Linear Pricing Research Articles

Prediction accuracy in mass appraisal: a comparison of modern approaches

The advancement of computational software within the last decade has facilitated enhanced uptake of mass appraisal methodologies by the valuation and prediction accuracy in computer-assisted mass appraisal community for price modelling, estimation and tribunal defence. Applying a sample of 2694 residential properties, this paper assesses and analyses a number of geostatistical approaches relative to an artificial neural network (ANN) model and the traditional linear hedonic pricing model for mass appraisal valuation accuracy and price estimation purposes. The findings demonstrate that the geostatistical localised regression approach is superior in terms of model explanation, reliability and accuracy. ANNs can be shown to perform very well in terms of predictive power, and therefore valuation accuracy, outperforming the traditional multiple regression analysis (MRA) and approaching the performance of spatially weighted regression approaches. However, ANNs retain a ‘black box’ architecture that limits their usefulness to practitioners in the field. In relation to cost-effectiveness and user-friendly applicability for the valuation community, the MRA approach outperforms the ‘black box’ nature of the ANN technique, with the geographically weighted regression approach providing the best balance of outright performance and transparency of methodology. It is this spatially weighted approach utilising absolute location which appears to represent the way forward in developing the practice of mass appraisal.

Joint Optimization of Electricity and Communication Cost for Meter Data Collection in Smart Grid

Smart grid is recently proposed as an enhancement for the next generation power grid. To achieve efficient status monitoring, control, and billing, a large number of smart meters are deployed and they would produce a huge amount of data. To efficiently collect them imposes a great challenge on the communication networks. In this paper, we study the efficient meter data collection problem by exploring the secondary spectrum market in cellular networks. The electricity power reserved by sending meter data via leased secondary channels would be charged at a lower price. With the objective of reducing the overall cost of both power and communication, we formulate a problem called cost minimization for meter data collection (CMM) that is to find optimal solution of channel selection and transmission scheduling. The CMM problem under a linear power pricing model is formulated as a mixed integer linear programming problem and is then solved by a branch-and-bound algorithm. Under a nonlinear power pricing model, we formulate it as a nonconvex mixed integer nonlinear programming problem and propose an optimal algorithm by integrating the sequential parametric convex approximation method into the branch-and-bound framework. Extensive simulation results show that our proposal can significantly reduce the overall cost.

On The Persistence Of Selectivity And Market Timing Skills In Hedge Funds

This paper investigates the persistence of hedge fund managers skills during periods of boom and/or recession. We consider a data set of monthly investment strategy indices published by Hedge Fund Research group. The data set spans from January 1995 to June 2010. We divide this sample period into four overlapping sub-sample periods that contain different economic cycles. We define a skilled manager as a manager who can outperform the market consistently during two consecutive sub-sample periods. We first estimate outperformance, selectivity and market timing skills using both linear and quadratic Capital Asset Pricing Model-CAPM. Persistence in performance is carried out in three different fashions: contingence table, chi-square test and cross-sectional auto-regression technique. The results show that fund managers have the skills to outperform the market during periods of positive economic growth only. This market outperformance is due to both selectivity and market timing skills. These results contradict the Efficient Market Hypothesis-EMH due to limited arbitrage opportunity.

Market-Share Contracts with Vertical Externalities

Abstract We construct a model of market-share contracts with vertical externalities. When a dominant supplier offers a linear wholesale price to a retailer, vertical externalities, well-recognized as double-marginalization problems, arise in the vertical relation. The dominant supplier facing vertical externalities charges a wholesale price that is excessively high for both the vertical relation and social welfare. Under market-share contracts, the retailer can commit to increase the sales of goods produced by the dominant supplier for a lower wholesale price. We point out that this induces the vertical relation to engage in market-share contracts even in the absence of exclusionary effects in the upstream market. We also show that such contracts mitigate vertical externalities and improve social welfare.

On the Antitrust Economics of the Electronic Books Industry

When Apple entered the ebook market, prices rose. A recent court decision found Apple guilty of colluding with publishers, blaming the price hike, in part, on agency agreements and prohibiting their use. Building a model to compare these with traditional wholesale agreements, we identify a single, pivotal condition that leads prices under agency to be higher than under wholesale with two-part tari s but lower with linear pricing. Our model shows that the increase in ebook prices can be explained, instead, by heightened competition for reading devices, and it guides our understanding of when restricting agency agreements is advisable.

Coordinating preventive lateral transshipment between two locations

We analyze preventive transshipment between two locations in anticipation of the mismatch between demands and inventories, and the effects of the preventive transshipment on ordering quantities. The time horizon for preventive transshipment includes two stages: the ordering stage and the shipping stage. At the ordering stage, the two locations order products from their supplier. During the replenishment lead-time, some demand signals (e.g., the realized demand for a complementary product) may be observed. Therefore, the locations may update their demand distributions and preventively transship to each other at the shipping stage. When the two locations make their ordering and transshipping decisions individually to maximize their own profits, there are incentive problems that prevent coordination. These problems arise even between the locations that pay each other for transshipped units. We examine two commonly used linear transfer price contracts: the ex ante transfer price contract and the ex post transfer price contract. However, neither of these contracts coordinates the transshipment quantities between the two locations. We then present a bidirectional revenue sharing contract that can coordinate the transshipment quantities. We find the conditions under which this proposed contract coordinates the ordering quantities. Finally, we investigate how the transportation cost and the amount of information updating affect the ordering quantities with the coordinating bidirectional revenue sharing contract.

