Linear Pricing Research Articles

The Nash bargaining solution in vertical relations with linear input prices

We re-examine the Nash bargaining solution when an upstream and N downstream firms bargain over a linear input price with unobservable contracts. We show that the profit sharing rule is given by a simple and instructive formula which depends on the parties’ disagreement payoffs, the profit weights in the Nash-product and the elasticity of derived demand. A downstream firm’s profit share increases in the equilibrium derived demand elasticity which in turn depends on the final goods’ demand elasticity.

Dynamic Risk Premia and Asset Pricing Puzzles

I apply a simple and intuitive econometric method to extract dynamic risk premia from the Fama-French (2015) multifactor asset pricing model. With all of the Fama-French (2015) state variables, this analysis is the first exploration of whether the pervasive asset pricing anomalies persist after the econometrician accounts for the time variation in multifactor risk premia. The ubiquitous anomalies of size, value, momentum, investment, profitability, short-term return reversal, and long-term return reversal, disappear after the econometrician takes into account the dynamic nature of multifactor risk premia. The prior linear empirical asset pricing models arise as special cases of this dynamic multifactor model. The main contribution of the current paper relates to the design of a workhorse model in the asset pricing literature. The previous linear empirical asset pricing models can be viewed as special cases of this more general dynamic multifactor model. This dynamic multifactor model carries important implications for equity cost estimation, corporate event assessment, financial risk management, and mutual fund performance evaluation. My dynamic analysis of multifactor risk premia from the Fama-French (2015) five-factor model proposes raising the hurdle for the conventional asset pricing tests. This recommendation serves as the time-series equivalent to the cross-sectional thesis of Harvey, Liu, and Zhu (2015).

Equilibrium prices and trade under ambiguous volatility

This article considers general equilibrium economies with a primitive uncertainty model that features ambiguity about continuous-time volatility. For the resulting non-equivalence of priors, an appropriate commodity-price space is introduced. Agents are heterogeneous in the size of captured ambiguity, endowment and preference for risk and ambiguity. Preferences are of variational type a la Maccheroni et al. (Econometrica 74(6):1447–1498, 2006). One important implication involves a problematic aspect of linear equilibrium price systems. Positive payoffs are for free on events outside the domain of the representing equilibrium pricing measure. Moreover, when aggregate risk is present and aggregate ambiguity is absent, the insurance properties of optimal allocations depend on the notion of ambiguity-free payoffs.

Weighted proportional fairness and pricing based resource allocation for uplink offloading using IP flow mobility

Mobile data offloading has been proposed as a solution for the network congestion problem that is continuously aggravating due to the increase in mobile data demand. However, the majority of the state-of-the-art is focused on the downlink offloading, while the change of mobile user habits, like mobile content creation and uploading, makes uplink offloading a rising issue. In this work we focus on the uplink offloading using IP Flow Mobility (IFOM). IFOM allows a LTE mobile User Equipment (UE) to maintain two concurrent data streams, one through LTE and the other through WiFi access technology, that presents uplink limitations due to the inherent fairness design of IEEE 802.11 DCF by employing the CSMA/CA scheme with a binary exponential backoff algorithm. In this paper, we propose a weighted proportionally fair bandwidth allocation algorithm for the data volume that is being offloaded through WiFi, in conjunction with a pricing-based rate allocation for the rest of the data volume needs of the UEs that are transmitted through the LTE uplink. We aim to improve the energy efficiency of the UEs and to increase the offloaded data volume under the concurrent use of access technologies that IFOM allows. In the weighted proportionally fair WiFi bandwidth allocation, we consider both the different upload data needs of the UEs, along with their LTE spectrum efficiency and propose an access mechanism that improves the use of WiFi access in uplink offloading. In the LTE part, we propose a two-stage pricing-based rate allocation under both linear and exponential pricing approaches, aiming to satisfy all offloading UEs regarding their LTE uplink access. We theoretically analyse the proposed algorithms and evaluate their performance through simulations. We compare their performance with the 802.11 DCF access scheme and with a state-of-the-art access algorithm under different number of offloading UEs and for both linear and exponential pricing-based rate allocation for the LTE uplink. Through the evaluation of energy efficiency, offloading capabilities and throughput performance, we provide an improved uplink access scheme for UEs that operate with IFOM for uplink offloading.

