Price Equation Research Articles

Selection and biodiversity change

There is a great need to understand how and why biodiversity, which we define as the variety of organisms found in a given place, changes over time. Current estimates suggest strikingly slow change in traditional measures of biodiversity. These estimates seem to contradict rapid shifts in the abundance of individual species and have led to a rethinking of the mechanisms shaping biodiversity. Conceptual models emphasise the role of competition among species or, more recently, selection on species identity (i.e. selection that favours some species at the expense of others). However, it is difficult to quantify how these mechanisms contribute to biodiversity change. To illustrate this point, we present cases where strong competition or selection on species identity leads to no biodiversity change. In view of this disconnect, we develop a new approach to studying biodiversity change using the Price equation. We show that biodiversity change responds to selection on species’ rarity, rather than to either competition or selection on species identity. We then show how this insight can be used to quantify the effects of the mechanisms previously thought to influence biodiversity: (1) selection, (2) (ecological) drift, (3) immigration and (4) speciation. Our results suggest the connection between species’ fates and their rarity is fundamental to understanding biodiversity change.

Price equation captures the role of drug interactions and collateral effects in the evolution of multidrug resistance.

Bacterial adaptation to antibiotic combinations depends on the joint inhibitory effects of the two drugs (drug interaction [DI]) and how resistance to one drug impacts resistance to the other (collateral effects [CE]). Here we model these evolutionary dynamics on two-dimensional phenotype spaces that leverage scaling relations between the drug-response surfaces of drug-sensitive (ancestral) and drug-resistant (mutant) populations. We show that evolved resistance to the component drugs - and in turn, the adaptation of growth rate - is governed by a Price equation whose covariance terms encode geometric features of both the two-drug-response surface (DI) in ancestral cells and the correlations between resistance levels to those drugs (CE). Within this framework, mean evolutionary trajectories reduce to a type of weighted gradient dynamics, with the drug interaction dictating the shape of the underlying landscape and the collateral effects constraining the motion on those landscapes. We also demonstrate how constraints on available mutational pathways can be incorporated into the framework, adding a third key driver of evolution. Our results clarify the complex relationship between drug interactions and collateral effects in multidrug environments and illustrate how specific dosage combinations can shift the weighting of these two effects, leading to different and temporally explicit selective outcomes.

The Role of Trust Indicators in a Digital Platform: A Differentiated Goods Approach in an Airbnb Market

We employed a differentiated goods market analysis where we utilized, in addition to the prevailing goods’ attributes, different types of the sellers’ attributes including trust indicators. We incorporated both sets of attributes into a structural model of the whole market including demand and pricing equations with the hotels as an outside good. Applying the model to Stockholm’s Airbnb market reveals that hosts’ attributes significantly affect market performance. Simulations of market scenarios show that the very high review scores and the Superhost certification help Airbnb compete with hotels and increase profitability. We also show that the “Airbnb plus” luxury program, which makes the apartments a closer substitute for hotels, leads to an increase in Airbnb’s market welfare. Our analysis provides a framework for understanding the full impact of the different attributes of the products, their providers, and their management in the sharing-economy accommodation market.

Win some, lose some: Mesocosm communities maintain community productivity despite lower phosphorus availability because of increased species diversity

AbstractAimsThe restoration of degraded ecosystems typically focuses on establishing assemblages of target species, but successful recovery should also be evaluated by the ecosystem's functioning to guarantee long‐term persistence. We investigated how the processes underlying community assembly (i.e. species loss, species gain and changes in abundance of resident species) influenced ecosystem functioning in experimental grassland communities in different states of restoration.LocationA greenhouse experiment in northern Flanders, Belgium.MethodsWe set up a mesocosm experiment with communities of 19 planted species, ranging from slow‐growing species from poorly productive Nardus grasslands to fast‐growing species from highly productive Lolium perenne grasslands. We categorised the mesocosms into different grassland restoration states based on known abiotic and biotic restoration barriers for semi‐natural grassland restoration: soil phosphorus levels and soil biota communities. After two growing seasons, we used the CAFE approach, an ecological application of the Price equation, to partition the effects of plant community assembly on ecosystem functioning (here community productivity) for the different restoration states.ResultsAdding soil biota communities sampled from reference Nardus grasslands vs more intensively managed grasslands did not have a significant effect on either plant species richness or biomass productivity. Lower soil phosphorus concentrations (i.e. abiotic restoration) resulted in a higher plant species richness. However, the net effect on productivity was close to zero. The increase in productivity caused by species gains was compensated through decreases in productivity caused by species loss and by decreases in the abundance or functioning of species that are present in both abiotically degraded and abiotically restored states.ConclusionsNot only species richness but also species identity resulted in changes in ecosystem functioning (i.e. productivity), even though the net functional effects were close to zero. More specifically, we found that species richness‐driven increases in productivity were counterbalanced by resource‐driven and species identity‐driven reductions in productivity.

