We overview different methods of modeling stock prices and exchange rates volatility, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of volatility change across the time scales of observations. Adequacy of volatility models for describe price dynamics at several time horizons simultaneously Special attention is a central topic of...

It is commonly accepted that certain financial data exhibit long-range dependence. We consider a continuous time stochastic volatility model in which the stock price is Geometric Brownian Motion with volatility described by a fractional Ornstein-Uhlenbeck process. We also study two discrete time models: a discretization of the continuous model via an Euler scheme and a discrete model in which t...

The Black-Scholes equation is a hallmark of mathematical finance, and any study of this growing field would be incomplete without having seen and understood the logic behind this equation. The initial focus of this paper will be to explore the arguments leading to the equation and the financial background necessary to understand the arguments. The problem of estimating the only parameter which ...

Exchanges adopted several circuit breakers and program trading limits following the 1987 Stock Market Crash. The intended purpose of these policies was to reduce volatility. Unfortunately, there has not been enough extreme volatility to conclusively determine whether they have been effective. The lack of volatility does not demonstrate their effectiveness since extreme volatility is very rare. ...

1 This paper was presented at the ECB workshop “The Measures and Determinants of Financial Market Uncertainty”, at the 2002 meeting of the European Finance Association in Berlin, the Bank for International Settlements and the Oesterreichische Nationalbank. We are grateful to Claudio Borio, Eli Remolona, Christian Upper and an anonymous referee for their helpful comments. The opinions expressed ...

The goal of this paper is to assess, for the rst time, the empirical impact of "Keynes’ beauty contest", or "higher order beliefs", on asset price volatility. The paper shows that heterogeneous expectations induce higher order beliefs and that heterogeneous expectation asset pricing models theoretically generate more volatility than rational expectation models. The paper also explains how, wit...

We empirically examine the impact of trading activities on the liquidity of individual equity options measured by the proportional bid–ask spread. There are three main findings. First, the option return volatility, defined as the option price elasticity times the stock return volatility, has a much higher power in explaining the spread variations than the commonly considered liquidity determina...

I document that durable consumption growth is highly persistent and predicted by the price-dividend ratio. This provides strong and direct evidence for the existence of a highly persistent expected component. I also document robust evidence that durable consumption growth is left skewed and exhibits time-varying volatility. These properties motivate a model for durable consumption growth as dri...

The goal of this paper is to assess, for the first time, the empirical impact of ”Keynes’ beauty contest”, or ”higher order beliefs”, on asset price volatility. The paper shows that heterogeneous expectations induce higher order beliefs and that asset pricing models with heterogeneous expectations theoretically generate more volatility than rational expectation models. The paper also explains h...

The stock market has always been an attractive area for researchers since no method has been found yet to predict the stock price behavior precisely. Due to its high rate of uncertainty and volatility, it carries a higher risk than any other investment area, thus the stock price behavior is difficult to simulation. This paper presents a “data mining-based evolutionary fuzzy expert system” (DEFE...