Aggregation of Nonparametric Estimators for Volatility Matrix

An aggregated method of nonparametric estimators based on time-domainand state-domain estimators is proposed and studied. To attenuatethe curse of dimensionality, we propose a factor modeling strategy.We first investigate the asymptotic behavior of nonparametricestimators of the volatility matrix in the time domain and inthe state domain. Asymptotic normality is separately establishedfor nonparametric estimators in the time domain and state domain.These two estimators are asymptotically independent. Hence,they can be combined, through a dynamic weighting scheme, toimprove the efficiency of volatility matrix estimation. Theoptimal dynamic weights are derived, and it is shown that theaggregated estimator uniformly dominates volatility matrix estimatorsusing time-domain or state-domain smoothing alone. A simulationstudy, based on an essentially affine model for the term structure,is conducted, and it demonstrates convincingly that the newlyproposed procedure outperforms both time- and state-domain estimators.Empirical studies further endorse the advantages of our aggregatedmethod.     

FX volatility forecasts and the informational content of market data for volatility

The paper examines the medium-term forecasting ability of several alternative models of currency volatility. The data period covers more than eight years of daily observations, January 1991 to March 1999, for the spot exchange rate, 1- and 3-month volatility of the DEM/JPY, GBP/DEM, GBP/USD, USD/CHF, USD/DEM and USD/JPY. Comparing with the results of ‘pure’ time series models, the reported work investigates whether market implied volatility data can add value in terms of medium-term forecasting accuracy. This is done using data directly available from the marketplace in order to avoid the potential biases arising from ‘backing out’ volatility from a specific option pricing model. On the basis of the over 34 000 out-of-sample forecasts produced, evidence tends to indicate that, although no single volatility model emerges as an overall winner in terms of forecasting accuracy, the ‘mixed’ models incorporating market data for currency volatility perform best most of the time.     

Exchange rate returns and volatility: the role of time-varying rare disaster risks

This paper provides empirical evidence to the theoretical claim that rare disaster risks have predictability for exchange rate returns and volatility using a nonparametric quantile-based methodology. Using dollar-based exchange rates for Brazil, Russia, India, China, and South Africa, the quantile-causality test shows that indeed rare disaster-risks affects both returns and volatility over the majority of their respective conditional distributions. In addition, these effects are much stronger when compared to those using the British pound, especially in terms of currency returns.     

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.     

The role of time‐varying rare disaster risks in predicting bond returns and volatility

This paper aims to provide empirical evidence to the theoretical claim that rare disaster risks affect government bond market movements. Using a nonparametric quantiles‐based methodology, we show that rare disaster‐risks affect only volatility, but not returns, of 10‐year government bond of the United States over the monthly period of 1918:01 to 2013:12. In addition, the predictability of volatility holds for the majority of the conditional distribution of the volatility, with the exception of the extreme ends. Moreover, in general, similar results are also obtained for long‐term government bonds of an alternative developed country (UK) and an emerging market (South Africa).     

Dynamic volatility and external security related shocks: The case of the Athens Stock Exchange

This paper analyses the impact of exogenous national security related shocks on the time-varying volatility structure of the Greek stock market. Alternative autoregressive conditional heteroscedastic models are estimated, in order to identify the best fit that adequately describes return volatility behavior, testing symmetric as well as asymmetric innovation responses. An external national security related shock factor is included as well as a military crisis dummy, in order to depict possible implications for the conditional variance. The empirical findings appear to support a statistically significant impact of both national security related factors on the Athens stock market returns.     

Investor sentiment and stock volatility: New evidence

This study investigates the predictability of sentiment measure on stock realized volatility. We propose a new investor sentiment index (NISI) based on the partial least squares method. This sentiment index outperforms many existing sentiment indicators in three aspects. First, in-sample result shows that the NISI has greater predictive power relative to the others. Most sentiment indicators show predictability in the non-crisis period only while the NISI is also effective in the crisis period. Furthermore, the NISI exhibits more prominent superiority in longer horizons forecasting. Second, further analysis indicates that the NISI has robust predictability before and after the Chinese stock market turbulence periods while the others not. Importantly, the NISI is still effective significantly after considering leverage effect while most of the others not. Finally, out-of-sample analysis demonstrates that the NISI is more powerful than other sentiment measures. This result is reproducible in different robustness checks.     

Forecasting oil price realized volatility using information channels from other asset classes

Motivated from Ross (1989) who maintains that asset volatilities are synonymous to the information flow, we claim that cross-market volatility transmission effects are synonymous to cross-market information flows or “information channels” from one market to another. Based on this assertion we assess whether cross-market volatility flows contain important information that can improve the accuracy of oil price realized volatility forecasting. We concentrate on realized volatilities derived from the intra-day prices of the Brent crude oil and four different asset classes (Stocks, Forex, Commodities and Macro), which represent the different “information channels” by which oil price volatility is impacted from. We employ a HAR framework and estimate forecasts for 1-day to 66-days ahead. Our findings provide strong evidence that the use of the different “information channels” enhances the predictive accuracy of oil price realized volatility at all forecasting horizons. Numerous forecasting evaluation tests and alternative model specifications confirm the robustness of our results.     

