Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval Dt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a nontrivial distribution of log-returns for a given time interval Dt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.
In this letter we examine two transport protocols, High-Speed TCP [1] and Scalable TCP [2] which are both sender-side varieties of TCP. Based on the fluid flow theory, we develop a general nonlinear model and use gain margin and phase margin to evaluate the stability of a closed-loop system which is composed of a transport protocol and an active queue management scheme. Our results indicate that HSTCP and STCP are stabler than standard TCP when link bandwidth, flow number and round-trip time vary.