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We study the convergence of day-ahead and balancing prices for the Italian power market. The zonal time-series of the prices are evaluated, seasonally adjusted and tested to assess their long-run properties. We focus on the dynamic behavior of the four continental price zones of Italy (North, Central-North, Central-South and South). Using a sample of data that spans the last decade and applying the fractional cointegration methodology, we show the existence of long-run relationships. This signals the existence of convergence between prices in each zone but zone Central-South, where prices are divergent. We also measure the average price difference, and analyse how it evolves over time. Price differences dynamically reduce for all zones except for Central-South. We comment the results and provide an interpretation for the differences across zones. We also discuss policy consequences for both Italian and other markets.

Using annual data from 1978 through 2016, and monthly data from January 2005 through November 2017 from Denmark, we provide a precise estimate of the upper bound on the potential impact of the adoption of wind energy on the reduction of CO2 emissions from energy production. We separate causal impacts from endogenous effects in regressions using instrumental variables including average wind speed, and from spurious effects in dynamic systems using impulse-response analysis and cointegration techniques. A one percentage point increase in the share of wind in total energy production is found to cause a reduction in CO2 emissions of the order 0.3%, based on endogeneity-corrected regression, and 0.5% over 2 years in a fractional vector error-correction model, after allowing the cumulative effects to take place. This corresponds to an upper bound estimate of 0.69 tonnes of CO2 emissions avoided per additional MWh of wind energy produced. We find that after a structural break at the time of introduction of the EU ETS and the Kyoto Protocol in 2005, the country has been on track towards meeting its long-term goals for emission reduction and green energy production, but not before.

We show that sudden and large price moves in bitcoin prices, which we call jumps, explain a large portion of the variation in bitcoin returns. In order to do so, we use the general utility specification adopted in Maheu et al. (2013) for characterizing the conditional mean of daily bitcoin excess returns (the crypto premium), and we relate higher order moments of the return conditional distribution to the stochastic discount factor on the bitcoin. The conditional skewness and kurtosis are both significantly priced, and a relevant portion of the variability of bitcoin returns can be attributed to compensation for the jump term. We show that the price of crypto risk is time-varying, and higher in bad times for investors, when the conditional variance and kurtosis are high.

Persistence and unpredictable large increments characterize the volatility of financial returns. We propose the Multiplicative Error Model with volatility jumps (MEM-J) to describe and predict the probability and the size of these extreme events. Under the MEM-J, the conditional density of the realized measure is a countably infinite mixture of Gamma and Kappa distributions, with closed form conditional moments. We derive stationarity conditions and the asymptotic theory for the maximum likelihood estimation. Estimates of the volatility jump component confirm that the probability of jumps dramatically increases during the financial crises. The MEM-J improves over other models with fat tails.

Time series of counts are often characterized by high overdispersion and persistence. These extreme features challenge the existing models. We approach this problem by combining the framework of INAR with a latent Markov structure. We call it HMM-INAR since it belongs to the class of hidden Markov models. We study the probabilistic properties of HMM-INAR model and illustrate conditions for the existence of an ergodic and stationary solution. We show that the HMM-INAR model is identifiable and can be estimated by maximum likelihood via an efficient expectation-maximization (EM) algorithm with steps available in closed form. The HMM-INAR well predicts the distributional and dynamic features of the time series of counts under investigation, i.e. the number of monthly bankruptcies in South Korea, and the number of trades and volume of several NYSE stocks observed at high frequency. Finally, the model proves empirically superior to other INAR specifications.

We explore the interplay between sovereign and bank credit risk in a setting where Danish authorities first let two Danish banks default and then left the country’s largest bank, Danske Bank, to recapitalize privately. We find that the correlation between bank and sovereign credit default swap (CDS) rates changed with these events. Following the non-bailout events, the sensitivity to external shocks, proxied by CDS rates on the European banking sector, declined both for Danske Bank and for Danish sovereign debt. After Danske Bank’s recapitalization, its exposure to the European banking sector reappeared while that did not happen for Danish sovereign debt. The decoupling between CDS rates on sovereign and private bank debt indicates that the vicious feedback loop between bank and sovereign risk weakened after the non-bailout policies were introduced.

