@incollection{statphys23_0393, title = {Statistical Physics Approach to High-Frequency Finance}, address = {Genova, Italy}, author = {M. Politi and E. Scalas}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=393}, year = {2007}, biburl = {http://www.bibsonomy.org/bibtex/23167c350008eef4a056086daec831755/statphys23}, abstract = {Based on the continuous-time random walk (CTRW) model for high-frequency financial data, we present some recent results on the following issues: \begin{itemize} \item We analyze the structure of waiting times between consecutive trades and fit them with Tsallis' $q$-exponentials and Weibull functions. Moreover, we discuss the activity spectrum based on a well-known inverse problem. \item We define stochastic integrals on CTRWs and we study the (non-Markovian) case of non-exponentially distributed waiting times. \item We price options written on CTRWs using Martingale methods. \end{itemize}}, keywords = {continuous-time econophysics integration option pricing random renewal statphys23 stochastic theory topic-11 walks } }