Estimation of nonstationary nonparametric regression model with multiplicative structure

Summary This paper presents a multiplicative nonstationary nonparametric regression model which allows for a broad class of nonstationary processes. We propose a three-step estimation procedure to uncover the conditional mean function and establish uniform convergence rates and asymptotic normality of our estimators. The new model can also be seen as a dimension-reduction technique for a general two-dimensional time-varying nonparametric regression model, which is especially useful in small samples and for estimating explicitly multiplicative structural models. We consider two applications: estimating a pricing equation for the US aggregate economy to model consumption growth and estimating the shape of the monthly risk premium for S&P 500 Index data.

Linking changes of forage production and digestibility with grassland community assembly under nitrogen enrichment

BackgroundForage production is the fundamental ecosystem service of grasslands. Although forage consumption occurs at community level, most studies focused on species-level changes of forage quality. The quantitative and qualitative changes of forage production are driven by species-specific trait, intra-specific plasticity, and species turnover. We examined the changes in forage production and digestibility after 5-year factorial treatments of nitrogen (N) addition and mowing in a temperate steppe and linked such changes to community assembly under the Price equation framework.ResultsNitrogen addition significantly reduced species richness, increased forage production, but did not change forage digestibility (indicated by the total Ca+Mg concentrations). Mowing did not affect forage production and digestibility. The positive effects of N addition on forage production were driven by the enhancement of abundance of the remaining species following N enrichment, rather than by species loss or species gain. The species identity effects could offset the effects of species richness loss or gain on forage production and digestibility.ConclusionsOur results highlight the importance of a community perspective in addressing the quantitative and qualitative changes of forage production under global change pressure of N enrichment. Species identity is important in determining the contribution of different processes of community assembly to ecosystem services.

Corporate Valuation: Analyzing the Theoretical Valuations of Stylized Corporates

Corporations are viewed as perpetual derivatives securities with cash flows defined by deterministic functions of state variables. In time homogeneous and Markovian contexts the valuation of corporate is given by a deterministic function of the state variables. The resulting value function solves an integro-differential equation with a boundary condition of zero at infinity. Solutions are illustrated in dimensions one, two and ten. It is observed that for positive and bounded cash flow functions the value functions cannot be linear. The attitude of a corporate to risk depends on the nonlinearity. In higher dimensions the corporate will typically be a risk taker in some directions and simultaneously a risk avoider in other directions. The valuation theory also leads to new asset pricing equations inferring asset variations from risk neutral covariations. The shift from mean returns and covariances is necessitated by the focus on instantaneous risk exposures represented by measures replacing probabilities.

Discounting the Discounted Projection Approach

U.K. equity release actuaries are using a flawed approach to value the no-negative equity guarantees in their equity release mortgages. The approach they use, the discounted projection approach, incorrectly uses projected future house prices as the underlying prices in their put option pricing equations. The correct approach uses forward house prices. The discounted projection approach entails significant undervaluations of no-negative equity guarantees and overvaluations of equity release mortgages and can produce valuations that violate rational pricing principles. The discounted projection approach is also inconsistent with both actuarial and accounting standards. Our results have significant ramifications for equity release industry practice and prudential regulation.

LOCALIZED RADIAL BASIS FUNCTIONS FOR NO-ARBITRAGE PRICING OF OPTIONS UNDER STOCHASTIC ALPHA–BETA–RHO DYNAMICS

AbstractClosed-form explicit formulas for implied Black–Scholes volatilities provide a rapid evaluation method for European options under the popular stochastic alpha–beta–rho (SABR) model. However, it is well known that computed prices using the implied volatilities are only accurate for short-term maturities, but, for longer maturities, a more accurate method is required. This work addresses this accuracy problem for long-term maturities by numerically solving the no-arbitrage partial differential equation with an absorbing boundary condition at zero. Localized radial basis functions in a finite-difference mode are employed for the development of a computational method for solving the resulting two-dimensional pricing equation. The proposed method can use either multiquadrics or inverse multiquadrics, which are shown to have comparable performances. Numerical results illustrate the accuracy of the proposed method and, more importantly, that the computed risk-neutral probability densities are nonnegative. These two key properties indicate that the method of solution using localized meshless methods is a viable and efficient means for price computations under SABR dynamics.

English

In this paper we study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial diferential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare obtained solutions to existing semi-closed pricing formulas. Special attention is paid to the solution of Heston model at the boundary with vanishing volatility.

