Price Equation Research Articles

Climbing the ladder? The gender gap in art prices across artists’ cohorts in the Dutch art market

This study focuses on gender-based price differences across age cohorts in the primary art market, where art is sold for the first time, largely by living artists. This is an area that remains underexplored due to a lack of data on artwork sales. We use an exclusive dataset from the Mondriaan Fund, consisting of 10,922 paintings sold, under the Kunstkoopregeling scheme, by 663 Dutch artists from 2000 to 2010 in the Netherlands. Given the presence of significant unobserved heterogeneity, we use finite mixture models to estimate hedonic painting price equations and to decompose the gender price gap. Additionally, we use the standard Oaxaca–Blinder model to compare our results with a more traditional approach to estimating gender differences. Our findings indicate that the significant gender price imbalance for the oldest cohort is smaller in the second cohort, and is insignificant for the youngest one. The present study provides important implications for understanding gender differentials in labour market outcomes within cultural markets and other creative industries.

An Integration of Sraffa's Price Equations inside Marx's Capitalist Monetary Circulation

ABSTRACT This paper explores the integration of Sraffa's prices in Marx's ‘money-commodity-money’ circuit. We develop our interpretation of Marx's theory of new value based on the so-called ‘New Interpretation’ by Foley, Duménil, and Lipietz. The value of money allows us to sum up at the aggregate level the two factors that enter the production process: the means of production (a monetary quantity) and the living labour. Regarding Sraffa, we aim to retrace the path that leads him to believe that the labour employed is not an arbitrary but a natural measure unit of prices. The main points on which to base our reasoning are: i. in Marx, the new value or value added is identified with the aggregate living labour; ii. the distinction between new value and surplus value (which is only a part of the former) is linked to the distinction between constant and variable capital; iii. in Sraffa, the equality between employed labour and national income is considered the ‘truly natural unit' of measure of prices; iv. consequently, in both approaches, the wage rate equals the share of national income that goes to labour. Finally, we develop Marx's capitalist monetary circuit including Sraffa’s prices.

Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance

The classical bond-pricing models, as important financial tools, show strong vitality in bond pricing. However, these models also expose their theoretical defects, which leads to inconsistencies with the actual observation results and usually causes the theoretical prices of bonds to be lower than the actual market prices in the financial market. In order to change this situation, considering that the price change of the underlying is regarded as a fractal transmission system, the fractal derivative is introduced into the bond-pricing equation. In order to solve the fractal bond-pricing equation, we first convert it into an equivalent equation by using a fractal two-scale transform. Only in this case can we start to study it by means of the Lie symmetry analysis method. Then the geometric vector fields, the symmetry reductions, and the exact solution to the equations are obtained. Furthermore, the dynamic behaviors of the fractal bond-pricing equation are discussed. The results show that the fractal dimension bond-pricing formula can better explain price changes in the capital market than the classical one. That is to say, the classical bond-pricing equation is only a special case of the fractal-bond pricing equation, which makes up for the defect that the theoretical bond price given by the classical bond-pricing equation is often lower than the actual market price. The results of this paper provide a basis for bond pricing in the financial market in order to seek a more appropriate and real price.

Numerical PDE-Based Pricing of Convertible Bonds Under Two-Factor Models

Convertible bonds are popular financial instruments by which firms raise capital. Owing to the various features of such bonds, especially the early-exercise call, put, and conversion provisions, they can be valued by numerical techniques only. The price of a convertible bond is driven by both the underlying stock price and the interest rate, and these two factors are correlated. Under the partial differential equation framework, a two-dimensional convection-diffusion-reaction equation containing a mixed derivative must be solved. In this work, we employ an Alternating-Direction-Implicit method, namely the Craig-Sneyd scheme to solve the two-factor pricing equation. Comparison against the commonly employed Crank-Nicolson method shows the merit of the scheme. Besides, we analyze how the different contractual features of a convertible bond affect its price.