Strict linear prices in non-convex European day-ahead electricity markets

The European power grid can be divided into several market areas where the price of electricity is determined in a day-ahead auction. Market participants can provide continuous hourly bid curves and combinatorial bids with associated quantities given the prices. The goal of our auction is to maximize the economic surplus of all participants subject to quantity constraints and price constraints. The price constraints ensure that no one incurs a loss. Only traders who submitted a combinatorial bid might miss a not-realized profit. The resulting problem is a large-scale mathematical program with equilibrium constraints (MPEC) and binary variables that cannot be solved efficiently by standard solvers. We present an exact algorithm and a fast heuristic for this type of problem. Both algorithms decompose the MPEC into a master problem (a mixed-integer quadratic program) and pricing subproblems (linear programs). The modelling technique and the algorithms are applicable to a wide variety of combinatorial auctions that are based on mixed-integer programs.

Drift Dependence of Optimal Order Execution Strategies Under Transient Price Impact

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting.

Drift dependence of optimal trade execution strategies under transient price impact

We give a complete solution to the problem of minimizing the expected liquidity costs in the presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting.

Selectivity and market timing skills in the hedge fund industry: Do they persist?

This paper investigates the persistence of hedge fund managers’ skills during periods of boom and/or recession. We consider a data set of monthly investment strategy indices published by Hedge Fund Research group. The data set spans from January 1995 to June 2010. We divide this sample period into four overlapping sub-sample periods that contain different economic cycles. We define a skilled manager as a manager who can outperform the market consistently during two consecutive sub-sample periods. We first estimate outperformance, selectivity and market timing skills using both linear and quadratic Capital Asset Pricing Model-CAPM. Persistence in performance is carried out in three different fashions: contingence table, chi-square test and cross-sectional auto-regression technique. The results show that fund managers have the skills to outperform the market during periods of positive economic growth only. This market outperformance is due to both selectivity and market timing skills. Key words: Selectivity and market timing skills, contingence table, chi-square test, market efficiency.

STRATEGIC EFFECTS OF THREE‐PART TARIFFS UNDER OLIGOPOLY

The distinct element of a three‐part tariff (3PT), compared with linear pricing (LP) or a two‐part tariff, is its quantity target within which the marginal price is zero. This quantity target instrument enriches the firm's strategy set in dictating the competition to a specific level, even in the absence of a usual price discrimination motive. With general differentiated linear demands, the competitive effect of a 3PT in contrast to LP depends on the degree of substitutability between products: Competition is intensified when two products are more differentiated, yet softened when two products are more substitutable.

PORTFOLIO LIQUIDATION IN DARK POOLS IN CONTINUOUS TIME

We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0, T] and can trade continuously at a traditional exchange (the “primary venue”) and in a dark pool. At the primary venue, trading yields a linear price impact. In the dark pool, no price impact costs arise but order execution is uncertain, modeled by a multidimensional Poisson process. We characterize the costs of trading by a linear‐quadratic functional which incorporates both the price impact costs of trading at the primary exchange and the market risk of the position. The solution of the cost minimization problem is characterized by a matrix differential equation with singular boundary condition; by means of stochastic control theory, we provide a verification argument. If a single‐asset position is to be liquidated, the investor slowly trades out of her position at the primary venue, with the remainder being placed in the dark pool at any point in time. For multi‐asset liquidations this is generally not the case; for example, it can be optimal to oversize orders in the dark pool in order to turn a poorly balanced portfolio into a portfolio bearing less risk.

The Price Impact of Order Book Events

We study the price impact of order book events - limit orders, market orders and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between supply and demand at the best bid and ask prices. Our study reveals a linear relation between order flow imbalance and price changes, with a slope inversely proportional to the market depth. These results are shown to be robust to seasonality effects, and stable across time scales and across stocks. We argue that this linear price impact model, together with a scaling argument, implies the empirically observed square-root relation between price changes and trading volume. However, the relation between price changes and trade volume is found to be noisy and less robust than the one based on order flow imbalance.