Pricing options on a mean-reverting asset by the analytical operator splitting method

In this paper, we propose an operator splitting method to valuate options on the inhomogeneous geometric Brownian motion. By exploiting the approximate dynamical symmetry of the pricing equation, we derive a simple closed-form approximate price formula for a European call option which resembles closely the Black–Scholes price formula for a European vanilla call option. Numerical tests show that the proposed method is able to provide very accurate estimates and tight bounds of the exact option prices. The method is very efficient and robust as well.

Pricing external barrier options under a stochastic volatility model

An external barrier option has a random variable which determines whether the option is knock-in or knock-out. In this paper, we deal with the pricing of the external barrier option under a stochastic volatility model incorporated by a fast mean-reverting process. By using a singular perturbation method (asymptotic analysis) on the given partial differential equation for the option price, and applying the double Mellin transform technique and the method of images, we derive the corrected option price, which is an explicit analytical approximated solution for the external barrier option. For numerical experiments, we verify the price accuracy of the external barrier option with a stochastic volatility model by comparing the approximated option price with the option price obtained by Monte Carlo simulation. Finally, we investigate the behavior and sensitivity of option prices to model parameters.

Economic valuation of cultural ecosystem services: The case of landscape aesthetics in the agritourism market

Natural and agricultural landscapes provide a wide range of ecosystem services, among which are aesthetic landscapes. As these services have no direct market value, land use decision makers often ignore them in favor of urban sprawl, resulting in suboptimal resource allocation. Here, we suggest a novel method to evaluate the aesthetic landscape services of natural and agricultural ecosystems using the case of the agritourism market in Israel. We model the agritourism market as an oligopolistic market with differentiated products and formulate an equilibrium model with structural, double nested logit demand and pricing equations. The structural equations are expressed as a function of the attributes of the agritourism firm, among which are the components of landscape view. We use aggregate market data and GIS data to estimate the structural model. In the case of urban sprawl, the welfare loss is estimated at US$29,000–53,000 per km2, depending on the type of ecosystem that is forgone, whereas in agricultural sprawl over natural areas, the welfare loss is estimated at US$38,000 per km2. This welfare loss can be considered the economic value of landscape aesthetics services to the agritourism market. These findings illustrate the potential of using this valuation method for other ecosystems in other markets.

Application of the Generalized Laplace Homotopy Perturbation Method to the Time-Fractional Black–Scholes Equations Based on the Katugampola Fractional Derivative in Caputo Type

In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations are a powerful tool in studying fractal geometry and fractal dynamics. Fractional differential equations are used in modeling the various important situations or phenomena in the real world such as fluid flow, acoustics, electromagnetic, electrochemistry and material science. There is an important question in finance: “Can the fractional differential equation be applied in the financial market?”. The answer is “Yes”. Due to the self-similar property of the fractional derivative, it can reply to the long-range dependence better than the integer-order derivative. Thus, these advantages are beneficial to manage the fractal structure in the financial market. In this article, the classical Black–Scholes equation with two assets for the European call option is modified by replacing the order of ordinary derivative with the fractional derivative order in the Caputo type Katugampola fractional derivative sense. The analytic solution of time-fractional Black–Scholes European call option pricing equation with two assets is derived by using the generalized Laplace homotopy perturbation method. The used method is the combination of the homotopy perturbation method and generalized Laplace transform. The analytic solution of the time-fractional Black–Scholes equation is carried out in the form of a Mittag–Leffler function. Finally, the effects of the fractional-order in the Caputo type Katugampola fractional derivative to change of a European call option price are shown.

Changes in tree size, not species diversity, underlie the low above‐ground biomass in natural forest edges

AbstractQuestionsForest's above‐ground biomass is an important component of the global carbon cycle and, in forest fragments, it tends to decrease near the edges. This edge effect on biomass can be due to the number and identity of species residing at edges or due to the context of edges constraining plant functioning regardless of the species. Here, we took advantage of species‐rich natural forest edges to test the role of species richness, composition, and context dependency in explaining why forest edges stock less above‐ground biomass than interiors.LocationGallery forests in Brazilian savanna (latitude 21° S, longitude 44° W).MethodsWe tested the relationship between species richness and above‐ground biomass in 49 forest plots (10,142 trees). We used a novel adaptation of the Price equation to calculate the impact of species composition (losses and gains) and context dependency on the differences of above‐ground biomass between edges and interiors.ResultsDifferences in species richness and composition did not explain the lower above‐ground biomass of forest edges when compared to interiors. Biomass responses were context‐dependent, in which the same species achieved smaller sizes when it grew in the edge than in the interior.ConclusionsOur study shows that edge effects on biomass may operate independently of biodiversity as edges and interiors had a similar number of species but distinct above‐ground biomass. Indeed, in the studied natural forest patches, the edge context itself limits plant size and, thus, the above‐ground biomass stock. Beyond unveiling the underlying causes of edge effects on forest biomass, our results call for distinct policies to conserve both the carbon stocks in forest interiors but also the unique diversity of natural edges.