Price's Theorem for Quaternion Variables

Price's Theorem for Quaternion Variables

A Cross-Country Examination of Mineral Import Demand and Wind Energy Generation: Empirical Insights from Leading Mineral Importers

The relevance of this research lies in the utilization of mineral goods as critical industrial inputs for the manufacture of renewable energy machinery, which has sparked an increase in demand and prices for essential minerals. The purpose of the study is to examine the import-demand function for metallic mineral goods by applying the quantiles via moments (MM-QR) approach, considering the potential heterogeneity across the sample of the top 5 mineral-consuming (importing) nations. The dataset, covering the years 1996-2021, is analysed to test the hypothesis regarding the influence of wind production capacity on mineral-import requirements, considering the price of mineral goods, exchange rates, and income growth. We observe a monotonic favourable response of mineral import demands to wind power generation across all quantiles. However, when considering the quadratic form of wind energy generation, the mineral import demand shows a monotonic reverse trend as the size of wind energy generation expands. Our results reveal the unexpected finding of a monotonic positive effect of copper prices on mineral import demand, which contradicts the Marshallian price theorem. Conversely, the reaction of mineral imports to exchange rates remains consistently positive without modulation. Additionally, we observe a non-monotonic association between the income factor and mineral imports, indicating that the mineral import response to economic growth remains positive until a specific threshold is reached, beyond which it tends to stabilize. The theoretical and practical significance of these findings lies in boosting mineral goods trade to advance the clean energy transition goal for a decarbonized global environment.

Effect of Monetary Indicators on Agricultural Prices: Evidence from Turkiye

This study sought to reveal the effects of Turkish Lira and US dollar exchange rate (EXR), money supply (M2) on agricultural commodity producers’ prices. The direction and the size of the relationship among the data was estimated using VECM Vector Error Correction Model (VECM). The results reveal that the causality runs from M2 to agricultural price (AP) in the short run, but not from AP to M2. In the long run the effect of EXR is more than M2. The coefficient of error correction term in the agricultural price equation is 0.0726 and is statistically significant at 1%. Referring to it, all of the system instability can be adjusted approximately in 14 months. This research shows that the exchange rate (EXR) and money supply (M2) have important long-run effects on agricultural prices (AP). In order to control agricultural prices, it is necessary to follow these macro variables closely.

Functional consequences of animal community changes in managed grasslands: An application of the CAFE approach.

In the midst of an ongoing biodiversity crisis, much research has focused on species losses and their impacts on ecosystem functioning. The functional consequences (ecosystem response) of shifts in communities are shaped not only by changes in species richness, but also by compositional shifts that result from species losses and gains. Species differ in their contribution to ecosystem functioning, so species identity underlies the consequences of species losses and gains on ecosystem functions. Such research is critical to better predict the impact of disturbances on communities and ecosystems. We used the "Community Assembly and the Functioning of Ecosystems" (CAFE) approach, a modification of the Price equation to understand the functional consequences and relative effects of richness and composition changes in small nonvolant mammal and dung beetle communities as a result of two common disturbances in North American prairie restorations, prescribed fire and the reintroduction of large grazing mammals. Previous research in this system has shown dung beetles are critically important decomposers, while small mammals modulate much energy in prairie food webs. We found that dung beetle communities were more responsive to bison reintroduction and prescribed fires than small nonvolant mammals. Dung beetle richness increased after bison reintroduction, with higher dung beetle community biomass resulting from changes in remaining species (context-dependent component) rather than species turnover (richness components); prescribed fire caused a minor increase in dung beetle biomass for the same reason. For small mammals, bison reintroduction reduced energy transfer through the loss of species, while prescribed fire had little impact on either small mammal richness or energy transfer. The CAFE approach demonstrates how bison reintroduction controls small nonvolant mammal communities by increasing prairie food web complexity, and increases dung beetle populations with possible benefits for soil health through dung mineralization and soil bioturbation. Prescribed fires, however, have little effect on small mammals and dung beetles, suggesting a resilience to fire. These findings illustrate the key role of re-establishing historical disturbance regimes when restoring endangered prairie ecosystems and their ecological function.

