Does the Hurst index matter for option prices under fractional volatility?

This study examines the effect of fractional volatility on option prices. To this end, we develop an approximation method for the pricing of European-style contingent claims when volatility follows a fractional Brownian motion. Through extensive numerical experiments, we confirm that the decrease in the smile amplitude under fractional volatility is much slower than that under the standard stochastic volatility model. We also show that the Hurst index under fractional volatility has a crucial impact on option prices when the maturity is short and speed of mean reversion is slow. On the contrary, the impact of the Hurst index on option prices reduces for long-dated options.     

Can the Chinese volatility index reflect investor sentiment?

The volatility index is the implied volatility calculated inversely from the option prices. This study investigates whether the official Chinese volatility index, iVX, can represent investor sentiment. In order to describe investor sentiment comprehensively, we build a three-dimensional investor sentiment measurement system composed of macro, meso and micro level, and decompose iVX into three components to obtain short-term, medium-term fluctuations and long-term trend by EEMD method. The relationships between iVX, its components and sentiment indexes at each level have been analyzed separately, and the empirical results reveal all components of iVX can reflect the investor sentiment at the corresponding level but to which extent they can reflect are not the same. Further we introduce the mixed-frequency dynamic factor analysis to extract the common sentiment factor, which shows stronger correlation with contemporaneous iVX, compared with the sentiment indexes at each level. The ADL model in robustness check also demonstrates the results. Our findings confirm iVX can represent the common sentiment and expectations of Chinese investors in different time scales.     

A behavioral explanation for the negative asymmetric return–volatility relation

We examine the short-term dynamic relation between the S&P 500 (Nasdaq 100) index return and changes in implied volatility at both the daily and intraday level. Neither the leverage hypothesis nor the volatility feedback hypothesis adequately explains the results. Alternatively, we propose that the behavior of traders (from the representativeness, affect, and extrapolation bias concepts of behavioral finance) is consistent with our empirical results of a strong daily and intraday negative return–implied volatility relation. Moreover, both the presence and magnitude of the negative relation and the asymmetry between return and implied volatility are most closely associated with extreme changes in the index returns. We also show that the strength of the relation is consistent with the implied volatility skew.     

Asymmetric information,volatility components and the volume–volatility relationship for the CAC40 stocks

This paper investigates the relationship between trading volume components and various realized volatility measures for the CAC40 index constituents. A mixture-of-distribution model is used to decompose trading volume into informed and liquidity components. Realized volatility is broken down into continuous volatility and jumps. Our findings confirm the strong positive contemporaneous relationship between total trading volume and volatility when realized volatility and its continuous component are considered. A limited evidence of the effect of total trading volume on discontinuous volatility is found. The positive volume–volatility relationship is mainly driven by the informed component of trading volume. Conversely, liquidity volume is negatively related to realized volatility lending some support to the view that liquidity trading dampens the volatility of stock returns. A stronger negative relationship between liquidity volume and volatility jump is uncovered.     

Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps

The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing high order asymptotic expansions for the at-the-money implied volatility skew, under a rich class of stochastic volatility models with independent stable-like jumps of infinite variation. The case of a pure-jump stable-like Lévy model is also considered under the minimal possible conditions for the resulting expansion to be well defined. Unlike recent results for “near-the-money” option prices and implied volatility, the results herein aid in understanding how the implied volatility smile near expiry is affected by important features of the continuous component, such as the leverage and vol-of-vol parameters. As intermediary results, we obtain high order expansions for at-the-money digital call option prices, which furthermore allow us to infer analogous results for the delta of at-the-money options. Simulation results indicate that our asymptotic expansions give good fits for options with maturities up to one month, underpinning their relevance in practical applications, and an analysis of the implied volatility skew in recent S&P 500 options data shows it to be consistent with the infinite variation jump component of our models.     

Comparison results for stochastic volatility models via coupling

The aim of this paper is to investigate the properties of stochastic volatility models, and to discuss to what extent, and with regard to which models, properties of the classical exponential Brownian motion model carry over to a stochastic volatility setting. The properties of the classical model of interest include the fact that the discounted stock price is positive for all t but converges to zero almost surely, the fact that it is a martingale but not a uniformly integrable martingale, and the fact that European option prices (with convex payoff functions) are convex in the initial stock price and increasing in volatility. We explain why these properties are significant economically, and give examples of stochastic volatility models where these properties continue to hold, and other examples where they fail. The main tool is a construction of a time-homogeneous autonomous volatility model via a time-change.     