Early Bird Discounts and Dealer Services

We study a widely used ordering process (“Early Bird Discounts”) whereby a profit-maximizing manufacturer permits his dealers to place advance orders at a discount before they set retail prices. We show that such discounts may be used to shift just enough channel profits to dealers to enable them to cover their fixed costs and stay in business. If the manufacturer instead simply cut his wholesale price in order to generate gross margins for his dealers, these margins would soon dissipate as price competition among dealers selling the same product forced retail prices back down to the per-unit cost. We show that when dealer fixed costs are low, the manufacturer offers an Early Bird Discount to his multiple dealers that induces all but two of them to exit; when fixed costs are high, the manufacturer offers no preorder discount (i.e. switches to linear pricing) and induces all but one dealer to exit. Although uniform slotting allowances could also be used to reward dealers, a sales-based alternative like an Early Bird Discount sometimes has a key advantage when the manufacturer has dealers in cities of different sizes. If the same Early Bird Discount is offered, dealers in markets with more consumers, who typically have larger fixed costs, will preorder larger amounts and will automatically receive higher gross margins. To duplicate such payments with slotting allowances, non-uniform allowances would have to be offered to firms in different markets, which is divisive and possibly illegal.

Real Estate and Consumption Growth as Common Risk Factors in Asset Pricing Models

AbstractUsing a linear multifactor pricing model, we study the influence of equity market, the consumption growth and the return on real estate wealth on asset returns. The real estate risk factor is proxied alternatively by the National Association of Real Estate Investment Trusts (NAREIT) index, unlevered NAREIT index and National Council of Real Estate Investment Fiduciaries property index. Estimates are based on CRSP's monthly decile portfolio returns from January 1972 to December 2013 (including the Vintage REIT era and the New REIT era). Generalized method of moment results show that the real estate factor is particularly useful to explain the cross‐sectional variation of returns in the last two decades generally associated with the so‐called real estate bubble.

Risk-Averse Dynamic Arbitrage in Illiquid Markets

Arguments on the existence of dynamic arbitrage and price manipulation strategies are often invoked to guide modeling price impacts of large trades. We revisit the concept of dynamic arbitrage in illiquid markets in the presence of time-varying stochastic price impact functions and a broad class of market price dynamics. We first establish a sufficient condition under which searching in the space of F0-measurable admissible round-trip trades is enough to attain a no-dynamic arbitrage certificate. This result simplifies identifying price impact structures that rule out dynamic arbitrage and accredits the analysis in some existing literature, where its assessment is limited to the search in the set of F0-measurable round-trip trades. For time-varying stochastic linear price impact functions, we show that this condition is necessary and sufficient for the absence of dynamic arbitrage. The present quantitative analysis implies that a trader’s opinion on the existence of dynamic arbitrage opportunities for a price impact model depends on his belief about expected future price changes and expected future price impacts, which can be revised over time by the collection of new information. This motivates us to let the existence of such arbitrage opportunities not only depend on the investor’s belief on expected price movements but also depend on the trader’s risk attitude. We thus introduce the concept of risk-averse dynamic arbitrage using a general time-consistent dynamic risk measure and a risk-aversion threshold level. Similar sufficient conditions are studied under which searching in the space of static round-trip trades enables us to conclude on no-risk-averse dynamic arbitrage.

OPTIMAL LIQUIDATION AND ADVERSE SELECTION IN DARK POOLS

AbstractWe consider an investor who has access both to a traditional venue and a dark pool for liquidating a position in a single asset. While trade execution is certain on the traditional exchange, she faces linear price impact costs. On the other hand, dark pool orders suffer from adverse selection and trade execution is uncertain. Adverse selection decreases order sizes in the dark pool while it speeds up trading at the exchange. For small orders, it is optimal to avoid the dark pool completely. Adverse selection can prevent profitable round‐trip trading strategies that otherwise would arise if permanent price impact were included in the model.

Market Power of the Input Supplier, Technology Transfer and Consumer Welfare

It is believed that market power of the input supplier, charging a linear price, is detrimental for the consumers since it creates the double marginalisation problem. We show that this view may not be true if the final goods producers can adopt strategies to reduce rent extraction by the input supplier. Market power of the input supplier may encourage a final goods producer either to license its technology to a competitor with a cost advantage or to adopt a less distortionary technology licensing contract. Both these effects may create higher consumer welfare under market power of the input supplier compared to a competitive input market.

Valuing water resources in Switzerland using a hedonic price model

AbstractIn this paper, linear and spatial hedonic price models are applied to the housing market in Switzerland, covering all 26 cantons in the country over the period 2005–2010. Besides structural house, neighborhood and socioeconomic characteristics, we include a wide variety of new environmental characteristics related to water to examine their role in explaining variation in sales prices. These include water abundance, different types of water bodies, the recreational function of water, and water disamenity. Significant spatial autocorrelation is found in the estimated models, as well as nonlinear effects for distances to the nearest lake and large river. Significant effects are furthermore found for water abundance and the distance to large rivers, but not to small rivers. Although in both linear and spatial models water related variables explain less than 1% of the price variation, the distance to the nearest bathing site has a larger marginal contribution than many neighborhood‐related distance variables. The housing market shows to differentiate between different water related resources in terms of relative contribution to house prices, which could help the housing development industry make more geographically targeted planning activities.