The formal foundation of an evolutionary theory of reinforcement

Reinforcement learning is often described by analogy to natural selection. However, there is no coherent theory relating reinforcement learning to evolution within a single formal model of selection. This paper provides the formal foundation of such a unified theory. The model is based on the most general description of natural selection as given by the Price equation. We extend the Price equation to cover reinforcement learning as the result of a behavioral selection process within individuals and relate it to the principle of natural selection via the concept of statistical fitness predictors by means of a multilevel model of behavioral selection.The main result is the covariance-based law of effect, which describes reinforcement learning on a molar level by means of the covariance between behavioral allocation and a statistical fitness predictor. We further demonstrate how this abstract principle can be applied to derive theoretical explanations of various empirical findings, like conditioned reinforcement, blocking, matching and response deprivation.Our model is the first to apply the abstract principle of selection to derive a unified description of reinforcement learning and natural selection within a single model. It provides a general analytical tool for behavioral psychology in a similar way that the theory of natural selection does for evolutionary biology. We thus lay the formal foundation of a general theory of reinforcement as the result of behavioral selection on multiple levels.

A fractional reduced differential transform method for solving time fractional Black Scholes American option pricing equation

In this paper, fractional reduced differential transform method (FRDTM) is operated to solve time fractional Black-Scholes American option pricing equation paying no dividends.The Black-Scholes model plays a significant role in the evaluation of European or American call and put options. The advantage of the proposed method to other existing methods is that it finds the solution without discretization or transformation. While using this method, no recommended assumptions are needed and hence the computational work reduces to a greater extent. Numerical experiments prove that the proposed method is efficient and valid for obtaining the solution of time fractional Black-Scholes equation governing American options. This method proves to be powerful for solving general fractional order partial differential equations (PDEs) existing in the field of Science, Engineering and other related fields.

ESTIMATING DEMAND FOR GOOD CLIMATE AND AIR QUALITY IN TAIWAN

We measure the amenity values of climate and air quality in Taiwan using the two-step hedonic price method (HPM). Separate hedonic housing price equations, one for each of three metropolitan areas that represent respective housing markets in Northern, Central, and Southern Taiwan, are estimated. We find evidence of a significant impact of climate and air quality on housing prices. As expected, residents in Taiwan prefer a warmer winter, cooler summer, lower humidity, and better air quality. Based on the results of the housing price regression, we compute implicit prices for environmental amenities, and then pool observations from all three metropolitan areas to estimate the demand for environmental amenities. The estimated demand functions for environmental amenities are used to evaluate the benefits and losses from changes in climate and air quality in Taiwan. Our results show that, compared to the benefits of a higher temperature in January, the losses from the rise in temperature in July are much higher in such a way that global warming is resulting in significant net losses in Taiwan. The area-specific welfare analysis in this study will help in informing climate change policy formulation and decision-making in Taiwan.

Electricity pricing using a periodic GARCH model with conditional skewness and kurtosis components

Abstract This paper extends the investigation of the stochastic properties of electricity price growth rates beyond their first two conditional moments allowing for the impact of seasonality on their parameters. The main contributions include the breakdown of electricity price risk into its pure and skewness price components and the development of a risk neutral forecasting equation for electricity prices. Empirical results using ten-years of hourly wholesale prices from the Day-Ahead electricity market in Germany depict the presence of seasonality, strong mean reversion and up-to third degree time-varying moments.

Hedonic housing prices and environmental quality in Lebanon

Purpose This study aims to examine the impact of local air pollution on housing prices in Lebanon. Design/methodology/approach The authors apply a hedonic pricing approach using a unique data set from Lebanon. To account for non-linearities in pricing, the authors use three different functional regression forms for the hedonic model approach. The authors also deal with potential omitted variable bias by estimating a hedonic frontier specification. Findings The authors find that, in all specifications, air pollution negatively and significantly affects housing prices. The estimated marginal willingness to pay for a one microgram per cubic meter change in particulate matter (PM10) concentration ranges between 2.88% and 3.18% of mean housing prices. The authors also provide evidence of a negative pricing gradient away from the city center, landing support for the monocentric urban development hypothesis. Research limitations/implications Given the lack of a data set linking household socioeconomic characteristics with housing data, the authors only consider the first-stage hedonic model. Practical implications The proposed hedonic pricing regression approximates a housing pricing equation that can be used by policymakers. Social implications The findings suggest that pollution is a significant factor in household behavior in Lebanon. Originality/value This paper adds to the scant literature studying the effects of air pollution on housing prices in developing countries. To the best of the authors’ knowledge, this is the first paper to study the impact of pollution on housing prices in a country in the Middle East and North Africa Region.