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on Econometric Time Series |
| By: | Jeroen V.K. Rombouts (HEC Montréal, CIRANO, CIRPEE and Université catholique de Louvain, CORE); Lars Stentoft (HEC Montréal, CIRANO, CIRPEÉ, and CREATES); Francesco Violante (Maastricht University and Université catholique de Louvain, CORE) |
| Abstract: | We assess the predictive accuracy of a large number of multivariate volatility models in terms of pricing options on the Dow Jones Industrial Average. We measure the value of model sophistication in terms of dollar losses by considering a set 248 multivariate models that differ in their specification of the conditional variance, conditional correlation, and innovation distribution. All models belong to the dynamic conditional correlation class which is particularly suited because it allows to consistently estimate the risk neutral dynamics with a manageable computational effort in relatively large scale problems. It turns out that the most important gain in pricing accuracy comes from increasing the sophistication in the marginal variance processes (i.e. nonlinearity, asymmetry and component structure). Enriching the model with more complex correlation models, and relaxing a Gaussian innovation for a Laplace innovation assumption improves the pricing in a smaller way. Apart from investigating directly the value of model sophistication in terms of dollar losses, we also use the model confidence set approach to statistically infer the set of models that delivers the best pricing performance. |
| Keywords: | Option pricing, Economic Loss, Forecasting, Multivariate GARCH, Model Confidence Set |
| JEL: | C10 C32 C51 C52 C53 G10 |
| Date: | 2012–01–27 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-04&r=ets |
| By: | Michael C. M\"unnix; Takashi Shimada; Rudi Sch\"afer; Francois Leyvraz Thomas H. Seligman; Thomas Guhr; H. E. Stanley |
| Abstract: | The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such time series, stationary situations have been extensively studied and correlations have been found to be a very powerful tool. Yet most natural processes are non-stationary. In particular, in times of crisis, accident or trouble, stationarity is lost. As examples we may think of financial markets, biological systems, reactors or the weather. In non-stationary situations analysis becomes very difficult and noise is a severe problem. Following a natural urge to search for order in the system, we endeavor to define states through which systems pass and in which they remain for short times. Success in this respect would allow to get a better understanding of the system and might even lead to methods for controlling the system in more efficient ways. We here concentrate on financial markets because of the easy access we have to good data and because of the strong non-stationary effects recently seen. We analyze the S&P 500 stocks in the 19-year period 1992-2010. Here, we propose such an above mentioned definition of state for a financial market and use it to identify points of drastic change in the correlation structure. These points are mapped to occurrences of financial crises. We find that a wide variety of characteristic correlation structure patterns exist in the observation time window, and that these characteristic correlation structure patterns can be classified into several typical "market states". Using this classification we recognize transitions between different market states. A similarity measure we develop thus affords means of understanding changes in states and of recognizing developments not previously seen. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.1623&r=ets |
| By: | Mikio Ito; Akihiko Noda |
| Abstract: | Focusing on market efficiency varying with time, we examine whether the U.S. stock market has been evolved or not. We find that (1) the U.S. stock market evolves over time and (2) the market efficiency in the U.S. stock market has a cyclical fluctuation with very long periodicity, from 30 to 40 years. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.0100&r=ets |
| By: | Amel Bentata; Rama Cont |
| Abstract: | We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior of call options with short maturity in a semimartingale model: whereas the behavior of \textit{out-of-the-money} options is found to be linear in time, the short time asymptotics of \textit{at-the-money} options is shown to depend on the fine structure of the semimartingale. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.1302&r=ets |
| By: | Sunil Kumar; Nivedita Deo |
| Abstract: | We apply RMT, Network and MF-DFA methods to investigate correlation, network and multifractal properties of 20 global financial indices. We compare results before and during the financial crisis of 2008 respectively. We find that the network method gives more useful information about the formation of clusters as compared to results obtained from eigenvectors corresponding to second largest eigenvalue and these sectors are formed on the basis of geographical location of indices. At threshold 0.6, indices corresponding to Americas, Europe and Asia/Pacific disconnect and form different clusters before the crisis but during the crisis, indices corresponding to Americas and Europe are combined together to form a cluster while the Asia/Pacific indices forms another cluster. By further increasing the value of threshold to 0.9, European countries France, Germany and UK constitute the most tightly linked markets. We study multifractal properties of global financial indices and find that financial indices corresponding to Americas and Europe almost lie in the same range of degree of multifractality as compared to other indices. India, South Korea, Hong Kong are found to be near the degree of multifractality of indices corresponding to Americas and Europe. A large variation in the degree of multifractality in Egypt, Indonesia, Malaysia, Taiwan and Singapore may be a reason that when we increase the threshold in financial network these countries first start getting disconnected at low threshold from the correlation network of financial indices. We fit Binomial Multifractal Model (BMFM) to these financial markets. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.0409&r=ets |
| By: | J. Shen; B. Zheng |
| Abstract: | With the daily and minutely data of the German DAX and Chinese indices, we investigate how the return-volatility correlation originates in financial dynamics. Based on a retarded volatility model, we may eliminate or generate the return-volatility correlation of the time series, while other characteristics, such as the probability distribution of returns and long-range time-correlation of volatilities etc., remain essentially unchanged. This suggests that the leverage effect or anti-leverage effect in financial markets arises from a kind of feedback return-volatility interactions, rather than the long-range time-correlation of volatilities and asymmetric probability distribution of returns. Further, we show that large volatilities dominate the return-volatility correlation in financial dynamics. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.0342&r=ets |
| By: | Jozef Barunik; Lukas Vacha |
| Abstract: | This paper proposes generalization of the popular realized volatility framework by allowing its measurement in the time-frequency domain and bringing robustness to both noise as well as jumps. Based on the generalization of Fan and Wang (2007) approach using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we present new, general theory for wavelet decomposition of integrated variance. Using wavelets, we not only gain decomposition of the realized variance into several investment horizons, but we are also able to estimate the jumps consistently. Basing our estimator in the two-scale realized variance framework of Zhang et al. (2005), we are able to utilize all available data and get unbiased estimator in the presence of noise as well. The theory is also tested in a large numerical study of the small sample performance of the estimators and compared to other popular realized variation estimators under different simulation settings with changing noise as well as jump level. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Another notable contribution lies in the application of the presented theory. Our time-frequency estimators not only produce more efficient estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. The results thus provide a better understanding of the dynamics of stock markets. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.1854&r=ets |
| By: | X. F. Jiang; B. Zheng |
| Abstract: | With the random matrix theory, we study the spatial structure of the Chinese stock market, American stock market and global market indices. After taking into account the signs of the components in the eigenvectors of the cross-correlation matrix, we detect the subsector structure of the financial systems. The positive and negative subsectors are anti-correlated each other in the corresponding eigenmode. The subsector structure is strong in the Chinese stock market, while somewhat weaker in the American stock market and global market indices. Characteristics of the subsector structures in different markets are revealed. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.6418&r=ets |
| By: | Jongwook Kim; Gabjin Oh |
| Abstract: | We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation and the closed form moment generating function is obtained, thus the cumulants are calculated and shown to be convergent. The other class of distributions are numerically investigated. The concoction of the two stochastic processes of the different signs of memory under regime switching mechanism does incarnate power-law decay behavior, which strongly implies that memory is the alternative origin of heavy-tail. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.5690&r=ets |
| By: | Giacomo Livan; Luca Rebecchi |
| Abstract: | We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.6535&r=ets |
| By: | Jo\~ao P. da Cruz; Pedro G. Lind |
| Abstract: | The study of heavy-tailed distributions in economic and financial systems has been widely addressed since financial time series has become a research subject.After the eighties, several "highly improbable" market drops were observed (e.g. the 1987 stock market drop known as "Black Monday" and on even more recent ones, already in the 21st century) that produce heavy losses that were unexplainable in a GN environment. The losses incurred in these large market drop events did not change significantly the market practices or the way regulation is done but drove some attention back to the study of heavy-tails and their underlying mechanisms. Some recent findings in these context is the scope of this manuscript. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.0142&r=ets |