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Efficiency with Linear Prices? A Game-Theoretical and Computational Analysis of the Combinatorial Clock Auction

Combinatorial auctions have been suggested as a means to raise efficiency in multi-item negotiations with complementarities among goods because they can be applied in procurement, energy markets, transportation, and the sale of spectrum auctions. The combinatorial clock (CC) auction has become very popular in these markets for its simplicity and for its highly usable price discovery, derived by the use of linear prices. Unfortunately, no equilibrium bidding strategies are known. Given the importance of the CC auction in the field, it is highly desirable to understand whether there are efficient versions of the CC auction providing a strong game theoretical solution concept. So far, equilibrium strategies have only been found for combinatorial auctions with nonlinear and personalized prices for very restricted sets of bidder valuations. We introduce an extension of the CC auction, the CC+ auction, and show that it actually leads to efficient outcomes in an ex post equilibrium for general valuations with only linear ask prices. We also provide a theoretical analysis on the worst case efficiency of the CC auction, which highlights situations in which the CC leads to highly inefficient outcomes. As in other theoretical models of combinatorial auctions, bidders in the field might not be able to follow the equilibrium strategies suggested by the game-theoretical predictions. Therefore, we complement the theoretical findings with results from computational and laboratory experiments using realistic value models. The experimental results illustrate that the CC+ auction can have a significant impact on efficiency compared to the CC auction.

Non-Cooperative Feedback Control Game for Secondary Transmitter in Cognitive Radio Network

In this letter, we propose a non-cooperative feedback control game for secondary transmitter, where we assume that secondary users are rational and thus selfish, i.e., they will choose the feedback rate to maximize their own utility functions. The utility function of each user is defined as the downlink data-rate minus a linear price function of the channel state information (CSI) feedback rate. The existence of the Nash-equilibrium of the proposed game is analyzed. Also, in order to satisfy the primary user's interference threshold, power control algorithms are proposed. Simulation results show that the sum-rate of the proposed game is better than that of the equally distributed feedback-size scheme.

Wholesale price discrimination with interdependent retailers

This paper examines the relationship between one manufacturer and two retailers who sell a product on their downstream markets. If a retailer invests in activities that enhance demand and, for example, improve the perceived image of the product, he or she might attract more customers, as well as increase the sales volumes of other retailers. In such a situation, free rider problems arise between the retailers, which finally lead to reduced sales efforts. We show that for linear wholesale prices, the manufacturer's pricing strategy depends on the retailers' investment costs and derive conditions for the optimality of wholesale price discrimination. We find that for low and high costs the manufacturer charges the retailers identical wholesale prices and thus does not have to bear any agency costs due to free riding. In all other cases, the manufacturer mitigates this problem by engaging in wholesale price discrimination. Our results indicate why it might make sense for a manufacturer to charge different wholesale prices even when the retailers have equal cost structures, market conditions, and investment options.

Reverse Pricing and Revenue Sharing in a Vertical Market

Advancing in information technology has empowered firms with unprecedented flexibility when interacting with each other. We compare welfare results in a vertical market (e.g., manufacturers and retailers) across several types of pricing strategies depending upon (1) which side (retailers or manufacturers) chooses retail prices and (2) whether there is revenue sharing or linear pricing between the two sides. Our results are as follows. Under revenue sharing, retail prices (and thus industry profits) are higher if and only if they are chosen by the side featuring less competition. Under linear pricing, however, retail prices are higher if they are chosen by the side featuring more competition (for linear demand functions). Relative to linear pricing, revenue sharing always leads to lower retail prices, higher consumer surplus and social surplus. However, the comparison on industry profits depends on the demand elasticity ratios. Revenue sharing raises industry profits when the elasticity ratios are small, but the results are reversed when the elasticity ratios are large.

Interference Pricing for SINR-Based Random Access Game

In this paper, we study the problem of random access with interference pricing in wireless ad hoc networks using non-cooperative game theory. While most of the previous works in random access games are based on the protocol model, we analyze the game under the more accurate signal-to-interference-plus-noise-ratio (SINR) model. First, under the setting with fixed interference linear pricing, we characterize the existence of the Nash equilibrium (NE) in the random access game. In particular, when the utility functions of all the players satisfy a risk aversion condition, we show that the game is a S-modular game and characterize the convergence of the strategy profile to the NE. Then, under the setting with adaptive interference linear pricing, we propose an iterative algorithm that aims to solve the network utility maximization (NUM) problem. Convergence of the solution to a Karush-Kuhn-Tucker (KKT) point of the NUM problem is studied. It can be shown that the solution obtained under the protocol model may result in starvation for some users due to the inaccurate interference pricing. Simulation results show that our proposed algorithm based on the SINR model achieves a higher average utility than the algorithm based on the protocol model and a carrier sense multiple access (CSMA) scheme implemented in a slotted time system.

Linear Beta Pricing with Inefficient Benchmarks

Current asset pricing models require mean-variance efficient benchmarks, which are generally unavailable because of partial securitization and free float restrictions. We provide a pricing model that uses inefficient benchmarks, a two-beta model, one induced by the benchmark and one adjusting for its inefficiency. While efficient benchmarks induce zero-beta portfolios of the same expected return, any inefficient benchmark induces infinitely many zero-beta portfolios at all expected returns. These make market risk premiums empirically unidentifiable and explain empirically found dead betas and negative market risk premiums. We characterize other misspecifications that arise when using inefficient benchmarks with models that require efficient ones. We provide a space geometry description and analysis of the specifications and misspecifications. We enhance Roll (1980), Roll and Ross's (1994), and Kandel and Stambaugh's (1995) results by offering a "Two Fund Theorem," and by showing the existence of strict theoretical "zero relations" everywhere inside the portfolio frontier.