Index Option Prices Research Articles

Equity Correlations Implied by Index Options: Estimation and Model Uncertainty Analysis

We propose a method for constructing an arbitrage-free multi-asset pricing model which is consistent with a set of observed single- and multi-asset derivative prices. The pricing model is constructed as a random mixture of N reference models, where the distribution of mixture weights is obtained by solving a well-posed convex optimization problem. Application of this method to equity and index options shows that, while multivariate diffusion models with constant correlation fail to match the prices of index and component options simultaneously, a jump-diffusion model with a common jump component affecting all stocks enables to do so. Furthermore, we show that even within a parametric model class, there is a wide range of correlation patterns compatible with observed prices of index options. Our method allows, as a by product, to quantify this model uncertainty with no further computational effort and propose static hedging strategies for reducing the exposure of multi-asset derivatives to model uncertainty.

Short Positions, Rally Fears and Option Markets

Index option pricing on world market indices are investigated using Lévy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a rally before a crash. Three models are used to effectively calibrate index options at an annual maturity, and it is observed that positive jumps may be needed for FTSE, N225 and HSI. Rally before a crash probabilities are shown to have fallen by 10 points after July 2007. Typical implied volatility curves for such models are also described and illustrated. They have smirks and never smile.

Regime switching stochastic volatility option pricing

Stochastic volatility option pricing has become popular in financial mathematics due to its theoretical and empirical consistencies. However, stochastic volatility models generally suffer from analytical and calibration intractability, except for regime switching stochastic volatility. However, regime switching models neither model volatility nor price options over short time periods accurately, hence they are of limited use. This paper proposes a general method of pricing regime switching options over short time periods. We achieve this by relating Fouque's perturbation based option pricing method to regime switching models. We conduct numerical experiments to validate our method using empirical S&P 500 index option prices and compare our results to Black-Scholes and Fouque's standard option pricing method. We demonstrate our pricing method which provides lower relative error compared to the Fouque's standard option pricing method and Black-Scholes pricing. In addition, this paper can be seen as an extension to Fouque's standard option pricing method.

Predictable dynamics in implied volatility surfaces from OTC currency options

Recent empirical studies report predictable dynamics in the volatility surfaces that are implied by observed index option prices, such as those prescribed by general equilibrium models. Using an extensive data set from the over-the-counter options market, we document similar predictability in the factors that capture the daily variation of surfaces implied by options on 25 different foreign exchange rates. We proceed to demonstrate that simple vector autoregressive specifications for the factors can help produce accurate out-of-sample forecasts of the systematic component of the surface at short horizons. Profitable delta-hedged positions can be set up based on these forecasts; however, profits disappear when typical transaction costs are taken into account and when trading rules on wide segments of the surface are sought.

Effects of Market Sentiment in Index Option Pricing: A Study of CNX Nifty Index Option

This paper provides evidence of the role of sentiments in pricing Indian CNX Nifty index call Option during the period from April 2002 to December 2008. It also shows that Black-Scholes option pricing model using the implied volatility of previous day is pricing the Index options much closer to the actual price compared to Modified Black-Scholes pricing model incorporating non-normal skewness and kurtosis suggested by Corrado & Sue [1996]. The market is pricing the call option higher than Black-Scholes price during bullish period compared to that of bearish period even though sentiments are incorporated in the underlying asset which in this case is the Nifty Index. The index call options are priced about 1.5 percent more than Black-Scholes price during Bullish period compared to that of Bearish period during the period of observation.

Recent Advances in Credit Risk Modeling

As is well known, most models of credit risk have failed to measure the credit risks in the context of the global financial crisis. In this context, financial industry representatives, regulators and academics worldwide have given new impetus to efforts to improve credit risk modeling for countries, corporations, financial institutions, and financial instruments. The paper summarizes some of the recent advances in this regard. It considers modifications of structural models, including of the classical Merton model, and efforts to reconcile the structural and the reduced-form models. It also discusses the reassessment of the default correlations using copulas, the pricing of credit index options, and the determination of the prices of distressed debt and estimation of recovery values.