Which sentiment index is more informative to forecast stock market volatility? Evidence from China

In this paper, we investigate the predictive ability of three sentiment indices constructed by social media, newspaper, and Internet media news to forecast the realized volatility (RV) of SSEC from in- and out-of-sample perspectives. Our research is based on the heterogeneous autoregressive (HAR) framework. There are several notable findings. First, the in-sample estimation results suggest that the daily social media and Internet media news sentiment indices have significant impact for stock market volatility, while the sentiment index built by traditional newspaper have no impact. Second, the one-day-ahead out-of-sample forecasting results indicate that the two sentiment indices constructed by social media and Internet media news can considerably improve forecast accuracy. In addition, the model incorporating the positive and negative social media sentiment indices exhibits more superior forecasting performance. Third, we find only the sentiment index built by Internet media news can improve the mid- and long-run volatility predictive accuracy. Fourth, the empirical results based on alternative prediction periods and alternative volatility estimator confirm our conclusions are robust. Finally, we examine the predictability of the monthly sentiment indices and find that the two sentiment indices of social media and Internet media news contain more informative to forecast the monthly RV of SSEC, CSI800, and SZCI, however invalid for CSI300.     

Misreaction or misspecification? A re-examination of volatility anomalies

Existing research examines the impact of volatility shocks on the relative pricing of long-term vs. short-term options and documents patterns of “short-horizon underreaction” and “long-horizon overreaction” in the options market. These studies, however, rely on implied volatilities derived from specific option-pricing models and are thus subject to model specification errors. In this paper, we show that these anomalous patterns are the result of model misspecification as opposed to market misreaction. We provide evidence that these patterns are consistent with, in both direction and magnitude, inherent biases in the misspecified models. We also apply a model-free approach to re-examine the anomalous patterns and find no evidence of market misreaction.     

Large shocks in the volatility of the Dow Jones Industrial Average index: 1928–2013

We determine the events that cause large shocks in volatility of the DJIA index over the period 1928–2013, using a new semi-parametric test based on conditional heteroscedasticity models. We find that these large shocks can be associated with particular events (financial crashes, elections, wars, monetary policies, etc.). We show that some shocks are not identified as extraordinary movements by the investors due to their occurring during high volatility episodes, especially the 1929–1934, 1937–1938 and 2007–2011 periods.     

Does futures trading increase stock market volatility? The case of the Nikkei stock index futures markets

We propose new tests to examine whether stock index futures affect stock market volatility. These tests decompose spot portfolio volatility into the cross-sectional dispersion and the average volatility of returns on the portfolio's constituent securities. Our tests show that for Nikkei stocks spot portfolio volatility increased and cross-sectional dispersion decreased compared with average volatility when Nikkei futures began trading on the Osaka Securities Exchange, but not on the Singapore International Monetary Exchange. For non-Nikkei stocks, no shift occurred when futures trading began on either exchange. These findings are consistent with the hypotheses that futures trading increases spot portfolio volatility but that there is no volatility “spillover” to stocks against which futures are not traded. However, the increase in volatility attributable to futures trading is small compared with volatility shifts induced by changes in broad economic factors.     

Is stochastic volatility relevant for dynamic portfolio choice under ambiguity?

Literature on dynamic portfolio choice has been finding that volatility risk has low impact on portfolio choice. For example, using long-run US data, Chacko and Viceira [2005. “Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets.” The Review of Financial Studies 18 (4): 1369–1402] found that intertemporal hedging demand (required by investors for protection against adverse changes in volatility) is empirically small even for highly risk-averse investors. We want to assess if this continues to be true in the presence of ambiguity. Adopting robust control and perturbation theory techniques, we study the problem of a long-horizon investor with recursive preferences that faces ambiguity about the stochastic processes that generate the investment opportunity set. We find that ambiguity impacts portfolio choice, with the relevant channel being the return process. Ambiguity about the volatility process is only relevant if, through a specific correlation structure, it also induces ambiguity about the return process. Using the same long-run US data, we find that ambiguity about the return process may be empirically relevant, much more than ambiguity about the volatility process. Anyway, intertemporal hedging demand is still very low: investors are essentially focused on the short-term risk–return characteristics of the risky asset.     

