Model specification of conditional jump intensity: Evidence from S&P 500 returns and option prices

This study investigates the model specification of the conditional jump intensity under option pricing models having a generalized autoregressive conditional heteroskedastic with jumps (GARCH-jump). We compare three GARCH-jump models of Chang, Chang, Cheng, Peng, and Tseng (2018) to examine whether specifying asymmetric jumps in conditional jump intensity can improve the empirical performance. The empirical results from S&P 500 returns and options show that specifying the asymmetric jumps into the conditional jump intensity does improve the in-sample pricing errors and implied volatility errors. However, the out-of-sample results depend on the error measurement.     

No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects,jumps and i.i.d. noise: Theory and testable distributional implications

We develop a sequential procedure to test the adequacy of jump-diffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects. A novel robust-to-jumps approach is utilized to alleviate microstructure frictions for realized volatility estimation. Size and power of the procedure are explored through Monte Carlo methods. Our empirical findings support the jump-diffusive representation for S&P500 futures returns but reveal it is critical to account for leverage effects and jumps to maintain the underlying semi-martingale assumption.     

Jump tails,extreme dependencies,and the distribution of stock returns

We provide a new framework for estimating the systematic and idiosyncratic jump tail risks in financial asset prices. Our estimates are based on in-fill asymptotics for directly identifying the jumps, together with Extreme Value Theory (EVT) approximations and methods-of-moments for assessing the tail decay parameters and tail dependencies. On implementing the procedures with a panel of intraday prices for a large cross-section of individual stocks and the S&P 500 market portfolio, we find that the distributions of the systematic and idiosyncratic jumps are both generally heavy-tailed and close to symmetric, and show how the jump tail dependencies deduced from the high-frequency data together with the day-to-day variation in the diffusive volatility account for the “extreme” joint dependencies observed at the daily level.     

Variance dynamics: Joint evidence from options and high-frequency returns

This paper analyzes the S&P 500 index return variance dynamics and the variance risk premium by combining information in variance swap rates constructed from options and quadratic variation estimators constructed from tick data on S&P 500 index futures. Estimation shows that the index return variance jumps. The jump arrival rate is not constant over time, but is proportional to the variance rate level. The variance jumps are not rare events but arrive frequently. Estimation also identifies a strongly negative variance risk premium, the absolute magnitude of which is proportional to the variance rate level.     

GARCH models,tail indexes and error distributions: An empirical investigation

We perform a large simulation study to examine the extent to which various generalized autoregressive conditional heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 stock market returns and compare these to the tail indexes produced by simulating GARCH models. Our results suggest that actual and simulated values differ greatly for GARCH models with normal conditional distributions, which underestimate the tail risk. By contrast, the GARCH models with Student's t conditional distributions capture the tail shape more accurately, with GARCH and GJR-GARCH being the top performers.     

Time-varying jump tails

We develop new methods for the estimation of time-varying risk-neutral jump tails in asset returns. In contrast to existing procedures based on tightly parameterized models, our approach imposes much fewer structural assumptions, relying on extreme-value theory approximations together with short-maturity options. The new estimation approach explicitly allows the parameters characterizing the shape of the right and the left tails to differ, and importantly for the tail shape parameters to change over time. On implementing the procedures with a panel of S&P 500 options, our estimates clearly suggest the existence of highly statistically significant temporal variation in both of the tails. We further relate this temporal variation in the shape and the magnitude of the jump tails to the underlying return variation through the formulation of simple time series models for the tail parameters.     

Variance trading and market price of variance risk

This paper develops a new approach for variance trading. We show that the discretely-sampled realized variance can be robustly replicated under very general conditions, including when the price can jump. The replication strategy specifies the exact timing for rebalancing in the underlying. The deviations from the optimal schedule can lead to surprisingly large hedging errors. In the empirical application, we synthesize the prices of the variance contract on S&P 500 index over the period from 01/1990 to 12/2009. We find that the market variance risk is priced, its risk premium is negative and economically very large. The variance risk premium cannot be explained by the known risk factors and option returns.     

On implied volatility for options—Some reasons to smile and more to correct

We analyze the properties of the implied volatility, the commonly used volatility estimator by direct option price inversion. It is found that the implied volatility is subject to a systematic bias in the presence of pricing errors, which makes it inconsistent to the underlying volatility. We propose an estimator of the underlying volatility by first estimating nonparametrically the option price function, followed by inverting the nonparametrically estimated price. It is shown that the approach removes the adverse impacts of the pricing errors and produces a consistent volatility estimator for a wide range of option price models. We demonstrate the effectiveness of the proposed approach by numerical simulation and empirical analysis on S&P 500 option data.     

