Related papers: On return rate implied by behavioural present valu…
The Price equation provides a formal account of selection building on a right-total mapping between two classes of individuals, that is usually interpreted as a parent-offspring relation. This paper presents a new formulation of the Price…
We calculate the realized volatility in the spin model of financial markets and examine the returns standardized by the realized volatility. We find that moments of the standardized returns agree with the theoretical values of standard…
This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the…
The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice non-trivial (non-Gaussian) fluctuations of the measured…
In this contribution we describe a novel procedure to represent fuzziness in rating scales in terms of fuzzy numbers. Following the rationale of fuzzy conversion scale, we adopted a two-step procedure based on a psychometric model (i.e.,…
Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…
We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention…
Here a novel idea to handle imprecise or vague set viz. Pseudo fuzzy set has been proposed. Pseudo fuzzy set is a triplet of element and its two membership functions. Both the membership functions may or may not be dependent. The hypothesis…
One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility…
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends…
This paper investigates how realized and option implied volatilities are related to the future quantiles of commodity returns. Whereas realized volatility measures ex-post uncertainty, volatility implied by option prices reveals the…
In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and…
We propose a mathematical model for the word-of-mouth communications among stock investors through social networks and explore how the changes of the investors' social networks influence the stock price dynamics and vice versa. An investor…
We give a geometrically motivated measure of skewness, define a mean value triangle number, and dispersion (in that order) of a fuzzy number without reference or seeking analogy to the namesake but parallel concepts in probability theory.…
In a discrete time stochastic model of a pension investment funds market Gajek and Kaluszka(2000a) have provided a definition of the average rate of return which satisfies a set of economic correctnes postulates. In this paper the average…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
In the information-based approach to asset pricing the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market…
The time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In…
We describe how the market-based average and volatility of the "actual" return, which the investors gain within their market sales, depend on the statistical moments, volatilities, and correlations of the current and past market trade…
A standard approach to building a fuzzy controller based on stochastic logic uses binary random signals with an average (expected value of a random variable) in the range [0, 1]. A different approach is presented, founded on a…