Volatility Jumps Research Articles

Impact of volatility jumps in a mean-reverting model: Derivative pricing and empirical evidence

This paper investigates the critical role of volatility jumps under mean reversion models. Based on the empirical tests conducted on the historical prices of commodities, we demonstrate that allowing for the presence of jumps in volatility in addition to price jumps is a crucial factor when confronting non-Gaussian return distributions. By employing the particle filtering method, a comparison of results drawn among several mean-reverting models suggests that incorporating volatility jumps ensures an improved fit to the data. We infer further empirical evidence for the existence of volatility jumps from the possible paths of filtered state variables. Our numerical results indicate that volatility jumps significantly affect the level and shape of implied volatility smiles. Finally, we consider the pricing of options under the mean reversion model, where the underlying asset price and its volatility both have jump components.

Volatility and Z-Type Jumps of Euro Exchange Rates Using Outlying Weighted Quarticity Statistics in the 2010s

Purpose – This paper examines the recently realized continuous volatility and discrete jumps of US Dollar/Euro returns using the frequency of five minute returns spanning the period from February 2010 through February 2018with periodicity filters. Design/Methodology – This paper adopts the nonparametric estimation. The realized volatility and Realized Outlying Weighted variations show non-Gaussian, fat-tailed, and leptokurtic distributions. Some significant volatility jumps in returns occurred from 2010 through 2018, and the very exceptionally large and irregular jumps occurred around 2010-2011, after the EU financial crisis, and 2015-2016. The outliers occurred somewhat frequently around the years of 2015 and 2016. Originality/value – When we include periodicity filters of volatility such as MAD, Short Half Scale, and WSD, the five minute returns of US Dollar/Euro exchange rates have smaller daily jump probabilities by 20-30% than when we do not include the periodicity filters of volatility. Thus, when we consider the periodicity filters of volatility such as MAD, Short Half Scale, and WSD, the five minute returns of US Dollar/Euro have considerably smaller jump probabilities.

Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book

An extensive empirical literature documents a generally negative relation, named the “leverage effect,” between asset returns and changes of volatility. It is more challenging to establish such a return–volatility relationship for jumps in high-frequency data. We propose new nonparametric methods to assess and test for a discontinuous leverage effect — i.e. a covariation between contemporaneous jumps in prices and volatility. The methods are robust to market microstructure noise and build on a newly developed price-jump localization and estimation procedure. Our empirical investigation of six years of transaction data from 320 NASDAQ firms displays no unconditional negative covariation between price and volatility cojumps. We show, however, that there is a strong and significant discontinuous leverage effect if one conditions on the sign of price jumps and whether the price jumps are market-wide or idiosyncratic.

Oil shocks and volatility jumps

In this paper, we analyse the role of oil price shocks, derived from expectations of consumers, economists, financial market, and policymakers, in predicting volatility jumps in the S&P500 over the monthly period of 1988:01–2015:02, with the jumps having been computed based on daily data over the same period. Standard linear Granger causality tests fail to detect any evidence of oil shocks causing volatility jumps. But given strong evidence of nonlinearity and structural breaks between jumps and oil shocks, we next employed a nonparametric causality-in-quantiles test, as the linear model is misspecified. Using this data-driven robust approach, we were able to detect overwhelming evidence of oil shocks predicting volatility jumps in the S&P500 over its entire conditional distribution, with the strongest effect observed at the lowest considered conditional quantile. Interestingly, the predictive ability of the four oil shocks on volatility jumps is found to be both qualitatively and quantitatively similar.

The Impact of Jumps on American Option Pricing: The S&P 100 Options Case.

This paper analyzes the importance of asset and volatility jumps in American option pricing models. Using the Heston (1993) stochastic volatility model with asset and volatility jumps and the Hull and White (1987) short rate model, American options are numerically evaluated by the Method of Lines. The calibration of these models to S&P 100 American options data reveals that jumps, especially asset jumps, play an important role in improving the models' ability to fit market data. Further, asset and volatility jumps tend to lift the free boundary, an effect that augments during volatile market conditions, while the additional volatility jumps marginally drift down the free boundary. As markets turn more volatile and exhibit jumps, American option holders become more prudent with their exercise decisions, especially as maturity of the options approaches.

Regime Heteroskedasticity in Bitcoin: A Comparison of Markov Switching Models

In response to Molnar and Thies (2018) demonstrating that the price data of Bitcoin contained structural breaks, we identify the optimal number of states for a Markov regime-switching (MRS) model to capture the regime heteroskedasticity of Bitcoin. We determined that the restricted 5-state MRS model provided the best goodness-of-fit scores (-AIC, -BIC, -HQIC) for the fitted sample. In addition, we found evidence of stylised characteristics in the price data of Bitcoin, namely: volatility clustering; volatility jumps; asymmetric volatility transitions; and the persistence of shocks.

