Paolo Santucci de Magistris
Aarhus University
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Featured researches published by Paolo Santucci de Magistris.
Journal of Business & Economic Statistics | 2017
Federico Carlini; Paolo Santucci de Magistris
ABSTRACT 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 . 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 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.
Econometric Reviews | 2014
Eduardo Rossi; Paolo Santucci de Magistris
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.
Computational Statistics & Data Analysis | 2014
Stefano Grassi; Paolo Santucci de Magistris
The finite sample properties of the state space methods applied to long memory time series are analyzed through Monte Carlo simulations. The state space setup allows to introduce a novel modeling approach in the long memory framework, which directly tackles measurement errors and random level shifts. Missing values and several alternative sources of misspecification are also considered. It emerges that the state space methodology provides a valuable alternative for the estimation of the long memory models, under different data generating processes, which are common in financial and economic series. Two empirical applications highlight the practical usefulness of the proposed state space methods.
Journal of Banking and Finance | 2013
Massimiliano Caporin; Angelo Ranaldo; Paolo Santucci de Magistris
Contrary to the common wisdom that asset prices are barely possible to forecast, we show that that high and low prices of equity shares are largely predictable. We propose to model them using a simple implementation of a fractional vector autoregressive model with error correction (FVECM). This model captures two fundamental patterns of high and low prices: their cointegrating relationship and the long memory of their difference (i.e. the range), which is a measure of realized volatility. Investment strategies based on FVECM predictions of high/low US equity prices as exit/entry signals deliver a superior performance even on a risk-adjusted basis.
CREATES Research Papers | 2009
Eduardo Rossi; Paolo Santucci de Magistris
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.
CREATES Research Papers | 2014
Massimiliano Caporin; Eduardo Rossi; Paolo Santucci de Magistris
The realized volatility of financial returns is characterized by persistence and occurrence of unpredictable large increments. To capture those features, we introduce the Multiplicative Error Model with jumps (MEM-J). When a jump component is included in the multiplicative specification, the conditional density of the realized measure is shown to be a countably infinite mixture of Gamma and K distributions. Strict stationarity conditions are derived. A Monte Carlo simulation experiment shows that maximum likelihood estimates of the model parameters are reliable even when jumps are rare events. We estimate alternative specifications of the model using a set of daily bipower measures for 7 stock indexes and 16 individual NYSE stocks. The estimates of the jump component confirm that the probability of jumps dramatically increases during the financial crises. Compared to other realized volatility models, the introduction of the jump component provides a sensible improvement in the fit, as well as for in-sample and out-of-sample volatility tail forecasts.
CREATES Research Papers | 2010
Bent Jesper Christensen; Paolo Santucci de Magistris
We propose a simple model in which realized stock market return volatility and implied volatility backed out of option prices are subject to common level shifts corresponding to movements between bull and bear markets. The model is estimated using the Kalman filter in a generalization to the multivariate case of the univariate level shift technique by Lu and Perron (2008). An application to the S&P500 index and a simulation experiment show that the recently documented empirical properties of strong persistence in volatility and forecastability of future realized volatility from current implied volatility, which have been interpreted as long memory (or fractional integration) in volatility and fractional cointegration between implied and realized volatility, are accounted for by occasional common level shifts.
Applied Economics Letters | 2012
Massimiliano Caporin; Paolo Santucci de Magistris
In the analysis of systemic risk, Marginal Expected Shortfall (MES) may be considered to evaluate the marginal impact of a single stock on the market Expected Shortfall (ES). 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 MES. We then suggest how to improve the evaluation of MES by means of a second-order approximation.
Archive | 2011
Massimiliano Caporin; Eduardo Rossi; Paolo Santucci de Magistris
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.
Social Science Research Network | 2017
Andrea Barletta; Paolo Santucci de Magistris; David Sloth
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.