Calibration of stochastic volatility models: A Tikhonov regularization approach

We aim to calibrate stochastic volatility models from option prices. We develop a Tikhonov regularization approach with an efficient numerical algorithm to recover the risk neutral drift term of the volatility (or variance) process. In contrast to most existing literature, we do not assume that the drift term has any special structure. As such, our algorithm applies to calibration of general stochastic volatility models. An extensive numerical analysis is presented to demonstrate the efficiency of our approach. Interestingly, our empirical study reveals that the risk neutral variance processes recovered from market prices of options on S&P 500 index and EUR/USD exchange rate are indeed linearly mean-reverting.     

S&P 500 futures market and the normal backwardation hypothesis

This paper examines the behavior of near term S&P 500 index futures contract prices in the context of the theory of normal backwardation. Daily S&P 500 futures prices for 41 contracts over the 1982–1992 period are examined. There is no evidence that S&P 500 futures prices are biased estimates of the expected future spot price on expiration. Daily futures prices usually lie below the expected future spot price on expiration and usually rise over the contract period, but these price movements are not statistically significant. The surprising result of this study is the number of observations where backwardation appears not to hold. Furthermore, changes in the U.S. dollar exchange rates, the Tax Reform Act of 1986 and the switching of S&P 500 contracts quarterly expiration day had no significant effect on the behavior of S&P 500 futures prices.     

Contagion testing in frontier markets under alternative stressful S&P 500 market scenarios

We use alternative approaches to identify stable and stressful scenarios in the S&P 500 market, to offer a new perspective for constructing contagion tests in recipient frontier markets vulnerable to disturbances from this source market. The S&P 500 market is decomposed into discrete conditions of: (1) tranquil versus turbulent volatility; (2) bull versus bear market phases; (3) normal periods versus asset bubbles and crashes. Based on these identified scenarios, we use various co-moment contagion tests to analyse the changing relationship between the S&P 500 market and major frontier markets in the Caribbean region that have prominent trade related exposure to the US. Our findings show that, outside of the events of the Great Recession, the Caribbean stock exchanges are largely independent of the S&P 500 market.     

Forecasting the volatility of asset returns: The informational gains from option prices

A new class of forecasting models is proposed that extends the realized GARCH class of models through the inclusion of option prices to forecast the variance of asset returns. The VIX is used to approximate option prices, resulting in a set of cross-equation restrictions on the model’s parameters. The full model is characterized by a nonlinear system of three equations containing asset returns, the realized variance, and the VIX, with estimation of the parameters based on maximum likelihood methods. The forecasting properties of the new class of forecasting models, as well as a number of special cases, are investigated and applied to forecasting the daily S&P500 index realized variance using intra-day and daily data from September 2001 to November 2017. The forecasting results provide strong support for including the realized variance and the VIX to improve variance forecasts, with linear conditional variance models performing well for short-term one-day-ahead forecasts, whereas log-linear conditional variance models tend to perform better for intermediate five-day-ahead forecasts.     

Option pricing with discrete time jump processes

In this paper we propose new option pricing models based on class of models with jumps contained in the Lévy-type based models (NIG-Lévy, Schoutens, 2003, Merton-jump, Merton, 1976 and Duan based model, Duan et al., 2007). By combining these different classes of models with several volatility dynamics of the GARCH type, we aim at taking into account the dynamics of financial returns in a realistic way. The associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel: we provide a characterization of the change in the probability measure using the Esscher transform and the Minimal Entropy Martingale Measure. We finally assess empirically the performance of this modelling approach, using a dataset of European options based on the S&P 500 and on the CAC 40 indices. Our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness. These results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist.     

Higher moment exchange rate exposure of S&P500 firms

We examine the impact of higher order moments of changes in the exchange rate on stock returns of U.S. large-cap companies in the S&P500. We find a robust negative effect of exchange rate volatility on S&P500 company returns. The consumer discretionary and the consumer staples sectors have significant negative exposure to exchange rate volatility suggesting that exchange rate volatility affects stock returns through the channel of international operations. In terms of industries, the household products and personal products industries have significant negative exposure as well. The impact in the financial sector suggests that derivatives and hedging activity can mitigate exposure to exchange rate volatility. We find weak evidence that exchange rate skewness has an effect on S&P500 stock returns, but, find evidence that exchange rate kurtosis affects returns of companies that are more exposed to exchange rate volatility.     