A general framework for the derivation of asset price bounds: an application to stochastic volatility option models

We present a generalization of Cochrane and Saá-Requejo’s good-deal bounds which allows to include in a flexible way the implications of a given stochastic discount factor model. Furthermore, a useful application to stochastic volatility models of option pricing is provided where closed-form solutions for the bounds are obtained. A calibration exercise demonstrates that our benchmark good-deal pricing results in much tighter bounds. Finally, a discussion of methodological and economic issues is also provided.      

Histogram-based prediction of directional price relatives

A model of directional prediction of price relatives is proposed following the histogram-based scheme developed in Györfi et al. (2006). This methodology allows us to exploit potential information contained in multivariate series of price relatives. The impact of the model is studied from the perspective of an economic agent through the use of double linear loss functions. A numerical example with real data is presented to illustrate the model.     

Determining the implied volatility for American options using the QAM

This paper describes an efficient numerical procedure which may be used to determine implied volatilities for American options using the quadratic approximation method. Simulation results are presented. The procedure usually converges in five or six iterations with extreme accuracy under a wide variety of option market conditions. A comparison of American implied volatilities with European model implied volatilities indicates that significant differences may arise. This suggests that reliance on European model volatilities estimates may lead to significant pricing errors.     

Sequential Monte Carlo for fractional stochastic volatility models

In this paper, we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behaviour. We propose a dynamic sequential Monte Carlo methodology that is applicable to both long memory and antipersistent processes in order to estimate the volatility as well as the unknown parameters of the model. We establish a central limit theorem for the state and parameter filters and we study asymptotic properties (consistency and asymptotic normality) for the filter. We illustrate our results with a simulation study and we apply our method to estimate the volatility and the parameters of a long-range dependent model for S& P 500 data.     

Using implied volatility jumps for realized volatility forecasting: Evidence from the Chinese market

This study examines the Chinese implied volatility index (iVIX) to determine whether jump information from the index is useful for volatility forecasting of the Shanghai Stock Exchange 50ETF. Specifically, we consider the jump sizes and intensities of the 50ETF and iVIX as well as cojumps. The findings show that both the jump size and intensity of the 50ETF can improve the forecasting accuracy of the 50ETF volatility. Moreover, we find that the jump size and intensity of the iVIX provide no significant predictive ability in any forecasting horizon. The cojump intensity of the 50ETF and iVIX is a powerful predictor for volatility forecasting of the 50ETF in all forecasting horizons, and the cojump size is helpful for forecasting in short forecasting horizon. In addition, for a one-day forecasting horizon, the iVIX jump size in the cojump is more predictive of future volatility than that of the 50ETF when simultaneous jumps occur. Our empirical results are robust and consistent. This work provides new insights into predicting asset volatility with greater accuracy.     

Asset price prediction using seasonal decomposition

We propose a new forecasting procedure for asset prices using seasonal decomposition methods (SD hereafter), e.g., SABL and X-11. Such SD's are based on moving average methods, and they are thus easy to use and are capable of computing the seasonal pattern that changes over time. A SD typically decomposes a series intoT (trend),S (seasonal component), andR (residual or sometimes referred to as the irregular component). We use an ARIMA model onR to obtain its forecast. TheS component is forecasted by an extrapolation taking into account its changing pattern within the sample period. We propose to set up some scenarios on theT component by examining its possibly nonlinear and nonstationary behavior, and in the paper we suggest one possible way for this. Suppose that the forecasting horizon is relatively short compared toT's several cycles just before the end of the sample. Then we may safely extrapolateT linearly into the forecasting period. LinearizingT in such a case, makes sense. As to the slope of the linear line, we suggest the average rate of change of the most recent upward phase of a cycle to be used if we needed an optimistic scenario. Obviously, that of the downward phase may be used for constructing a pessimistic scenario, and that of one entire cycle is suitable for ‘average’ scenario. Once the forecasted values of the three components are obtained, we may put them back to make predictions on the original series based upon various different scenarios. In addition to proposing a new prediction method, we looked into the following issues, among others, in the paper: (1) on what sort of asset prices would our forecasting method work well? (2) Any significant differences if we used X-11 instead of SABL?     

A multivariate nonparametric test for return and volatility timing

This paper develops a novel approach to simultaneously test for market timing in stock index returns and volatility. The tests are based on the estimation of a system of regression equations with indicator variables and provide detailed information about the statistical significance of alternative market timing components.     