The tick structure of the financial markets entails that price changes observed at very high frequency are discrete. Departing from this empirical evidence we develop a new model to describe the dynamic properties of multivariate time-series of high frequency price changes, including the high probability of observing no variations (price staleness). We assume the existence of two independent latent/hidden Markov processes determining the dynamic properties of the price changes and the excess probability of the occurrence of zeros. We study the probabilistic properties of the model that generates a zero-inflated mixture of Skellam distributions and we develop an EM estimation procedure with closed-form M step. In the empirical application, we study the joint distribution of the price changes of four assets traded on NYSE. Particular focus is dedicated to the precision of the univariate and multivariate density forecasts, to the quality of the predictions of quantities like the volatility and correlations across assets, and to the possibility of disentangling the different sources of zero price variation as generated by absence of news, microstructural frictions or by the offsetting positions taken by the traders.

We propose a non-structural method to retrieve the risk-neutral density (RND) implied by options on the CBOE Volatility Index (VIX). The methodology is based on orthogonal polynomial expansions around a kernel density and yields the RND of the underlying asset without the need for a parametric specification. The classic family of Laguerre expansions is extended to include the GIG and the generalized Weibull kernels. We show that orthogonal polynomial expansions yield accurate approximations of the RND of VIX and they generally outperform commonly used non-parametric methods when controlling for accuracy. Based on a panel of observed VIX options, we retrieve the variance swap term structure, the time series of VVIX, the VIX risk-neutral moments and the Volatility-at-Risk, which reveal a number of stylized facts on the RND of VIX.

In a regime of floating FX rates and open economies, it is important to understand the way through which FX rates, volatility, and trading volume interrelate. To uncover this, we provide a simple theoretical framework to jointly explore these factors in a multi-currency environment. Through the use of a unique intraday data representative for the global FX market, the empirical analysis validates our theoretical predictions: (i) more disagreement increases FX trading volume, volatility, and illiquidity, (ii) stronger commonalities pertain to more efficient (arbitrage-free) currencies, and (iii) the Amihud (2002) measure, for which we provide a theoretical underpinning, is effective in measuring FX illiquidity. Not only do these findings support an integrated analysis of FX rate evolution and risk, but our work also offers a straightforward method to measure FX illiquidity and commonality. For investors, these insights should increase the efficiency of trading and risk analysis. For policy makers, our work highlights the developments of FX global volume, volatility, and illiquidity across time and currencies, which can be important for the implementation of monetary policy and financial stability.

We propose the indirect inference estimator as a consistent method to estimate the parameters of a structural model when the observed series are contaminated by measurement error by considering the noise as a structural feature. We show that the indirect inference estimates are asymptotically biased if the error is neglected. Instead, if the condition for identification is satisfied, the measurement error parameters can be estimated jointly with the structural ones leading to a consistent and asymptotically Gaussian estimator. The issues of identification and misspecification of ME are discussed in detail. Based on the encompassing principle, we show that II can still be consistent for the parameters of interest when the conditional distribution of ME is misspecified, as long as the structural model for the observed series encompasses the auxiliary. We illustrate the reliability of this procedure in the estimation of stochastic volatility models based on realized volatility measures contaminated by microstructure noise. The empirical application stresses the importance of a realistic specification of the microstructure noise distribution to match the features of the observed log-returns at high frequencies.

We show that the model for fractional cointegration proposed by Granger (1986) allows for a representation of the solution that demonstrates the fractional and co-fractional properties. Moreover, we show that the stability of the system can be studied by means of the argument principle inherited from complex analysis. As opposed to the FCVARd,b specification of Johansen (2008b), the model is identified for any combination of number of lags and cointegration rank, while being able to generate polynomial co-fractionality. Finally, we characterize the set of recursions to obtain the impulse response functions and we derive the asymptotic theory for the maximum likelihood estimator of the coefficients.

In the paper we study the convergence of prices in the electricity markets, both at the day-ahead level and for the dispatching services (such as balancing and reserves). We introduce two concepts of price convergence, the convergence of zonal prices within each market (within convergence), and the converge of prices in a given zone between the two markets (between convergence). We provide an extensive analysis based on Italian data of within and between convergence. The zonal time-series of the prices are evaluated, seasonally adjusted and tested to assess their long-run properties. This evaluation induces us to focus on the behavior of the three largest and most interconnected continental zones of Italy (North, Center-North and Center-South). The fractional cointegration methodology used in the analysis shows the existence of long-run relationships among the series used in our study. This signals the existence of price convergence within markets, even though for the dispatching services market the evidence is less robust. The analysis also shows the existence of price convergence between markets in each zone, even though the evidence is more clearly affirmed for the North (the largest Italian zone), less so for the other two zones. Results are interpreted on the basis of the characteristics of the markets and the zones.