Monotonicity and Market Equilibrium

Economic theory relates prices to quantities via ” market curves.” Typically, such curves are monotone, hence they admit functional representations. The latter invoke linear pricing of quantities so as to obtain market values. Specifically, if higher prices call forward greater supply, a convex function, bounded below by market values, represents the resulting supply curve. Likewise, if demand decreases at higher prices, a concave function, bounded above by market values, represents the attending demand curve. In short, grantedmonotonicity, market curves are described by bivariate functions, either convex or concave, appropriately bounded by linear valuations of quantities. The bounding supply (demand) function generates ask (resp. bid)valuations. Exchange and trade, as modelled here, are driven by valuation differentials, called bid-ask spreads. These disappear, and market equilibrium prevails, if all ”inverse market curves” intersect in a common price. A main issue is whether and how market agents, by themselves, may reach such equilibrium. The paper provides positive and constructive answers. As vehicle it contends with bilateral transactions.

Partial equilibrium modelling of world crude oil demand, supply and price

Oil production strategies define to a large extent the future of the world crude oil market. This paper aims at modelling the long-term world crude oil supply and demand, as well as the global oil price. The main assumption is that non-OPEC and OPEC oil producers act as price-taker and strategic players respectively. The world crude oil demand is modelled as a linear price dependent function. We compare four scenarios to diagnose the OPEC’s supply behaviour: “cartel”, “oligopoly”, “mixed-cartel” and “mixed-oligopoly”. A Mixed Complementarity Problem, MCP, is used to find the Nash equilibrium point of each game scenario. The OPEC countries maximize their individual total discounted profits in “oligopoly” scenario and their joint profit in “cartel” scenario. In “mixed-cartel” and “mixed-oligopoly” scenarios, OPEC members implement their market power on the quantities allocated to export rather than their total supply. It seems to happen often that OPEC members change their level of collaboration. As the historical statistics of 2012–2015 lie between the model results of “mixed-cartel” and “oligopoly” scenarios, it seems that OPEC’s strategy has been a mixture of the both scenarios and the reason of price collapse in 2015 was that OPEC cartel structure weakened. Model outputs show that oil price will soar again in all scenarios. OPEC’s production strategy can push this price soar back most in the “mixed-oligopoly” scenario to 2026.

Effects of Oil Price Shocks on the Ghanaian Economy

The economy of Ghana is highly vulnerable to fluctuations in the international price of crude oil. This is due to the fact that oil as a commodity plays a central role in the economic activities of the nation. The objective of this paper is to investigate the dynamic relationship between oil price shocks and macroeconomic variables in the Ghanaian economy. This is achieved through the use of Vector Autoregressive (VAR) and Vector Error Correction (VECM) models. The variables considered in the study include: real oil price, real government expenditure, real industry value added, real imports, inflation and the real effective exchange rate. The study points out the asymmetric effects of oil price shocks; for instance, positive as well as negative oil price shocks on the macroeconomic variables used. The empirical findings of this study suggest that both linear and nonlinear oil price shocks have adverse impact on macroeconomic variables in Ghana. Positive oil price shocks are stronger than negative shocks with respect to government expenditure, inflation and the real effective exchange rate. Industry value added and imports have stronger responses to negative oil price shocks. Positive oil price shocks account for about 30% of fluctuations in government expenditure, 5% of imports, 6% of industry value added, 17% of inflation and 2% of the real effective exchange rate in the long run. Negative oil price shocks account for about 8% of fluctuations in government spending, 20% of imports, 8% of inflation and 2% of the real effective exchange rate in the long run. The data was obtained from the United States Energy Information Administration and the World Bank’s World Development Indicators.

Profitable Double Marginalization

When successive monopolies transact through noncooperative linear pricing, the resulting double markup decreases their joint profits relative to vertical integration. However, if there are downstream rivals (which are not double marginalized), the same noncooperative interaction often inadvertently raises their joint profits. Profit effects depend on how the well-understood harm from misaligned interests compares to the value of the resulting strategic effect. When profitable, vertical noncooperation incidentally approximates strategic delegation a la Bonanno & Vickers (1988), but avoids its credibility problem, suggesting an inability to bargain may be indirectly beneficial. The conjectural consistency concept helps to explain the disparate profit effects, and to synthesize the literature on strategic delegation and vertical control. The optimal way to distort a downstream firm's behavior is always to make it behave as if it has a conjecture, no matter the distortion mechanism. If upstream competitors do this in parallel, they induce a consistent conjectures equilibrium (CCE) -- or else a close analogue -- evincing a strong link between ordinary Nash games and the CCE.

