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Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the…
We investigate statistics of dynamical exchange events in coarse--grained models of supercooled liquids in spatial dimensions $d=1$, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
Analogies between the price dynamics in the foreign exchange market and 3-dimensional fully developed turbulence were recently presented in Nature vol. 381, 767-769 (1996). Independently, we have carried out a study comparing the parallel…
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such…
We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that…
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely…
Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and quantify the relation between trading activity - measured by the number of…
In this note we investigate the consistency under inversion of jump diffusion processes in the Foreign Exchange (FX) market. In other terms, if the EUR/USD FX rate follows a given type of dynamics, under which conditions will USD/EUR follow…
Statistical dynamics of financial systems is investigated, based on a model of a randomly coupled equation system driven by a stochastic Langevin force. Anticorrelations of price returns, and subdiffusion of prices is found from the model,…
We study the performance of the euro/Swiss franc exchange rate in the extraordinary period from September 6, 2011 and January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Based on the…
The decentralized international market of currency trading is a prototypical complex system having a highly heterogeneous composition. To understand the hierarchical structure relating the price movement of different currencies in the…
We propose the sum and the difference of the normalized velocity of two-joint systems to describe its long-range interaction. It is found that the conditional probability distribution function (CPDF) of the normalized velocity between…
The paper focuses on the link between information, investors' expectations and market price movement. EUR/USD market is examined from communication-theoretical perspective on the dynamics of information and meaning. We build upon the…
The Foreign Exchange market is a significant market for speculators, characterized by substantial transaction volumes and high volatility. Accurately predicting the directional movement of currency pairs is essential for formulating a sound…
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model…
We show that time-dependent fluctuations $\{\Delta x\}$ in foreign exchange rates are accurately described by a random walk in a complex plane that is demarcated into the gain (+) and loss (-) sectors. $\{\Delta x\}$ is the outcome of $N$…
In this article, we provide representations of European and American exchange option prices under stochastic volatility jump-diffusion (SVJD) dynamics following models by Merton (1976), Heston (1993), and Bates (1996). A Radon-Nikodym…
An empirical analysis on Eurodollar interest rates daily data in the time period 1990-1996, is performed and compared with Libor data in the time period 1984-1998. The complementary cumulative distributions for the daily fluctuations at…
The modelling of financial markets presents a problem which is both theoretically challenging and practically important. The theoretical aspects concern the issue of market efficiency which may even have political implications…