arXiv subjects

Victor Olkhov

Publications and source records attributed to Victor Olkhov.

29 records · Page 2Linked to original sources

arXiv2021

Price, Volatility and the Second-Order Economic Theory

We introduce the price probability measure η(p;t) that defines the mean price p(1;t), mean square price p(2;t), price volatility σp2(t)and all price n-th statistical moments p(n;t) as ratio of sums of n-th degree values C(n;t) and volumes U(n;t) of market trades aggregated during certain time interval Δ. The definition of the mean price p(1;t) coincides with definition of the volume weighted average price (VWAP) introduced at least 30 years ago. We show that price volatility σp2(t) forecasting requires modeling evolution of the sums of second-degree values C(2;t) and volumes U(2;t). We call this model as second-order economic theory. We use numerical continuous risk ratings as ground for risk assessment of economic agents and distribute agents by risk ratings as coordinates. We introduce continuous economic media approximation of squares of values and volumes of agents trades and their flows aggregated during time interval Δ. We take into account expectations that govern agents trades and introduce aggregated expectations alike to aggregated trades. We derive equations for continuous economic media approximation on the second-degree trades. In the linear approximation we derive mean square price p(2;t) and volatility σp2(t) disturbances as functions of the first and second-degree trades disturbances. Description of each next n-th price statistical moment p(n;t) with respect to the unit price measure η(p;t) depends on sums of n-th degree values C(n;t) and volumes U(n;t) of market trades and hence requires development of the corresponding n-th order economic theory.

q-fin.GN↗

arXiv2021

Classical Option Pricing and Some Steps Further

This paper considers the asset price p as relations C=pV between the value C and the volume V of the executed transactions and studies the consequences of this definition for the option pricing equations. We show that the classical BSM model implicitly assumes that value C and volume V of transactions follow identical Brownian processes. Violation of this identity leads to 2-dimensional BSM-like equation with two constant volatilities. We show that agents expectations those approve execution of transactions can further increase the dimension of the BSM model. We study the case when agents expectations may depend on the option price data and show that such assumption can lead to the nonlinear BSM-like equations. We reconsider the Heston stochastic volatility model for the price determined by the value and the volume and derive 3-dimensional BSM-like model with stochastic value volatility and constant volume volatility. Variety of the BSM-like equations states the problem of reasonable balance between the accuracy and the complexity of the option pricing equations.

q-fin.PR↗

arXiv2020

Business Cycles as Collective Risk Fluctuations

We suggest use continuous numerical risk grades [0,1] of R for a single risk or the unit cube in Rn for n risks as the economic domain. We consider risk ratings of economic agents as their coordinates in the economic domain. Economic activity of agents, economic or other factors change agents risk ratings and that cause motion of agents in the economic domain. Aggregations of variables and transactions of individual agents in small volume of economic domain establish the continuous economic media approximation that describes collective variables, transactions and their flows in the economic domain as functions of risk coordinates. Any economic variable A(t,x) defines mean risk XA(t) as risk weighted by economic variable A(t,x). Collective flows of economic variables in bounded economic domain fluctuate from secure to risky area and back. These fluctuations of flows cause time oscillations of macroeconomic variables A(t) and their mean risks XA(t) in economic domain and are the origin of any business and credit cycles. We derive equations that describe evolution of collective variables, transactions and their flows in the economic domain. As illustration we present simple self-consistent equations of supply-demand cycles that describe fluctuations of supply, demand and their mean risks.

econ.GN↗

arXiv2020

Econophysics of Asset Price, Return and Multiple Expectations

This paper describes asset price and return disturbances as result of relations between transactions and multiple kinds of expectations. We show that disturbances of expectations can cause fluctuations of trade volume, price and return. We model price disturbances for transactions made under all types of expectations as weighted sum of partial price and trade volume disturbances for transactions made under separate kinds of expectations. Relations on price allow present return as weighted sum of partial return and trade volume "return" for transactions made under separate expectations. Dependence of price disturbances on trade volume disturbances as well as dependence of return on trade volume "return" cause dependence of volatility and statistical distributions of price and return on statistical properties of trade volume disturbances and trade volume "return" respectively.

