How Crashes Develop: Intradaily Volatility and Crash Evolution

This paper explores whether affine models with volatility jumps estimated on intradaily S&P 500 futures data over 1983 to 2008 can capture major daily outliers such as the 1987 stock market crash. Intradaily jumps in futures prices are typically small; self‐exciting but short‐lived volatility spikes capture intradaily and daily returns better. Multifactor models of the evolution of diffusive variance and jump intensities improve fits substantially, including out‐of‐sample over 2009 to 2016. The models capture reasonably well the conditional distributions of daily returns and realized variance outliers, but underpredict realized variance inliers. I also examine option pricing implications.     

Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence

American options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2009) from 1983 to 2006 are identified as potentially profitable trades. Call bid prices more frequently violate their upper bound than put bid prices do, while violations of the lower bounds by ask prices are infrequent. In out‐of‐sample tests of stochastic dominance, the writing of options that violate the upper bound increases the expected utility of any risk‐averse investor holding the market and cash, net of transaction costs and bid‐ask spreads. The results are economically significant and robust.     

Futures Options and the Volatility of Futures Prices

Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at-the-money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.     

Effects of market default risk on index option risk-neutral moments

We investigate the relative importance of market default risk in explaining the time variation of the S&P 500 Index option-implied risk-neutral moments. The results demonstrate that market default risk is positively (negatively) related to the index risk-neutral volatility and skewness (kurtosis). These relations are robust in the presence of other factors relevant to the dynamics and microstructure nature of the spot and option markets. Overall, this study sheds light on a set of economic determinants which help to understand the daily evolution of the S&P 500 Index option-implied risk-neutral distributions. Our findings offer explanations of why theoretical predictions of option pricing models are not consistent with what is observed in practice and provide support that market default risk is important to asset pricing.     

The Crash of ʼ87: Was It Expected? The Evidence from Options Markets

Transactions prices of S&P 500 futures options over 1985-1987 are examined for evidence of expectations prior to October 1987 of an impending stock market crash. First, it is shown that out-of-the-money puts became unusually expensive during the year preceding the crash. Second, a model is derived for pricing American options on jump-diffusion processes with systematic jump risk. The jump-diffusion parameters implicit in options prices indicate that a crash was expected and that implicit distributions were negatively skewed during October 1986 to August 1987. Both approaches indicate no strong crash fears during the 2 months immediately preceding the crash.     

Do economic statistics contain information to predict stock indexes futures prices and returns? Evidence from Asian equity futures markets

This research examines the impact of local and international market factors on the pricing of stock indexes futures in East Asian countries. The purpose of this paper is to present a study of the significant factors that determine the major stock indexes futures’ prices of Hong Kong, Malaysia, Singapore, South Korea and Taiwan. This study first investigates the relationships between Hang Seng Index Futures, KLCI Futures, SiMSCI Futures, KOSPI Futures, Taiwan Exchange Index Futures and local interest rates, dividend yields, local exchange rates, overnight S&P500 index and a newly constructed index, Asian Tigers Malaysia Index (ATMI). 11 years historical data of stock indexes futures and the economic statistics are studied; 10 years in-sample data are used for testing and developing the pricing models, and 1 year out-of-sample data is used for the purpose of verifying the predicted values of the stock indexes futures. Using simple linear regressions, local interest rates, dividend yields, exchange rates, overnight S&P500 and ATMI are found to have significant impact on these futures contracts. In this research, the next period close is predicted using simple linear regression and non-linear artificial neural network (ANN). An examination of the prediction results using nonlinear autoregressive ANN with exogenous inputs (NARX) shows significant abnormal returns above the passive threshold buy and hold market returns and also above the profits of simple linear regression (SLR). The empirical evidence of this research suggests that economic statistics contain information which can be extracted using a hybrid SLR and NARX trading model to predict futures prices with some degree of confidence for a year forward. This justifies further research and development of pricing models using fundamentally significant economic determinants to predict futures prices.

     

THE ECONOMIC VALUE OF USING REALIZED VOLATILITY IN FORECASTING FUTURE IMPLIED VOLATILITY

We examine the economic benefits of using realized volatility to forecast future implied volatility for pricing, trading, and hedging in the S&P 500 index options market. We propose an encompassing regression approach to forecast future implied volatility, and hence future option prices, by combining historical realized volatility and current implied volatility. Although the use of realized volatility results in superior performance in the encompassing regressions and out-of-sample option pricing tests, we do not find any significant economic gains in option trading and hedging strategies in the presence of transaction costs.     

