Wavelet Multiresolution Analysis of High-Frequency Asian FX Rates, Summer 1997

A General Fractional White Noise Theory And Applications To Finance

“…Our work extends that of Hu and Øksendal (2000) to the case where the Hurst parameter can be any number H in the interval (0, 1), rather than only in (1/2, 1). This is not only of mathematical interest but is motivated by work of Los and Karuppiah (1997) where empirical evidence is given of a Hurst parameter with values in (0, 1/2) for foreign exchange rates. Anderson and Bollerslev (1997) and Müller, Dacorogna and Pictet (1998) demonstrate the presence of long‐term dependence and heavy tailed distributions in high frequency financial data.…”

Ruin probability at a given time for a model with liabilities of the fractional Brownian motion type: A partial differential equation approach

“…[5], foreign exhange rates, see e.g. [6] and weather derivatives [7] and references therein). Furthermore, fractional Brownian motion (as a special case of self similar process) has been used recently to model the claims an insurance business may face (see eg.…”

Construction of Models for Bounded Price Processes: The Case of the HKD Exchange Rate

“…There is overlap between the various statistical distributions proposed for stock prices and foreign exchange rates, for example, the Gaussian distribution which was used by Black and Scholes (1973), stable distributions (Mandelbrot, 1963;Fama, 1963;McFarland et al, 1982), the Student distribution (Blattberg and Gonedes, 1974;Boothe and Glassman, 1987) and distributions with time-varying parameters (Hsieh, 1988). Foreign exchange processes have also been characterized as autoregressive time series with conditional heteroscedasticity (ARCH) (Baillie and Bollerslev, 2002) and self-similar fractals (Müller et al, 1990;Los and Karuppiah, 2002) especially when highfrequency intraday data is considered.…”