econ.GN↗

arXiv2018

Econophysics Beyond General Equilibrium: the Business Cycle Model

Current business cycle theory is an application of the general equilibrium theory. This paper presents the business cycle model without using general equilibrium framework. We treat agents risk assessments as their coordinates x on economic space and establish distribution of all economic agents by their risk coordinates. We suggest aggregation of agents and their variables by scales large to compare with risk scales of single agents and small to compare with economic domain on economic space. Such model is alike to transition from kinetic description of multi-particle system to hydrodynamic approximation. Aggregates of agents extensive variables with risk coordinate x determine macro variables as functions of x alike to hydrodynamic variables. Economic and financial transactions between agents define evolution of their variables. Aggregation of transactions between agents with risk coordinates x and y determine macro transactions as functions of x and y and define evolution of macro variables at points x and y. We describe evolution and interactions between macro transactions by hydrodynamic-like system of economic equations. We show that business cycles are described as consequence of the system of economic equations on macro transactions. As example we describe Credit transactions CL(tax,y) that provide Loans from Creditors at point x to Borrowers at point y and Loan-Repayment transactions LR(t,x,y) that describe repayments from Borrowers at point y to Creditors at point x. We use hydrodynamic-like economic equations and derive from them the system of ordinary differential equations that describe business cycle fluctuations of macro Credits C(t) and macro Loan-Repayments LR(t) of the entire economics. The nature of business cycle fluctuations is explained as oscillations of "mean risk" of economic variables on bounded economic domain of economic space.

econ.GN↗

arXiv2017

Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks

This paper presents hydrodynamic-like model of business cycles aggregate fluctuations of economic and financial variables. We model macroeconomics as ensemble of economic agents on economic space and agent's risk ratings play role of their coordinates. Sum of economic variables of agents with coordinate x define macroeconomic variables as functions of time and coordinates x. We describe evolution and interactions between macro variables on economic space by hydrodynamic-like equations. Integral of macro variables over economic space defines aggregate economic or financial variables as functions of time t only. Hydrodynamic-like equations define fluctuations of aggregate variables. Motion of agents from low risk to high risk area and back define the origin for repeated fluctuations of aggregate variables. Economic or financial variables on economic space may define statistical moments like mean risk, mean square risk and higher. Fluctuations of statistical moments describe phases of financial and economic cycles. As example we present a simple model relations between Assets and Revenue-on-Assets and derive hydrodynamic-like equations that describe evolution and interaction between these variables. Hydrodynamic-like equations permit derive systems of ordinary differential equations that describe fluctuations of aggregate Assets, Assets mean risks and Assets mean square risks. Our approach allows describe business cycle aggregate fluctuations induced by interactions between any number of economic or financial variables.

econ.GN↗

arXiv2017

Non-Local Macroeconomic Transactions and Credits-Loans Surface-Like Waves

This paper describes surface-like waves of macroeconomic Credits-Loans transactions on economic space. We use agent's risk ratings as their coordinates and describe evolution of macro variables by transactions between agents. Aggregations of agent's variables with risk coordinates x on economic space define macro variables as function of x. Aggregations of transactions between agents at point x and y determine functions of two variables (x,y) on economic space. As example we study Credits transactions provided from agents at point x to agents at point y and thus amount of Loans received by agents at point y from agents at point x at moment t during time term dt. We model evolution of macro transactions by hydrodynamic-like equations. Agents fill macro domain on economic space that is bounded by minimum risk ratings of most secure and maximum risk ratings of most risky agents. Economic and financial shocks can disturb steady borders of macro domain and cause perturbations of transactions. Such disturbances can generate waves that can propagate along risk borders alike to surface waves in fluids. As example, we describe simple model interactions between two transactions by hydrodynamic like equations in a closed form. We introduce notions of "macro accelerations" and their potentials that establish steady state distributions of transactions on economic space. For this model in linear approximation we describe surface-like waves and show that perturbations induced by surface-like waves can exponentially grow up inside macro domain and induce macro instabilities in a low risk area. Description of possible steady state distributions of transactions and surface-like waves on economic space might be important for macro modeling and policy-making.

econ.GN↗

arXiv2017

Econophysics of Macro-Finance: Local Multi-fluid Models and Surface-like Waves of Financial Variables

This paper models macro financial variables alike to financial fluids with local interactions and describes surface-like waves of Investment and Profits. We regard macro-finance as ensemble of economic agents and use their risk ratings as coordinates on economic space. Aggregations of agent's financial variables with risk coordinates x on economic space define macro financial variables as function of x. We describe evolution and interactions between macro financial variables alike to financial fluids by hydrodynamic-like equations. Minimum and maximum risk grades define most secure and most risky agents respectively. That determines borders of macro-finance domain that is filled by economic agents. Perturbations of agent's risk coordinates near risk borders of macro domain cause disturbances of macro financial variables like Investment and Profits. Such disturbances can generate waves that propagate along risk borders. These waves may exponentially amplify perturbations inside of macro domain and impact financial sustainability. We study simple model Investment and Profits and describe linear approximation of steady state distributions of Investment and Profits on macro-finance domain that fulfill dreams of Investors: "more risks-more Profits". We describe Investment and Profits waves on risk border of economic space alike to surface waves in fluids. We present simple examples that specify waves as possible origin of time fluctuations of macro financial variables. Description of possible steady state distributions of macro financial variables and financial risk waves on economic space could help for better policy-making and managing sustainable macro-finance.

econ.GN↗

arXiv2017

Econophysics of Macroeconomics: "Action-at-a-Distance" and Waves

We present macroeconomic model that describes evolution of macroeconomic variables and macroeconomic waves on economic space. Risk ratings of economic agents play role of their coordinates on economic space. Aggregation of economic variables like Assets and Investment, Credits and Loans of economic agents at point x define corresponding macroeconomic variables as functions of time t and coordinates x on economic space. Evolution of macroeconomic variables is determined by economic and financial transactions between economic agents. Such transactions can occur between economic agents with any coordinates x and y and that reflect non-local "action-at-a-distance" character of internal macroeconomic interactions. For instance, Buy-Sell transactions between points x and y on economic space define dynamics of Assets at point x and Investment at point y. Aggregates of transactions between economic agents at point x and y on economic space define economic fields as functions of two coordinates. To describe dynamics of economic fields on economic space we derive hydrodynamic-like equations. For simple models of interactions between economic fields we derive hydrodynamic-like equations in a closed form and obtain wave equations for their perturbations. Economic field waves propagate on economic space and their amplitudes can grow up as exponent in time and may disturb economic stability. Diversities of macroeconomic and financial waves on economic space in simple models uncover importance of wave processes for macroeconomic modeling and forecasting.

econ.GN↗

arXiv2017

Econophysics Macroeconomic Model

This paper presents macroeconomic model that is based on parallels between macroeconomic multi-agent systems and multi-particle systems. We use risk ratings of economic agents as their coordinates on economic space. Aggregates of economic or financial variables like Investment, Assets, Demand, Credits and etc. of economic agents near point x define corresponding macroeconomic variables as functions of time t and coordinates x on economic space. Parallels between multi-agent and multi-particle systems on economic space allow describe transition from economic kinetic-like to economic hydrodynamic-like approximation and derive macroeconomic hydrodynamic-like equations on economic space. Economic or financial transactions between economic agents determine evolution of macroeconomic variables This paper describes local macroeconomic approximation that takes into account transactions between economic agents with coordinates near same point x on economic space only and describes interaction between macroeconomic variables by linear differential operators. For simple model of interaction between macroeconomic variables as Demand on Investment and Interest Rate we derive hydrodynamic-like equations in a closed form. For perturbations of these macroeconomic variables we derive macroeconomic wave equations. Macroeconomic waves on economic space can propagate with exponential growth of amplitude and cause irregular time fluctuations of macroeconomic variables or induce economic crises.

econ.GN↗

arXiv2001

Coordinate System, Temperature and Gravity

We discuss the problem of applicability of Coordinate Systems (or Frames) that determine (t,x,y,z) values - the initial notions for most physical theories. Equipment that measure these values - Clocks and Meters - are based at Reference System and are the primary measuring units. We discus when and why physical phenomena might prevent to provide measurements of (t,x,y,z). We show that Temperature may be the factor that can significantly influence on the measurements of (t,x,y,z) by Reference System and that action may violate the usage of Coordinate System. We discuss possible origin of such unmovable Temperature and assume that it should be Gravity.

gr-qc↗