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Fundamental variables in financial market are not only price and return but a very important role is also played by trading volumes. Here we propose a new multivariate model that takes into account price returns, logarithmic variation of…
We present a simple approach to forecasting conditional probability distributions of asset returns. We work with a parsimonious specification of ordered binary choice regression that imposes a connection on sign predictability across…
We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are…
Applications of Quantum Tunneling effect have long gone beyond the traditional physical meaning. Initially created by Gamow to explain {\alpha}-decay of nuclear particles, along the time, quantum tunneling found fertile domain of research…
In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As…
A new approach to the understanding of the complex behavior of financial markets index using tools from thermodynamics and statistical physics is developed. Physical complexity, a magnitude rooted in the Kolmogorov-Chaitin theory is applied…
A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is…
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation…
We present an algorithm which efficiently estimates the intrinsic long-term value of a portfolio of assets on a quantum computer. The method relies on quantum amplitude estimation to estimate the mean of a novel implementation of the…
New theoretical approaches about forecasting stock markets are proposed. A mathematization of the stock market in terms of arithmetical relations is given, where some simple (non-differential, non-fractal) expressions are also suggested as…
Using the Donsker-Prokhorov invariance principle we extend the Kim-Stoyanov-Rachev-Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the…
A new approach to the understanding of complex behavior of financial markets index using tools from thermodynamics and statistical physics is developed. Physical complexity, a magnitude rooted in Kolmogorov-Chaitin theory is applied to…
Tracking a financial index boils down to replicating its trajectory of returns for a well-defined time span by investing in a weighted subset of the securities included in the benchmark. Picking the optimal combination of assets becomes a…
We introduce a new system of stochastic differential equations which models dependence of market beta and unsystematic risk upon size, measured by market capitalization. We fit our model using size deciles data from Kenneth French's data…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
In financial time series there are periods in which the value increases or decreases monotonically. We call those periods elemental trends and study the probability distribution of their duration for the indices DJIA, NASDAQ and IPC. It is…
We prove the Ito-Tanaka formula and the existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced…
Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in log normalized returns, the…
The trade of a fixed stock can be regarded as the basic process that measures its momentary price. The stock price is exactly known only at the time of sale when the stock is between traders, that is, only in the case when the owner is…
We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling…