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on Market Microstructure |
| By: | Emmanuel Bacry; Jean-Francois Muzy |
| Abstract: | We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix by a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequently that the second-order properties fully characterize Hawkes processes. The numerical inversion of the system of integral equations allows us to propose a fast and efficient method to perform a non-parametric estimation of the Hawkes kernel matrix. We discuss the estimation error and provide some numerical examples. Applications to high frequency trading events in financial markets and to earthquakes occurrence dynamics are considered. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1401.0903&r=mst |
| By: | Torben G. Andersen (Northwestern University and CREATES); Oleg Bondarenko (University of Illinois at Chicago); Viktor Todorov (Northwestern University and CREATES); George Tauchen (Duke University) |
| Abstract: | We analyze the high-frequency dynamics of S&P 500 equity-index option prices by constructing an assortment of implied volatility measures. This allows us to infer the underlying fine structure behind the innovations in the latent state variables driving the movements of the volatility surface. In particular, we focus attention on implied volatilities covering a wide range of moneyness (strike/underlying stock price), which load differentially on the different latent state variables. We conduct a similar analysis for high-frequency observations on the VIX volatility index as well as on futures written on it. We find that the innovations in the risk-neutral intensity of the negative jumps in the S&P 500 index over small time scales are best described via non-Gaussian shocks, i.e., jumps. On the other hand, the innovations over small time scales of the diffusive volatility are best modeled as Gaussian with occasional jumps. |
| Keywords: | VPIN, high-frequency data, implied volatility, jump activity, Kolmogorov-Smirnov test, stable process, stochastic volatility, VIX index |
| JEL: | C51 C52 G12 |
| Date: | 2013–01–11 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2013-52&r=mst |
| By: | Wei Chen |
| Abstract: | The target of this paper is to establish the bid-ask pricing frame work for the American contingent claims against risky assets with G-asset price systems (see \cite{Chen2013b}) on the financial market under Knight uncertainty. First, we prove G-Dooby-Meyer decomposition for G-supermartingale. Furthermore, we consider bid-ask pricing American contingent claims under Knight uncertain, by using G-Dooby-Meyer decomposition, we construct dynamic superhedge stragies for the optimal stopping problem, and prove that the value functions of the optimal stopping problems are the bid and ask prices of the American contingent claims under Knight uncertain. Finally, we consider a free boundary problem, prove the strong solution existence of the free boundary problem, and derive that the value function of the optimal stopping problem is equivalent to the strong solution to the free boundary problem. |
| Date: | 2013–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1401.0677&r=mst |
| By: | Chester Curme; Michele Tumminello; Rosario N. Mantegna; H. Eugene Stanley; Dror Y. Kenett |
| Abstract: | According to the leading models in modern finance, the presence of intraday lead-lag relationships between financial assets is negligible in efficient markets. With the advance of technology, however, markets have become more sophisticated. To determine whether this has resulted in an improved market efficiency, we investigate whether statistically significant lagged correlation relationships exist in financial markets. We introduce a numerical method to statistically validate links in correlation-based networks, and employ our method to study lagged correlation networks of equity returns in financial markets. Crucially, our statistical validation of lead-lag relationships accounts for multiple hypothesis testing over all stock pairs. In an analysis of intraday transaction data from the periods 2002--2003 and 2011--2012, we find a striking growth in the networks as we increase the frequency with which we sample returns. We compute how the number of validated links and the magnitude of correlations change with increasing sampling frequency, and compare the results between the two data sets. Finally, we compare topological properties of the directed correlation-based networks from the two periods using the in-degree and out-degree distributions and an analysis of three-node motifs. Our analysis suggests a growth in both the efficiency and instability of financial markets over the past decade. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1401.0462&r=mst |