Pricing American Options With Jumps in Asset and Volatility

Jump risk plays an important role in current financial markets, yet it is a risk that cannot be easily measured and hedged. We numerically evaluate American call options under stochastic volatility, stochastic interest rates and jumps in both the asset price and volatility. By employing the Method of Lines (Meyer (2015)), the option price, the early exercise boundary and the Greeks are computed as part of the solution, which makes the numerical implementation time efficient. We conduct a numerical study to gauge the impact of jumps and stochastic interest rates on American call option prices and on their free boundaries. Jumps tend to increase the values of OTM and ATM options while decreasing the value of ITM options. The option delta is affected in a similar way. The impact of jumps on the free boundary is substantial and depends on the time to maturity. Near expiry, including asset jumps lowers the free boundary and the option holder is more likely to exercise the option, whilst including asset-volatility jumps elevates the free boundary and the option holder is less likely to exercise the option. This relation reverses at the beginning of the options life. The volatility, interest rates and their volatilities have a positive impact on the free boundaries and the option holder is less likely to exercise as these parameters increase.

NONPARAMETRIC STOCHASTIC VOLATILITY

We provide nonparametric methods for stochastic volatility modeling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, and jumps in returns and volatility with possibly state-dependent jump intensities, among other features. In the first stage, we identify spot volatility by virtue of jump-robust nonparametric estimates. Using observed prices and estimated spot volatilities, the second stage extracts the functions and parameters driving price and volatility dynamics from nonparametric estimates of the bivariate process’ infinitesimal moments. For these infinitesimal moment estimates, we report an asymptotic theory relying on joint in-fill and long-span arguments which yields consistency and weak convergence under mild assumptions.

Optimal portfolio allocation with volatility and co-jump risk that Markowitz would like

We study a continuous time optimal portfolio allocation problem with volatility and co-jump risk, allowing prices, variances and covariances to jump simultaneously. Differently from the traditional approach, we deviate from affine models by specifying a flexible Wishart jump-diffusion for the co-precision (the inverse of the covariance matrix). The optimal portfolio weights that solve the dynamic programming problem are genuinely dynamic and proportional to the instantaneous co-precision, reconciling optimal dynamic allocation with the static Markowitz-type economic intuition. An application to the optimal allocation problem across hedge fund investment styles illustrates the importance of having jumps in volatility associated with jumps in price.

Does Perception Matter in Asset Pricing? Modeling Volatility Jumps and Returns Using Twitter-Based Sentiment Indices

In this paper, I argue that we can use consumer and investor perceptions to forecast short-term fluctuations in asset prices. Using tweets scraped from Twitter between 2009 and 2019, I perform textual analysis to construct daily sentiment indices. While other scholars have relied on third-party companies to complete this task, doing so limits our potential understanding of sentiments' effects on asset pricing. The sentiment indices I constructed are numerical, not dichotomous, scores, which allows to control for sentiment strength. Results indicate that sentiments can forecast daily stock returns and volatility jumps.

Pricing Cryptocurrency Options: The Case of CRIX and Bitcoin

Cryptocurrencies, especially Bitcoin (BTC), which comprise a new revolutionary asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/ BTC include a high level of speculation, extreme volatility and price discontinuity. In this paper, we propose a pricing mechanism based on a stochastic volatility with correlated jump (SVCJ) model and compare it to a flexible co-jump model by Bandi and Reno (2016) allowing for non-affine structure. The calibration results of both models confirm the impact of jumps and co-jumps on options obtained via simulation and an analysis of the implied volatility curve. We show that a sizeable proportion of price jumps are significantly and contemporaneously anti-correlated with jumps in volatility. Our study comprises pioneering research on pricing BTC options. We show how proposed pricing mechanism underscores the importance of jumps in the cryptocurrency derivatives markets.

Volatility jumps and macroeconomic news announcements

While prior literature documents a link between macroeconomic news and price jumps, this paper demonstrates two channels through which economic announcements also manifest in volatility jumps. First, there is a strong coincidence of volatility jumps with scheduled announcements. Second, the mean jump size is an asymmetric function of the news surprise, with bad news resulting in larger jumps than good news. Furthermore, realized volatility (RV) and option‐implied volatility (IV) behave very differently over the days surrounding announcements. RV increases sharply on announcement days, while IV tends to decline consistent with the resolution of heightened uncertainty embedded in option prices.

Information about price and volatility jumps inferred from options prices

High‐frequency jump tests are applied to the prices of both futures contracts and their options, to infer the properties of jumps in the price and volatility of the underlying asset. Empirical results for FTSE 100 contracts detect frequent jumps in futures, call, and put prices. Jumps in futures prices are more important than any jumps in volatility when the market determines option prices. The empirical evidence is consistent with futures prices following affine jump‐diffusion processes, containing either futures price jumps or contemporaneous futures price, and volatility jumps, providing jump risk premia are included in the price dynamics.