Flight ticket taxes in Europe: Environmental and economic impact

We examine the causal impact of flight ticket taxes on airline flights and derived CO2 emissions and analyse its distributional effects between airlines and travellers and within travellers. We use a dataset on flights within Europe at the airline-route level and apply a staggered difference-in-differences approach considering potential bias of the standard two-way fixed effects and the potential distorting effects of heterogeneities between treated and control routes. The main analysis focuses on low-cost airlines because connecting passengers are typically excluded from the tax. We find that flight ticket taxes have a significant overall effect on low-costs airlines supply and derived emissions: ticket taxes reduce the number of flights per airline-route by 12% on average compared to the counterfactual scenario, resulting in a 14% reduction in carbon emissions. In addition, we estimate a pricing equation using a quantile model to identify the cost pass-through rate over the distribution of the fare variable. The burden of the tax is higher for passengers paying low fares, so taxes have a stronger effect on avoidable flights with less added value and a smaller internalization of the total costs of flying.

Competition and Competitors: Evidence from the Retail Fuel Market

Policy makers and antitrust authorities are concerned about the lack of competition in the fuel retail market and its impact on consumer prices. The aim of this article is to empirically evaluate the role of the intensity of competition and competitors’ brand affiliation on retail fuel prices. To this end, we use a panel data set with detailed daily on nearly 8,500 gas stations and 2 million price observations; we estimate a reduced-form fuel price equation that accounts for supply (input costs and local competition) and demand shifters (income, traffic intensity, and location) as well as for brand and time fixed effects. We use an instrumental variable estimation strategy, to account for the endogeneity of the intensity of competition. Our results show that premium brands and low-cost brands affect the prices of rival firms in an opposite way. On the one hand, premium brands soften competition in the local markets where they operate and thereby allow their rivals to set higher prices. Besides, price setting by premium-brand stations react differently depending on whether the nearest rival sells the same brand (a friendly competitor) or some other brand. By contrast, low-cost brands contribute to reducing prices through their own prices (direct effect), thereby encouraging competitors to lower their prices (indirect effect). Our results suggest that regulation limiting the entry of premium operators whilst promoting the entry of low cost gas stations will enhance competition at the retail level.

The modified homotopy perturbation method and its application to the dynamics of price evolution in Caputo-fractional order Black Scholes model

BackgroundFollowing a financial loss in trades due to lack of risk management in previous models from market practitioners, Fisher Black and Myron Scholes visited the academic setting and were able to mathematically develop an option pricing equation named the Black–Scholes model. In this study, we address the solution of a Caputo fractional-order Black–Scholes model using an analytic method named the modified initial guess homotopy perturbation method.MethodologyForemost, the classical Black Scholes model relaxed for European option style is generalized to be of Caputo derivative. The introduced method is established by coupling a power series function of arbitrary order with the renown He’s homotopy perturbation method. The convergence of the method is demonstrated using the fixed point theorem, and its methodology is illustrated by solving a generalized theoretical form of the fractional order Black Scholes model. The applicability of the method is proven by solving three different fractional order Black–Scholes equations derived from different market scenarios and its effectiveness is confirmed as feasible series of arbitrary orders that accelerate fast to the exact solution at an integer order were obtained. The computation of these results was carried out using Mathematica 12 software. Subsequently, the obtained outcomes were utilized in Maple 18 software to conduct a series of numerical simulations. These simulations aimed to analyze the influence of the fractional order on the dynamics of payoff functions regarding the share value as the option approached its expiration date under varying market constraints. In all three scenarios, the results showed that option values decrease as the expiration date approaches the integer order. Furthermore, the comparative outcomes reveal that Caputo fractional order derivatives control the flexibility of the classical Black–Scholes model because its payoff curve exhibits more sensitivity to changes associated with market characteristic parameters, such as volatility and interest rates.RecommendationsWe propose that the results of this work should be examined and implemented by mathematicians and economists to better comprehend the influence of Caputo-fractional order derivatives in understanding the dynamics of option price evolution of financial assets.

Widespread shifts in body size within populations and assemblages.

Biotic responses to global change include directional shifts in organismal traits. Body size, an integrative trait that determines demographic rates and ecosystem functions, is thought to be shrinking in the Anthropocene. Here, we assessed the prevalence of body size change in six taxon groups across 5025 assemblage time series spanning 1960 to 2020. Using the Price equation to partition this change into within-species body size versus compositional changes, we detected prevailing decreases in body size through time driven primarily by fish, with more variable patterns in other taxa. We found that change in assemblage composition contributes more to body size changes than within-species trends, but both components show substantial variation in magnitude and direction. The biomass of assemblages remains quite stable as decreases in body size trade off with increases in abundance.