Central bank intervention and exchange rate volatility — Australian evidence

This paper examines the key characteristics of foreign exchange intervention by the Reserve Bank of Australia in the period 1983–1997, which can be broken into five distinct phases. We investigate the changing effectiveness of daily intervention on the $US/$A exchange rate by decomposing the exchange rate response to the intervention into various separate components. We find contemporaneous positive correlation between the direction of intervention and the conditional mean and variance of exchange rate returns. We show that sustained and large interventions have a stabilising influence in the foreign exchange market in terms of direction and volatility. Without these interventions, the market would have moved further and exhibited more volatility.     

Do structural breaks in volatility cause spurious volatility transmission?

We show through extensive Monte Carlo simulations that structural breaks in volatility (volatility shifts) across two independently generated return series cause spurious volatility transmission when estimated with popular bivariate GARCH models. However, using a dummy variable for the induced volatility shift virtually eliminates this bias. We also show that structural breaks in volatility have a substantial impact on the estimated hedge ratios. We confirm our simulation findings using the US stock market data.     

The forecasting ability of solar and space weather data on NASDAQ’s finance sector price index volatility

We examine the impact of solar and space weather events on the Financial Select Sector SPDR Fund (XLF) price index volatility, spanning the period 1998-2018. Comparing MAPE and RMSFE forecasting criteria, for the ARIMA-GARCH model, augmented with exogenous variables, we find that solar and space weather variables contribute statistically significant information with regard to volatility forecasting.     

Implied Lévy volatility

We study the cause of large fluctuations in prices on the London Stock Exchange. This is done at the microscopic level of individual events, where an event is the placement or cancellation of an order to buy or sell. We show that price fluctuations caused by individual market orders are essentially independent of the volume of orders. Instead, large price fluctuations are driven by liquidity fluctuations, variations in the market's ability to absorb new orders. Even for the most liquid stocks there can be substantial gaps in the order book, corresponding to a block of adjacent price levels containing no quotes. When such a gap exists next to the best price, a new order can remove the best quote, triggering a large midpoint price change. Thus, the distribution of large price changes merely reflects the distribution of gaps in the limit order book. This is a finite size effect, caused by the granularity of order flow: in a market where participants place many small orders uniformly across prices, such large price fluctuations would not happen. We show that this also explains price fluctuations on longer timescales. In addition, we present results suggesting that the risk profile varies from stock to stock, and is not universal: lightly traded stocks tend to have more extreme risks.     

SMIC 74—A method for constructing and ranking scenarios

A valid concept of what the future could be implies the existence of an overall conjectural framework which makes full allowance for the dynamics and complexity of the various systems involved. Such a framework must integrate the variable factors which determine the behaviour of all the economic and other agents contributing to the shape of the future, even when these variables are of a qualitative, subjective nature. A new method based on the cross-impact analysis is proposed to improve decision-making processes. A simple example is given to illustrate how this method can be used in forecasting studies and scenarios.     

Japanese Banks—A Risk Factor for the Japanese Economy

Original Papers

Japanese Banks—A Risk Factor for the Japanese Economy     

Is the realized volatility good for option pricing during the recent financial crisis?

The contributions of this paper are threefold. The first contribution is the proposed logarithmic HAR (log-HAR) option-pricing model, which is more convenient compared with other option pricing models associated with realized volatility in terms of simpler estimation procedure. The second contribution is the test of the empirical implications of heterogeneous autoregressive model of the realized volatility (HAR)-type models in the S&P 500 index options market with comparison of the non-linear asymmetric GARCH option-pricing model, which is the best model in pricing options among generalized autoregressive conditional heteroskedastic-type models. The third contribution is the empirical analysis based on options traded from July 3, 2007 to December 31, 2008, a period covering a recent financial crisis. Overall, the HAR-type models successfully predict out-of-sample option prices because they are based on realized volatilities, which are closer to the expected volatility in financial markets. However, mixed results exist between the log-HAR and the heterogeneous auto-regressive gamma models in pricing options because the former is better than the latter in times of turmoil, whereas it is worse during the rather stable periods.