Pricing combinatorial auctions by a set of linear price vectors

In combinatorial auctions, items are sold simultaneously. A substantial component of an auction mechanism is the pricing scheme. Prices determine the auctioneer's revenue and, ideally, justify the outcome of the auction to the bidders. Each bidder should be able to see why he won or lost a certain bundle by comparing the determined price of a bundle and his bid's value. In this paper, we pick up a non-linear anonymous pricing scheme from the literature that consists of a set of linear price vectors. We investigate whether this scheme can guarantee to find prices that support the winner allocation. Furthermore, we refine the pricing scheme by suggesting various objectives in order to evaluate different prices. We consider the computational complexity of the corresponding optimization problems and compare different objectives by means of a computational study using a well-established combinatorial auction test suite.

The skewness risk premium in equilibrium and stock return predictability

In this study, we investigate the skewness risk premium in the financial market under a general equilibrium setting. Extending the long-run risks (LRR) model proposed by Bansal and Yaron (J Financ 59:1481–1509, 2004) by introducing a stochastic jump intensity for jumps in the LRR factor and the variance of consumption growth rate, we provide an explicit representation for the skewness risk premium, as well as the volatility risk premium, in equilibrium. On the basis of the representation for the skewness risk premium, we propose a possible reason for the empirical facts of time-varying and negative risk-neutral skewness. Moreover, we also provide an equity risk premium representation of a linear factor pricing model with the variance and skewness risk premiums. The empirical results imply that the skewness risk premium, as well as the variance risk premium, has superior predictive power for future aggregate stock market index returns, which are consistent with the theoretical implication derived by our model. Compared with the variance risk premium, the results show that the skewness risk premium plays an independent and essential role for predicting the market index returns.

A pricing scheme for combinatorial auctions based on bundle sizes

In combinatorial auctions not only single items but also bundles of items are sold simultaneously. A substantial ingredient to an auction mechanism is the way prices of bundles are determined. Prices determine the auctioneer׳s revenue and, ideally, justify the outcome of the auction to the bidder. Each bidder should be able to see why he won or lost a certain bundle comparing the determined price for a bundle and his bid׳s value. It is well known that linear prices cannot guarantee such a justification. We propose a new pricing scheme adding prices for bundle sizes to the traditional linear prices for items. We analyze this scheme and evaluate its ability to provide prices supporting a given allocation by means of a computational study using a well established combinatorial auctions test suite. We also compare our scheme to a scheme from literature with respect to the ability to generate market clearing prices.

Price discrimination, entry, and switching costs in network competition

This paper reviews theoretical models of network competition in telecommunications. We will discuss two alternative approaches. The first approach assumes Hoteling?s horizontal differentiation and the second approach is based on switching costs. We will first analyse spatial competition with linear prices and continue with price discrimination between on-net and off-net calls. Price discrimination can also be used to deter entry to the market. We will also deal with the regulator?s optimal choice of access price, which should be designed to induce entry of new firms. Furthermore, pricing of roaming services and the switching cost approach to network competition will be considered. Finally, we will illustrate the theoretical results with data from the Serbian mobile and fixed telephony market.

Time-Varying Risk Premium in Large Cross-Sectional Equity Data Sets

We develop an econometric methodology to infer the path of risk premia from a large unbalanced panel of individual stock returns. We estimate the time-varying risk premia implied by conditional linear asset pricing models where the conditioning includes both instruments common to all assets and asset-specific instruments. The estimator uses simple weighted two-pass cross-sectional regressions, and we show its consistency and asymptotic normality under increasing cross-sectional and time series dimensions. We address consistent estimation of the asymptotic variance by hard thresholding, and testing for asset pricing restrictions induced by the no-arbitrage assumption. We derive the restrictions given by a continuum of assets in a multi-period economy under an approximate factor structure robust to asset repackaging. The empirical analysis on returns for about ten thousand U.S. stocks from July 1964 to December 2009 shows that risk premia are large and volatile in crisis periods. They exhibit large positive and negative strays from time-invariant estimates, follow the macroeconomic cycles, and do not match risk premia estimates on standard sets of portfolios. The asset pricing restrictions are rejected for a conditional four-factor model capturing market, size, value, and momentum effects.

Microsimulation-Based Real-Time Congestion Pricing Strategy for Managed Lane

A real-time toll that accurately reflects the congestion and delays of a system enhances a high-occupancy toll (HOT) lane system. This paper extends an existing system-optimal real-time congestion pricing strategy by relaxing the assumption of constant capacity, which allows one to implement the strategy on a dynamic microsimulation of the HOT lane, whose capacity and that of general purpose lanes vary because of the weaving activity at the end of the HOT lane. It was found that the proposed model was superior in total delay savings, particularly when bottleneck capacities varied significantly. A clear linear relationship was also found between the pricing coefficient and dimensionless delays and the pricing coefficient and revenue. These findings strengthen the system-optimal linear toll pricing strategy and suggest that departments of transportation can implement practical toll systems that incorporate the real-time discharge rates of bottlenecks.