The persistent nature of equity volatility is investigated by means of a multi-factor stochastic volatility model with time varying parameters. The parameters are estimated by means of a sequential matching procedure which adopts as an auxiliary model a time-varying generalization of the HAR model for the realized volatility series. It emerges that during the recent financial crisis the relative weight of the daily component dominates over the monthly term. The estimates of the two factor stochastic volatility model suggest that the change in the dynamic structure of the realized volatility during the financial crisis is due to the increase in the volatility of the persistent volatility term. A set of Monte Carlo simulations highlights the robustness of the methodology adopted in tracking the dynamics of the parameters.

A stylized fact is that realized variance has long memory. We show that, when the instantaneous volatility is a long memory process of order d, the integrated variance is characterized by the same long-range dependence. We prove that the spectral density of realized variance is given by the sum of the spectral density of the integrated variance plus that of a measurement error, due to the sparse sampling and market microstructure noise. Hence, the realized volatility has the same degree of long memory as the integrated variance. The additional term in the spectral density induces a finite-sample bias in the semiparametric estimates of the long memory. A Monte Carlo simulation provides evidence that the corrected local Whittle estimator of Hurvich et al. (2005) is much less biased than the standard local Whittle estimator and the empirical application shows that it is robust to the choice of the sampling frequency used to compute the realized variance. Finally, the empirical results suggest that the volatility series are more likely to be generated by a nonstationary fractional process.

This article discusses identification problems in the fractionally cointegrated system of Johansen and Johansen and Nielsen. It is shown that several equivalent reparametrizations of the model associated with different fractional integration and cointegration parameters may exist for any choice of the lag-length when the true cointegration rank is known. The properties of these multiple nonidentified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d). This is a generalization of the well-known I(1) condition to the fractional case. Imposing a proper restriction on the fractional integration parameter, d, is sufficient to guarantee identification of all model parameters and the validity of the F(d) condition. The article also illustrates the indeterminacy between the cointegration rank and the lag-length. It is also proved that the model with rank zero and k lags may be an equivalent reparameterization of the model with full rank and k − 1 lags. This precludes the possibility to test for the cointegration rank unless a proper restriction on the fractional integration parameter is imposed.

We propose and study the finite-sample properties of a modified version of the self-perturbed Kalman filter of Park and Jun (1992) for the on-line estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is now weighted by the estimate of the measurement error variance. This avoids the calibration of a design parameter as the perturbation term is scaled by the level of uncertainty in the data. It is shown by Monte Carlo simulations that this perturbation method is associated with a good tracking of the dynamics of the parameters compared to other on-line, classical and Bayesian methods. The standardized self-perturbed Kalman filter is adopted to forecast the equity premium on the S&P 500 index under several model specifications, and determine the extent to which realized volatility can be used to predict excess returns.

The no-arbitrage relation between futures and spot prices implies an analogous relation between futures and spot daily ranges. The long-memory features of the range-based volatility estimators are analyzed, and fractional cointegration is tested in a semi-parametric framework. In particular, the no-arbitrage condition is used to derive a long-run relationship between volatility measures and to justify the use of a fractional vector error correction model (FVECM) to study their dynamic relationship. The out-of-sample forecasting superiority of FVECM, with respect to alternative models, is documented. The results highlight the importance of incorporating the long-run equilibrium in volatilities to obtain better forecasts, given the information content in the volatility of futures prices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:77–102, 2013

The volatility of financial returns is characterized by rapid and large increments. We propose an extension of the Heterogeneous Autoregressive model to incorporate jumps into the dynamics of the ex post volatility measures. Using the realized range measures of 36 NYSE stocks, we show that there is a positive probability of jumps in volatility. A common factor in the volatility jumps is shown to be related to a set of financial covariates (such as variance risk premium (VRP), S&P500 volume, credit default swap (CDS), and federal fund rates). The CDS on U.S. banks and VRP have predictive power on expected jump moves, thus confirming the common interpretation that sudden and large increases in equity volatility can be anticipated by credit deterioration of the U.S. bank sector as well as changes in the market expectations of future risks. Finally, the model is extended to incorporate the CDS and the VRP in the dynamics of the jump size and intensity.