Day-of-the-week effect on the VIX. A parsimonious representation

The study of significant deterministic seasonal patterns in financial asset returns is of high importance to academia and investors. This paper analyzes the presence of seasonal daily patterns in the VIX and S&P 500 returns series using a trigonometric specification. First, we show that, given the isomorphism between the trigonometrical and alternative seasonality representations (i.e., daily dummies), it is possible to test daily seasonal patterns by employing a trigonometrical representation based on a finite sum of weighted sines and cosines. We find a potential evolutive seasonal pattern in the daily VIX that is not in the daily S&P 500 log-returns series. In particular, we find an inverted Monday effect in the VIX level and changes in the VIX, and a U-shaped seasonal pattern in the changes in the VIX when we control for outliers. The trigonometrical representation is more robust to outliers than the one commonly used by literature, but it is not immune to them. Finally, we do not find a day-of-the-week effect in S&P 500 returns series, which suggests the presence of a deterministic seasonal pattern in the relation between VIX and S&P 500 returns.     

Modeling dynamic conditional correlations with leverage effects and volatility spillover effects: Evidence from the Chinese and US stock markets affected by the recent trade friction

In this article, we investigate the dynamic conditional correlations (DCCs) with leverage effects and volatility spillover effects that consider time difference and long memory of returns, between the Chinese and US stock markets, in the Sino-US trade friction and previous stable periods. The widespread belief that the developed markets dominate the emerging markets in stock market interactions is challenged by our findings that both the mean and volatility spillovers are bidirectional. We do find that most of the shocks to these DCCs between the two stock markets are symmetric, and all the symmetric shocks to these DCCs are highly persistent between Shanghai’s trading return and S&P 500′s trading or overnight return, however all the shocks to these DCCs are short-lived between S&P 500′s trading return and Shanghai’s trading or overnight return. We also find clear evidence that the DCC between Shanghai’s trading return and S&P 500′s overnight return has a downward trend with a structural break, perhaps due to the “America First” policy, after which it rebounds and fluctuates sharply in the middle and later periods of trade friction. These findings have important implications for investors to pursue profits.     

Twitter’s daily happiness sentiment,economic policy uncertainty,and stock index fluctuations

This research applies quantile Granger causality and impulse-response analyses to evaluate the causal linkages among Twitter’s daily happiness sentiment, economic policy uncertainty (EPU), and S&P 500 indices across the U.S. stock market cycles. We present notable evidence of bi-directional causality among cyclical components of Twitter’s daily happiness sentiment, economic policy uncertainty, and S&P 500 indices for most quantiles. The causal linkage of Twitter’s daily happiness sentiment and S&P 500 indices identified in this study reconciles the so-called Easterlin Paradox and Easterlin Illusion arguments from previous studies on income-happiness relationship. Moreover, given a high (low) EPU level, the positive (negative) impulse-response effects between the Twitter’s daily happiness sentiment and the S&P 500 indices are justified during a stock market bust cycle, but the signs of these correlations change to negative (positive) during a stock market boom cycle. These findings imply that investors’ hedging strategies can be linked to the surveillance of the Twitter’s daily happiness sentiment index.     

Estimation of objective and risk-neutral distributions based on moments of integrated volatility

In this paper, we present an estimation procedure which uses both option prices and high-frequency spot price feeds to estimate jointly the objective and risk-neutral parameters of stochastic volatility models. The procedure is based on a method of moments that uses analytical expressions for the moments of the integrated volatility and series expansions of option prices and implied volatilities. This results in an easily implementable and rapid estimation technique. An extensive Monte Carlo study compares various procedures and shows the efficiency of our approach. Empirical applications to the Deutsche mark–US dollar exchange rate futures and the S&P 500 index provide evidence that the method delivers results that are in line with the ones obtained in previous studies where much more involved estimation procedures were used.     

Quadratic hedging schemes for non-Gaussian GARCH models

We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan׳s (1995) delta hedge. Since the minimal martingale measure fails to produce a probability measure in this setting, we construct local risk minimization hedging strategies with respect to a pricing kernel. These approaches are investigated in the context of non-Gaussian driven models. Furthermore, we analyze these methods for non-Gaussian GARCH diffusion limit processes and link them to the corresponding discrete time counterparts. A detailed numerical analysis based on S&P 500 European call options is provided to assess the empirical performance of the proposed schemes. We also test the sensitivity of the hedging strategies with respect to the risk neutral measure used by recomputing some of our results with an exponential affine pricing kernel.