Short Positions, Rally Fears and Option Markets

Index option pricing on world market indices are investigated using Levy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a Rally Before a Crash (RBC). Three models are used to effectively calibrate index options at an annual maturity and it is observed that positive jumps may be needed for FTSE, N225 and HSI. RBC probabilities are shown to have fallen by 10 points after July 2007. Typical implied volatility curves for such models are also described and illustrated. They have smirks and never smile.

Empirical of the Taiwan stock index option price forecasting model – applied artificial neural network

This work presents a novel neural network model for forecasting option prices using past volatilities and other options market factors. Out of different approaches to estimating volatility in the option pricing model, this study uses backpropagation neural network to forecast prices for Taiwanese stock index options. The ability to develop accurate forecasts of grey prediction volatility enables practitioners to establish an appropriate hedging strategy at in-the-money option.

The Volatility Risk Premium in the KOSPI200 Index Options

This study examines whether the volatility risk premium is reflected on the prices of the KOSPI200 index options. By applying the empirical method of Bakshi and Kapadia (2003), we analyze the performance of delta-hedging strategy in the KOSPI200 index market. They showed the existence of the negative volatility risk premium in the S&P 500 index options as well as derived theoretical positive relationship between the volatility risk premium and delta-hedging gains. However, in the results of this study, contrary to those in the S&P 500 index options market, we do not observe the volatility risk premium. Delta-hedged gains of ATM options are not significantly negative. Delta-hedged gains are not more negative as historical volatility increases and as options' vega and remaining maturity increase. However, the notable finding of this study is that delta-hedged gains of OTM options and put options are negative and signigicant. This results can be caused by the phenomenon of overpriced puts or by market microstructure factors, such as relatively wide bid-ask spread and high tick size. In a simple examination of comparison between changes in traded option prices and changes in the Black-Scholes option prices during delta-hedging period, negative delta-hedged gains seem to be attributed to too small changes in call option prices and too large changes in put option prices. In conclusion, by analyzing the delta-hedged gains, the volatility risk risk premium seems not be observed in the KOSPI200 index options market.

Uncertainty, Time-Varying Fear, and Asset Prices

I construct an equilibrium model that captures salient properties of index option prices, equity returns, variance, and the risk-free rate. A representative investor makes consumption and portfolio choice decisions that are robust to his uncertainty about the true economic model. He pays a large premium for index options because they hedge important model misspecification concerns, particularly concerning jump shocks to cash flow growth and volatility. A calibration shows that empirically-consistent fundamentals and a reasonable level of model uncertainty explain option prices and the variance premium. Time variation in investor uncertainty generates variance premium fluctuations and helps explain their power to predict stock returns.

The Effects of Investor Sentiment on Speculative Trading and Prices of Stock and Index Options

We find that the demand for stock option positions that increase exposure to the underlying is positively related to measures of investor sentiment and past market returns, while the demand for index options is invariant to these factors. These differences in trading patterns are reflected in differences in the composition of traders in the different types of options -- Options on stocks are actively traded by individual investors, while trades in index options are more often motivated by hedging demands of sophisticated investors. Consistent with a demand based view of option pricing, we find that sentiment is related to time-series variation in the slope of the implied volatility smile of stock options, but has little impact on the prices of index options. The pricing impact is more pronounced in options with a higher concentration of unsophisticated investors and in options with higher hedging costs. Our results provide new evidence factors not related to fundamentals affect price of securities actively traded by noise traders.

The Effects of Investor Sentiment on Speculative Trading and Prices of Stock and Index Options

We find that speculative demand for equity options is positively related to investor sentiment, while hedging demand is invariant to sentiment. Consistent with a demand based view of option pricing, we find that sentiment is related to time-series variation in the slope of the implied volatility smile of stock options, but has little impact on the prices of index options. The pricing impact is more pronounced in options with higher concentration of speculative trading, higher transactions costs, higher stock return volatility, and smaller stock size. Our results suggest that the correlated biases of noise traders affect the trading and prices of securities that are subject to speculation, but do not affect prices of securities in which demand is driven by hedging motives unrelated to sentiment. JEL Classification Code: G1

Recent Advances in Credit Risk Modeling

As is well known, most models of credit risk have failed to measure the credit risks in the context of the global financial crisis. In this context, financial industry representatives, regulators and academics worldwide have given new impetus to efforts to improve credit risk modeling for countries, corporations, financial institutions, and financial instruments. The paper summarizes some of the recent advances in this regard. It considers modifications of structural models, including of the classical Merton model, and efforts to reconcile the structural and the reduced-form models. It also discusses the reassessment of the default correlations using copulas, the pricing of credit index options, and the determination of the prices of distressed debt and estimation of recovery values.