During the last decades a wide literature has focused on the relationship volumevolatility on financial markets. This paper investigates the temporal dynamics of volatility and volumes, supposing, as in Bollerslev and Jubinski (1999), that the link has to be found in their long-run dependencies, that are supposed to be driven by the same informative process. We analyze the volume-volatility relationship using IBM stocks data. In particular, we rely on the realized volatility based on five minutes stock prices. Tail dependence analysis is carried out with two alternative estimators of the continuous part of the volatility process. The analysis shows that log-realized volatility and logvolumes are characterized by upper and lower tail dependence, where the positive tail dependence is mainly due to the jump component. We also investigate the possibility that volumes and volatility are driven by a common fractionally integrated stochastic trend, i.e. they have the same degree of long memory and are fractionally cointegrated as the Mixture Distribution Hypotesis prescribes. Moreover, we estimate a bivariate FIVAR specification that explicitly considers the long run relationship between the two series and the tail dependence in the shocks, by parameterizing the joint density by means of different copula functions. The evidence from the model estimates, the simulation results and the forecasts comparison with HAR model highlight the ability of the bivariate FIVAR with copula density specification to account for the common long memory pattern and tail dependence.

The long memory properties of the integrated and realized volatility are investigated under the assumption that the instantaneous volatility is driven by a fractional Brownian motion. The equality of their long memory degrees is proved in the ideal situation when prices are observed continuously. In this case, the spectral density of the integrated and realized volatility coincide.

In the analysis of systemic risk, Marginal Expected Shortfall may be considered to evaluate the marginal impact of a single stock on the market Expected Shortfall. These quantities are generally computed using log-returns, in particular when there is also a focus on returns conditional distribution. In this case, the market log-return is only approximately equal to the weighed sum of equities log-returns. We show that the approximation error is large during turbulent market phases, with a subsequent impact on Marginal Expected Shortfall. We then suggest how to improve the evaluation of Marginal Expected Shortfall by means of a second order approximation.

The volatility of financial returns is affected by rapid and large increments. Such movements can be hardly generated by a pure diffusive process for stochastic volatility. On the contrary jumps in volatility are important because they allow for rapid increases, like those observed during stock market crashes. We propose an extension of HAR model for estimating the presence of jumps in volatility, using the realized-range measure as a volatility proxy. By focusing on a set of 36 NYSE stocks, we show that, once that squared jumps in prices are disentangled from integrated variance, then there is a positive probability of jumps in volatility, conditional on the past information set. We then focus on the contribution of jumps during periods of financial turmoil. We analyze the dependence between the first principal component of the volatility jumps with a set of financial covariates including VIX, S&P500 volume, CDS, and Federal Fund rates. We observe that CDS captures large part of the expected jumps moves, verifying the common interpretation that large and sudden increases in volatility in stock markets over some days in the recent financial crisis have been caused by credit deterioration of US bank sector. Finally, we extend the model incorporating the credit-default swap in the dynamics of the jump size and intensity. The estimates confirm the significant contribution of the credit-default swap to the dynamics of the volatility jump size.

The no arbitrage relation between futures and spot prices implies an analogous relation between futures and spot volatilities as measured by daily range. Long memory features of the range-based volatility estimators of the two series are analyzed, and their joint dynamics are modeled via a fractional vector error correction model (FVECM), in order to explicitly consider the no arbitrage constraints. We introduce a two-step estimation procedure for the FVECM parameters and we show the properties by a Monte Carlo simulation. The out-of-sample forecasting superiority of FVECM, with respect to competing models, is documented. The results highlight the importance of giving fully account of long-run equilibria in volatilities in order to obtain better forecasts.

We propose a novel non-structural method for hedging European options, relying on two model-independent results: First, under suitable regularity conditions, an option price can be disentangled into a linear combination of risk-neutral moments. Second, there exists an explicit approximate functional form linking the risk-neutral moments to the futures price of the underlying asset and the related variance swap contracts. We show that S{\&}P 500 call prices are mainly explained by two factors that are related to level and volatility of the underlying index. We empirically compare the performance of two strategies where the vega exposure is adjusted either by a direct position in a variance swap contract or, indirectly, through an at-the-money call. While both strategies ensure effective immunization in periods of market turmoil, taking direct exposure on variance swaps is not optimal during extended periods of subdued volatility.