Multilevel selection 1, multilevel selection 2, and the Price equation: a reappraisal

The distinction between multilevel selection 1 (MLS1) and multilevel selection 2 (MLS2) is classically regarded as a distinction between two multilevel selection processes involving two different kinds of higher-level fitness. It has been invoked to explain evolutionary transitions in individuality as a shift from an MLS1 to an MLS2 process. In this paper, I argue against the view that the distinction involves two different kinds of processes. I show, starting from the MLS2 version of the Price equation, that it contains the MLS1 version if, following the assumption that a collective constitutively depends (i.e., mereologically supervenes) on its particles, one considers that a necessary map between fitness at two levels exists. I defend the necessity of such a map, making the distinction between MLS1 and MLS2 a matter of perspective and limited knowledge (i.e., epistemic limitations) rather than objective facts. I then provide some reasons why the MLS1/MLS2 distinction nonetheless has some pragmatic value and might be invoked usefully in some contexts, particularly within the context of explaining evolutionary transitions in individuality.

Fractional Pricing Models: Transformations to a Heat Equation and Lie Symmetries

The study of fractional partial differential equations is often plagued with complicated models and solution processes. In this paper, we tackle how to simplify a specific parabolic model to facilitate its analysis and solution process. That is, we investigate a general time-fractional pricing equation, and propose new transformations to reduce the underlying model to a different but equivalent problem that is less challenging. Our procedure leads to a conversion of the model to a fractional 1 + 1 heat transfer equation, and more importantly, all the transformations are invertible. A significant result which emerges is that we prove such transformations yield solutions under the Riemann–Liouville and Caputo derivatives. Furthermore, Lie point symmetries are necessary to construct solutions to the model that incorporate the behaviour of the underlying financial assets. In addition, various graphical explorations exemplify our results.

Do petrol prices rise faster than they fall? Evidence from the UK retail and wholesale petrol sectors

This study investigates the presence of price asymmetries in the UK retail and wholesale petrol sectors over the period of January 2020–July 2022. The scope of this research is to explore whether petrol prices rise faster than they fall according to changes in input costs, namely fuel and international crude oil prices for the retail and wholesale sector respectively. As the time sample considers the shocks of covid-19 restrictions and rising inflation, the presence of structural breaks is assumed which may contribute to asymmetric behaviour. The Autoregressive Distributive Lag (ARDL) approach is implemented in the pricing equation of the model by formulating four versions for each sector, according to the presence of asymmetries and price-cost margins. The results provide significant evidence of price asymmetries in the retail petrol sector; however, such asymmetries are less pronounced over high margin periods. The wholesale sector is found to be more flexible to changes in crude oil prices as asymmetries are less persistent throughout the sample. Therefore, consumers face rigid petrol prices because of retail firms’ decisions, which should be the focus of policy makers.

Niche construction and the environmental term of the price equation: How natural selection changes when organisms alter their environments.

Organisms construct their own environments and phenotypes through the adaptive processes of habitat choice, habitat construction, and phenotypic plasticity. We examine how these processes affect the dynamics of mean fitness change through the environmental change term of the Price Equation. This tends to be ignored in evolutionary theory, owing to the emphasis on the first term describing the effect of natural selection on mean fitness (the additive genetic variance for fitness of Fisher's Fundamental Theorem). Using population genetic models and the Price Equation, we show how adaptive niche constructing traits favorably alter the distribution of environments that organisms encounter and thereby increase population mean fitness. Because niche-constructing traits increase the frequency of higher-fitness environments, selection favors their evolution. Furthermore, their alteration of the actual or experienced environmental distribution creates selective feedback between niche constructing traits and other traits, especially those with genotype-by-environment interaction for fitness. By altering the distribution of experienced environments, niche constructing traits can increase the additive genetic variance for such traits. This effect accelerates the process of overall adaption to the niche-constructed environmental distribution and can contribute to the rapid refinement of alternative phenotypic adaptations to different environments. Our findings suggest that evolutionary biologists revisit and reevaluate the environmental term of the Price Equation: owing to adaptive niche construction, it contributes directly to positive change in mean fitness; its magnitude can be comparable to that of natural selection; and, when there is fitness G × E, it increases the additive genetic variance for fitness, the much-celebrated first term.