Common asset pricing factors in volatilities and returns in futures markets

Factor-based asset pricing models have been used to explain the common predictable variation in excess asset returns. This paper combines means with volatilities of returns in several futures markets to explain their common predictable variation. Using a latent variables methodology, tests do not reject a single factor model with a common time-varying factor loading. The single common factor accounts for up to 53% of the predictable variation in the volatilities and up to 14% of the predictable variation in the means. S&P500 futures volatility predicted by the factor model is highly correlated with volatility implied in S&P500 futures options. But both the factor and implied volatilities are significant in predicting future volatility. In derivatives pricing, both implied volatility from options and factors extracted from asset pricing models should be employed.     

Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model

The profound financial crisis generated by the collapse of Lehman Brothers and the European sovereign debt crisis in 2011 have caused negative values of government bond yields both in the USA and in the EURO area. This paper investigates whether the use of models which allow for negative interest rates can improve option pricing and implied volatility forecasting. This is done with special attention to foreign exchange and index options. To this end, we carried out an empirical analysis on the prices of call and put options on the US S&P 500 index and Eurodollar futures using a generalization of the Heston model in the stochastic interest rate framework. Specifically, the dynamics of the option’s underlying asset is described by two factors: a stochastic variance and a stochastic interest rate. The volatility is not allowed to be negative, but the interest rate is. Explicit formulas for the transition probability density function and moments are derived. These formulas are used to estimate the model parameters efficiently. Three empirical analyses are illustrated. The first two show that the use of models which allow for negative interest rates can efficiently reproduce implied volatility and forecast option prices (i.e. S&P index and foreign exchange options). The last studies how the US three-month government bond yield affects the US S&P 500 index.     

The October 1987 S&P 500 Stock-Futures Basis

Five-minute changes in the S&P 500 index and futures contract are examined over a ten-day period surrounding the October 1987 stock market crash. Since nonsynchronous trading problems are severe in these data, new index estimators are derived and used. The estimators use the complete transaction history of all 500 stocks. Nonsynchronous trading explains part of the large absolute futures-cash basis observed during the crash. The remainder may be due to disintegration of the two markets. Even after adjustment for nonsynchronous trading, the index displays more autocorrelation than does the futures and the futures leads the index.     

Generative Bayesian neural network model for risk-neutral pricing of American index options

Financial models with stochastic volatility or jumps play a critical role as alternative option pricing models for the classical Black–Scholes model, which have the ability to fit different market volatility structures. Recently, machine learning models have elicited considerable attention from researchers because of their improved prediction accuracy in pricing financial derivatives. We propose a generative Bayesian learning model that incorporates a prior reflecting a risk-neutral pricing structure to provide fair prices for the deep ITM and the deep OTM options that are rarely traded. We conduct a comprehensive empirical study to compare classical financial option models with machine learning models in terms of model estimation and prediction using S&P 100 American put options from 2003 to 2012. Results indicate that machine learning models demonstrate better prediction performance than the classical financial option models. Especially, we observe that the generative Bayesian neural network model demonstrates the best overall prediction performance.     

The Price of Immediacy

This paper models transaction costs as the rents that a monopolistic market maker extracts from impatient investors who trade via limit orders. We show that limit orders are American options. The limit prices inducing immediate execution of the order are functionally equivalent to bid and ask prices and can be solved for various transaction sizes to characterize the market maker's entire supply curve. We find considerable empirical support for the model's predictions in the cross-section of NYSE firms. The model produces unbiased, out-of-sample forecasts of abnormal returns for firms added to the S&P 500 index.     

Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes

We analyze the specifications of option pricing models based on time-changed Lévy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. Our estimation of a variety of model specifications indicates that to better capture the behavior of the S&P 500 index options, we need to incorporate a high frequency jump component in the return process and generate stochastic volatilities from two different sources, the jump component and the diffusion component.     

Assessing the performance of symmetric and asymmetric implied volatility functions

This study examines several alternative symmetric and asymmetric model specifications of regression-based deterministic volatility models to identify the one that best characterizes the implied volatility functions of S&P 500 Index options in the period 1996–2009. We find that estimating the models with nonlinear least squares, instead of ordinary least squares, always results in lower pricing errors in both in- and out-of-sample comparisons. In-sample, asymmetric models of the moneyness ratio estimated separately on calls and puts provide the overall best performance. However, separating calls from puts violates the put-call-parity and leads to severe model mis-specification problems. Out-of-sample, symmetric models that use the logarithmic transformation of the strike price are the overall best ones. The lowest out-of-sample pricing errors are observed when implied volatility models are estimated consistently to the put-call-parity using the joint data set of out-of-the-money options. The out-of-sample pricing performance of the overall best model is shown to be resilient to extreme market conditions and compares quite favorably with continuous-time option pricing models that admit stochastic volatility and random jump risk factors.     