Using neural network to forecast stock index option price: a new hybrid GARCH approach

This study aims to apply a new hybrid approach to estimate volatility in neural network option-pricing model. The analytical results also indicate that the new hybrid method can be used to forecast the prices of derivative securities. Owing to combines the grey forecasting model with the GARCH to improve the estimated ability, the empirical evidence shows that the new hybrid GARCH model outperforms the other approaches in the neural network option-pricing model.

Stock index volatility: evidence for stock index options in Taiwan

This study applies artificial neural network to forecast Taiwan stock index option prices from 2005 to 2006. This study compares the option pricing model using three approaches to volatility: GARCH, EGARCH and GJR-GARCH, and compares estimators with three sets of criteria: RMSE, MAE and MAPE. The analytic results indicate that the asymmetric GARCH model is useful in predicting neural networks for stock index option prices.

Arbitrages and Arrow-Debreu Prices

The goal of this work is to check that there are no arbitrage opportunities in the CBOE market for SP in Section 2 we consider two models which seem to be consistent with the market prices of index options: the CEV model and the Merton model; finally, in Section 3 we estimate the state-price density consistent with the Merton model. Some conclusions follow.

Reconciling Smiles for Index and Stock Options

The fact that the implied volatility smiles for equity indices are strongly downward sloping, while the typical individual stock exhibits either a at or even an upward sloping smile is sometimes considered puzzling. We show that this eect can easily be generated in a simple and parsimonious two-factor stochastic volatility model in the spirit of Bates (2000). From a theoretical perspective our paper adds to the literature by proving a ’diversication’ result with respect to idiosyncratic stochastic volatility components of individual stocks, so that in the limit for innitely many stocks, the prices of index options are solely based on the common volatility component. This result holds without restrictive assumptions on the structure of the correlations between stock returns and volatility changes. We employ Monte Carlo simulation to show that our model can reproduce the empirical observations quite well for an index of 30 stocks similar to the Dow Jones Industrial Average.

Artificial neural network model of the hybrid EGARCH volatility of the Taiwan stock index option prices

This investigation integrates a novel hybrid asymmetric volatility approach into an Artificial Neural Networks option-pricing model to upgrade the forecasting ability of the price of derivative securities. The use of the new hybrid asymmetric volatility method can simultaneously decrease the stochastic and nonlinearity of the error term sequence, and capture the asymmetric volatility. Therefore, analytical results of the ANNS option-pricing model reveal that Grey-EGARCH volatility provides greater predictability than other volatility approaches.

Arbitrage-Free Pricing of Credit Index Options: The No-Armageddon Pricing Measure and the Role of Correlation after the Subprime Crisis

In this work we consider three problems of the standard market approach to the pricing of credit index options: the definition of the index spread is not valid in general, the payoff considered leads to a pricing which is not always defined, and the candidate numeraire to define a pricing measure is not strictly positive, which would lead to an inequivalent pricing measure. We give to the three problems a general mathematical solution, based on a novel way of modelling the flow of information through the definition of a new subfiltration. Using this subfiltration, we take into account consistently the possibility of default of all names in the portfolio, that is neglected in the standard market approach. We show that, while this mispricing can be negligible for standard options in normal market conditions, it can become highly relevant for different options or in stressed market conditions. In particular, we show on 2007 market data that after the subprime credit crisis the mispricing of the market formula compared to the no arbitrage formula we propose has become financially relevant even for the liquid Crossover Index Options.

The Effects of Investor Sentiment on Speculative Trading and Prices of Stock and Index Options

The Effects of Investor Sentiment on Speculative Trading and Prices of Stock and Index Options