Volatility jumps: The role of geopolitical risks

In this paper we analyse the role of a news-based index of geopolitical risks (GPRs), in predicting volatility jumps in the Dow Jones Industrial Average (DJIA) over the monthly period of 1899:01 to 2017:12, with the jumps having been computed based on daily data over the same period. Standard linear Granger causality test failed to detect any evidence of GPRs causing volatility jumps. But given strong evidence of nonlinearity and structural breaks between jumps and GPRs, we next used a nonparametric causality-in-quantiles test, since the linear model is misspecified. Using this data-driven robust approach we were able to detect overwhelming evidence of GPRs predicting volatility jumps of the DJIA over its entire conditional distribution. In addition, a cross-quantilogram analysis shows that what matters most for increases in volatility jumps are relatively higher GPRs than lower values of the same.

Sequential Gibbs Particle Filter Algorithm with an Application to Stochastic Volatility and Jumps Estimation

The aim of this paper is to propose and test a novel PF method called Sequential Gibbs Particle Filter allowing to estimate complex latent state variable models with unknown parameters. The framework is applied to a stochastic volatility model with independent jumps in returns and volatility. The implementation is based on a novel design of adapted proposal densities making convergence of the model relatively efficient as verified on a testing dataset. The empirical study applies the algorithm to estimate stochastic volatility with jumps in returns and volatility model based on the Prague stock exchange returns. The results indicate surprisingly weak jump in returns components and a relatively strong jump in volatility components with jumps in volatility appearing at the beginning of crisis periods.

Common price and volatility jumps in noisy high-frequency data

We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process. The proposed test is based on high-frequency tick-data and is robust to market microstructure frictions. To localize volatility jumps, we design and analyze a nonparametric spectral estimator of the spot volatility process. A simulation study and an empirical example with NASDAQ order book data demonstrate the practicability of the proposed methods and highlight the important role played by price volatility co-jumps.

Resolution of policy uncertainty and sudden declines in volatility

We introduce downward volatility jumps into a general non-affine modeling framework of the term structure of variance. With variance swaps and S&P 500 returns, we find that downward volatility jumps are associated with a resolution of policy uncertainty, mostly through statements from FOMC meetings and speeches of the Federal Reserve’s chairman. Ignoring such jumps may lead to an incorrect interpretation of the tail events, and hence biased estimates of variance risk premia. On the modeling side, we explore the structural differences and relative goodness-of-fits of factor specifications. We find that log-volatility models with at least one Ornstein–Uhlenbeck factor and double-sided jumps are superior in capturing volatility dynamics and pricing variance swaps, compared to the affine model prevalent in the literature or non-affine specifications without downward jumps.

Nonparametric change-point analysis of volatility

In this work, we develop change-point methods for statistics of high-frequency data. The main interest is in the volatility of an Ito semimartingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths with volatility jumps, and it is shown that the test can be embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency setting, we prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. Moreover, we develop methods to infer changes in the Hurst parameters of fractional volatility processes. A simulation study is conducted to demonstrate the performance of our methods in finite-sample applications.

Market Reaction to News and Investor Attention in Real Time

This paper develops a new framework to study investor attention in real time at high frequency. Using information retrieval approach, we construct a proxy for attention from the Twitter messages of financial experts, hedge funds and portfolio managers around the release of unscheduled news announcements. We then examine how markets react to new information in the absence and presence of attention. On implementing our methodology with high-frequency data for large-cap U.S. stocks, we find evidence that news events receiving attention on social media lead to large and persistent changes in trading activity, volatility and price jumps. When the attention is limited, however, the news effects on such trading patterns tend to be smaller and vanish quickly. With respect to reaction timing, we find that approximately one fourth of the news stories arrive first on Twitter before being reported by Bloomberg newswire. This result suggests that movements prior to news releases may not be explained only by private information, but could also be related to timestamp delays. We control for such potential biases by incorporating attention and correcting newswire timestamps. This adjustment considerably eliminates the pre-announcement effects in the data.

Jump spillover between oil prices and exchange rates

In this paper, we investigate the jump spillover effects between oil prices and exchange rates. To identify the latent historical jumps for exchange rates and oil prices, we use a Bayesian MCMC approach to estimate the stochastic volatility model with correlated jumps in both returns and volatilities for each. We examine the simultaneous jump intensities and the conditional jump spillover probabilities between oil prices and exchange rates, finding strong evidence of jump spillover effects. Further analysis shows that the jump spillovers are mainly due to exogenous events such as financial crises and geopolitical events. Thus, the findings have important implications for financial risk management.