S&P 100 Index Option Volatility

Using transaction data on the S&P 100 index options, we study the effect of valuation simplifications that are commonplace in previous research on the timeseries properties of implied market volatility. Using an American-style algorithm that accounts for the discrete nature of the dividends on the S&P 100 index, we find that spurious negative serial correlation in implied volatility changes is induced by nonsimultaneously observing the option price and the index level. Negative serial correlation is also induced by a bid/ask price effect if a single option is used to estimate implied volatility. In addition, we find that these same effects induce spurious (and unreasonable) negative cross-correlations between the changes in call and put implied volatility.     

An Empirical Investigation of Alternative Contingent Claims Models for Pricing Residential Mortgages

Researchers have employed option pricing techniques to analyze mortgage financing and valuation. Alternative models (one-, two-, and three-variable models) employing different variables (short- and long-term interest rates and building value) have been designed to price mortgage securities. No prior research has addressed the question of whether the pricing accuracy of these contingent claims models improves as states increase or whether contingent claims models' valuation abilities generate reasonable estimates of primary mortgage market prices. The articles investigates the relative efficiency of each of these alternative mortgage valuation models in predicting primary market mortgage values. Our results show that a two-variable model (short rate and building value) is the most efficient. Valuation results indicate a positive pricing spread between the primary market and the theoretically estimated value.     

INSTITUTIONAL TRADING AND SECURITY PRICES: THE CASE OF CHANGES IN THE COMPOSITION OF THE S&P 500 INDEX

This paper examines the common stock valuation and liquidity effects of firms being added to and deleted from the S&P 500 Index. Three potential pricing and trading volume hypotheses are discussed and tested—an Information Content Hypothesis (ICH), a Price Pressure Hypothesis (PPH), and a Liquidity Cost Hypothesis (LCH). The empirical findings indicate that firms being added to (deleted from) the S&P 500 Index over the 1977 to 1983 period experience positive (negative) abnormal common stock returns on the day following the addition. An analysis of common stock liquidity around additions to the Index reveals that while relative trading activity increases in the month of addition, it actually declines in subsequent months. The valuation and liquidity results are consistent to some degree with both the PPH and the LCH and are most likely due to index fund managers adjusting their holdings to reflect changes in the Index.     

A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks

We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network-pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with the no-arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1991.     

The Split of the S&P 500 Futures Contract: Effects on Liquidity and Market Dynamics

The Chicago Mercantile Exchange reduced the size of its S&P 500 futures contract when it reduced the multiplier from 500 to 250 and increased the minimum tick from 0.05 to 0.10 on November 3, 1997. This is a rare major change in a very successful contract's specifications. We analyze effects of this change on liquidity and market dynamics in both a univariate and a multivariate context. The main contribution of this study is the use of multiple intervention analysis with various dynamic response functions to examine the effects of the split while taking into account several other major market events surrounding it. A multivariate analysis is also used to test the impact of the split using a structural model of liquidity and market dynamics. Empirical findings offer limited support for the hypotheses that smaller contract size resulted in smoother trading, and that more public customers trade the S&P 500 futures contract following its split. We observe a reduction in the average transaction size as well as a temporary narrowing of the bid-ask spreads, but no significant change in volatility that can be attributed to the split. We do not find any significant and lasting impact on other liquidity and market variables.     

Index-futures arbitrage and the behavior of stock index futures prices

This article examines intraday transaction data for S&P500 stock index futures prices and the intraday quotes for theunderlying index. The data indicate that the futures price changesare uncorrelated and that the variability of these price changesexceeds the variability of price changes in the S&P 500index. This excess variability of the futures over the indexremains even after controlling for the nonsynchronous pricesin the index quotes, which induces auto-correlation in the indexchanges. We advance and examine empirically two hypotheses regardingthe difference between the futures price and its theoreticalvalue: that this 'mispricing' increases on average with maturity,and that it is path-dependent. Evidence supporting these hypothesesis presented.