A continuous heterogeneous agent model for multi-asset pricing and portfolio construction under market matching friction

We propose a novel continuous Heterogeneous Agent Model (HAM) that applies to the general n>1 risky assets. In this model, every heterogeneous investor is identified with the continuous variables reflecting their personal characteristics. The heterogeneity of the market is captured by the distribution of these variables. By introducing market friction via a matching-based pricing mechanism, we derive a pricing equation from market clearing. The equation extends the classical CAPM and specifies how the bounded rationality and heterogeneity of investors can drive the actual price of risky assets away from their CAPM price. A system of ordinary (stochastic) differential equations are derived to govern the evolution of the total wealth and market value of risky assets held by the entire market (individual investors). From the equation system, a rolling-window-based maximum likelihood algorithm is developed to calibrate the model, which turn our HAM to a forecast tool for stock returns and an adaptive adjustment strategy for portfolio construction. This bridges the theoretical study on HAMs with the empirical studies of asset pricing and portfolio theory. We apply this tool to the Chinese A-share market and make a comparative analysis on its performance. The results demonstrate that compared to the classical forecast approaches in literature, our HAM has the advantage in identifying the tail risk in real market, which results in a more profitable portfolio in a variety of different investment horizons.

Calculations of fractional derivative option pricing models based on neural network

The work adopts the neural network algorithm to derive optimized series solutions of fractional option pricing equations. The studied models include Caputo time-fractional equation and space-time fractional differential equations. The solutions of fractional derivative models are made up of the time variable and the kernel functions of RBF neural network. According to the characteristics of the models, the information function, the test solution, the output function and the loss function are established in turn. And then the optimal parameters of the solution structures of fractional derivative models are calculated by the designed neural network in conjunction with Chinese market data. For Caputo time-fractional model, the pricing results under different kernel functions, with or without cluster analysis, are compared through numerical analysis and illustration. The results of cluster analysis are better than those without cluster analysis. For space-time fractional models, comparative studies between the pricing results under Caputo and conformable fractional derivatives and those from conformable fractional derivative are made and analyzed by the market data. The numerical simulations indicate that the space-time fractional derivative models have strong predictive abilities. Application analyses show that it is feasible and operable for fractional calculus tool and neural network algorithm to jointly act on the pricing problems of financial derivatives.

Heuristic Rules for the Dynamic Pricing Problem

This paper is devoted to the development of heuristics for the dynamic pricing problem. A discrete time model of dynamic pricing on the fixed time horizon is proposed. It is applicable to products that satisfy two properties: 1) product value expires at a certain predetermined date, and 2) consumers demand at most a single unit of the product. This type of demand structure allows deriving a simple system of recursive equations for optimal prices using dynamic programming techniques. Optimal pricing policy is expressed as a function of time to expiration and inventory levels of unsold products. An analytical solution to this problem was obtained for special cases, while for the general case, a numerical algorithm has been developed. Qualitative characteristics of the optimal pricing policy are established, and their implications for dynamics of inventories and prices are discussed. Based on these observations, a simple heuristic rule for dynamic price adjustments is proposed. Performance of this heuristic is evaluated against the optimal dynamic and fixed-price policies using Monte-Carlo experiments. Results demonstrate high efficiency of the proposed heuristic strategy and its even simpler derivatives. Heuristics’ adaptability and ease of implementation should make it suitable and attractive for small and medium businesses.

Analytical Solution of Biological Population of Fractional Differential Equations by Reconstruction of Variational Iteration Method

This article presents a brand-new approximation analytical technique we refer to as the reconstruction of variational iteration method. For the goal of solving fractional biological population option pricing equations, this methodology was created. In certain circumstances, you may actually use the well-known Mittag-Leffer function to get an explicit response. The usage of the three examples below demonstrates the precision and effectiveness of the suggested method. The results show that the RVIM is not only quite straightforward but also very successful at resolving non-linear problems.