A realistic ARCH process is set up so as to duplicate, for all practical purposes, the properties of stock time series from 1 day to 1 year. The process includes heteroskedasticity with long memory, leverage, fat-tail innovations, relative return, price granularity, and holidays. Its adequacy to...

The behavior of the implied volatility surface for European options was analysed in detail by Zumbach and Fernandez for prices computed with a new option pricing scheme based on the construction of the risk-neutral measure for realistic processes with a finite time increment. The resulting...

Long-term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default spread,...

This paper presents a complete computation of option prices based on a realistic process for the underlying and on the construction of a risk-neutral measure as induced by a no-arbitrage replication strategy. The underlying is modelled with a long-memory ARCH process, with relative returns,...

Recent progresses in option pricing using ARCH processes for the underlying are summarized. The stylized facts are multiscale heteroscedasticity, fat-tailed distributions, time reversal asymmetry, and leverage. The process equations are based on a finite time increment, relative returns,...

type="main" xml:lang="en" <p>Estimates of daily volatility are investigated. Realized volatility can be computed from returns observed over time intervals of different sizes. For simple statistical reasons, volatility estimators based on high-frequency returns have been proposed, but such...</p>

This paper investigates the scaling dependencies between measures of "activity" and of "size" for companies included in the FTSE 100. The "size" of companies is measured by the total market capitalization. The "activity" is measured with several quantities related to trades (transaction value...

This is a short review in honor of B. Mandelbrot's 80st birthday, to appear in W ilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial time series, in particular the intermittent, long-memory...