models with coskewness risk indicates that the new estimates of the price of risk improve the models’ performance compared with regression-based estimates.

Inferring information from the S&P 500, CBOE VIX, and CBOE SKEW indices

AbstractThis paper compares the information extracted from the S&P 500, CBOE VIX, and CBOE SKEW indices for the S&P 500 index option pricing. Based on our empirical analysis, VIX is a very informative index for option prices. Whether adding the SKEW or the VIX term structure can improve the option pricing performance depends on the model we choose. Roughly speaking, the VIX term structure is informative for some models, while the SKEW is very noisy and does not contain much important information for option prices. This paper also extends Zhang et al. (2017, J Futures Markets, 37, 211–237) into three typical affine models.