A new technique for calibrating stochastic volatility models: the Malliavin gradient method

We discuss the application of gradient methods to calibrate mean reverting stochastic volatility models. For this we use formulas based on Girsanov transformations as well as a modification of the Bismut–Elworthy formula to compute the derivatives of certain option prices with respect to the parameters of the model by applying Monte Carlo methods. The article presents an extension of the ideas to apply Malliavin calculus methods in the computation of Greek's.     

What is the correct meaning of implied volatility?

This paper presents a closed-form solution for the valuation of European options under the assumption that the excess returns of an underlying asset follow a diffusion process. In light of our model, the implied volatility computed from the Black–Scholes formula should be viewed as the volatility of excess returns rather than as the volatility of gross returns. Using the SPX and the OMX options data, we test whether implied volatility obtained from Black-Scholes option price explains the volatilities of excess returns better than gross returns, even though the result is not statistically significant.     

A new approach for option pricing under stochastic volatility

We develop a new approach for pricing European-style contingent claims written on the time T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic volatility literature, we assume continuous dynamics for the price of the underlying asset. In contrast to most of the stochastic volatility literature, we do not directly model the dynamics of the instantaneous volatility. Instead, taking advantage of the recent rise of the variance swap market, we directly assume continuous dynamics for the time T variance swap rate. The initial value of this variance swap rate can either be directly observed, or inferred from option prices. We make no assumption concerning the real world drift of this process. We assume that the ratio of the volatility of the variance swap rate to the instantaneous volatility of the underlying asset just depends on the variance swap rate and on the variance swap maturity. Since this ratio is assumed to be independent of calendar time, we term this key assumption the stationary volatility ratio hypothesis (SVRH). The instantaneous volatility of the futures follows an unspecified stochastic process, so both the underlying futures price and the variance swap rate have unspecified stochastic volatility. Despite this, we show that the payoff to a path-independent contingent claim can be perfectly replicated by dynamic trading in futures contracts and variance swaps of the same maturity. As a result, the contingent claim is uniquely valued relative to its underlying’s futures price and the assumed observable variance swap rate. In contrast to standard models of stochastic volatility, our approach does not require specifying the market price of volatility risk or observing the initial level of instantaneous volatility. As a consequence of our SVRH, the partial differential equation (PDE) governing the arbitrage-free value of the contingent claim just depends on two state variables rather than the usual three. We then focus on the consistency of our SVRH with the standard assumption that the risk-neutral process for the instantaneous variance is a diffusion whose coefficients are independent of the variance swap maturity. We show that the combination of this maturity independent diffusion hypothesis (MIDH) and our SVRH implies a very special form of the risk-neutral diffusion process for the instantaneous variance. Fortunately, this process is tractable, well-behaved, and enjoys empirical support. Finally, we show that our model can also be used to robustly price and hedge volatility derivatives.     

Nonparametric Tests for Positive Quadrant Dependence

We consider distributional free inference to test for positivequadrant dependence, that is, for the probability that two variablesare simultaneously small (or large) being at least as greatas it would be were they dependent. Tests for its generalizationto higher dimensions, namely positive orthant dependence, arealso analyzed. We propose two types of testing procedures. Thefirst procedure is based on the specification of the dependenceconcepts in terms of distribution functions, while the secondprocedure exploits the copula representation. For each specification,a distance test and an intersection-union test for inequalityconstraints are developed for time-dependent data. An empiricalillustration is given for U.S. insurance claim data, where wediscuss practical implications for the design of reinsurancetreaties. Another application concerns detection of positivequadrant dependence between the HFR and CSFB/Tremont marketneutral hedge fund indices and the S&P 500 index.     

Distilling private information from plain-vanilla options to predict future underlying stock price volatility: Evidence from the H-shares of Chinese banks

Deviations from put-call parity may arise in response to private information that a select group of investors possess. From a practical perspective, if one possesses private information, using options to speculate or hedge amplifies potential gains given the leverage embedded in options with respect to price changes in the underlying asset. In light of this, and if we assume that the average investor does not possess private information, it is perhaps possible though to infer such information through implied variance spreads and use it to predict future volatility in the underlying asset. In this piece I examine the extent to which such information is economically informative in predicting the intraday return variability of H-shares issued by China's state and joint-stock banks, respectively. Generally speaking, I uncover the following; firstly, call-put implied variance spreads are mean-reverting across time. Secondly, at any given point in time, the magnitude of the deviation from put-call parity is informative in predicting rises in future spot price volatility. Thirdly, straddle/strangle trades predict, at times one week in advance, rises in future spot price volatility. These findings hold after controlling for market-wide implied volatility, the flow and shock in information disseminating to the market, and implicit transactions costs.