Bilateral Price Research Articles

Preference changes and index number theory

AbstractThe economic approach to the cost of living index assumes that consumer preferences remain constant over time. This assumption poses little risk in calculating a short‐run intertemporal bilateral price index. The assumption, however, breaks down in the case of a fixed‐based time series index spanning a long period and in the context of international comparison. The economic analysis of preference changes, however, is not well‐established. In this paper, we review the economic approach in index numbers under preference changes. Suggestions are made on how to approach the problem and their implications for the measurement of price and quantity indices.

HPR107 Bilateral Price Comparison of 50 Particularly Cost-Intensive Drugs – What Is the Impact of Different Reimbursement Rules?

HPR107 Bilateral Price Comparison of 50 Particularly Cost-Intensive Drugs – What Is the Impact of Different Reimbursement Rules?

Bilateral Pricing of Ride-Hailing Platforms Considering Cross-Group Network Effect and Congestion Effect

The pricing of ride-hailing platforms (e.g., Didi Rider and Uber) is heavily and simultaneously influenced by the cross-group network effect and congestion effect. To analyze the bilateral pricing of ride-hailing platforms under the influence of these two effects, in this paper we construct a game-theoretic model under four different scenarios and analyze the equilibrium outcomes. The results show that: (1) when both passengers and drivers are sensitive to hassle costs, if the cross-group network effect on the passenger side is higher than that on the driver side, then the platform’s pricing on both sides increases with the increase in the congestion effect, otherwise the prices on both sides of the platform decrease with the increase in the congestion effect; (2) when passengers are sensitive to hassle costs and drivers are sensitive to price, if the ratio for passengers’ and drivers’ different perceptions of price and hassle cost is greater than a certain threshold, then the platform’s pricing on the passenger side increases with the increase in the congestion effect and the platform’s pricing on the driver side decreases with the increase in the congestion effect, otherwise the platform’s pricing on the passenger side decreases with the increase in the congestion effect and the platform’s pricing on the drivers’ side increases with the increase in the congestion effect; (3) when passengers are sensitive to price and drivers are sensitive to hassle costs, if the ratio for passengers’ and drivers’ different perceptions of price and hassle costs is greater than a certain threshold, then the platform’s pricing on the passenger side decreases with the increase in the congestion effect and the platform’s pricing on the drivers’ side increases with the increase in the congestion effect, otherwise the platform’s pricing on the passenger side increases with the increase of the congestion effect and the platform’s pricing on the driver side decreases with the increase in the congestion effect; (4) when both passengers and drivers are price-sensitive, if the cross-group network effect on the passengers’ side is larger than that on the drivers’ side, then the platform should decrease its pricing on both sides with the increase in the congestion effect, otherwise, if the cross-group network effect on the passengers’ side is less than that on the drivers’ side, the platform should increase its pricing on both sides with the increase in the congestion effect; (5) the platform is able to generate the highest profit in each scenario, and the results of the profit comparison between the four scenarios depends on the cross-group network effects and the congestion effects on both the passengers’ and the drivers’ sides.

Nested Bilevel Energy Hub Bidding and Pricing With Price-Responsive Demand

The increasing interdependence among different energy systems has led to the development of the integrated energy system (IES), where the energy hub (EH) is a primary market player in the distribution-level energy market. In an EH, subsystems such as electric, natural gas, and heating systems coexist and are interdependent. This paper proposes an innovative bilevel strategic decision-making framework of an EH that maximizes profit in the energy market and simultaneously reallocates profit among EH subsystems through a dynamic pricing mechanism. In the upper level, the EH acts as a price maker in the day-ahead distribution electricity market for profit maximization. In the lower level, Nash-Bargaining-based profit redistribution is realized through bilateral pricing between energy subsystems in the EH, where the fairness and interests of individual subsystems are respected. The price-responsive load couples the profit maximization and profit reallocation problems. Case studies demonstrate that the proposed framework can effectively solve the bidding and pricing problem of an EH in a day-ahead market, and the cooperation within energy subsystems contributes to higher overall profit and better fairness for the EH subsystems.

Multiperiod Portfolio of Energy Purchasing Strategies including Climate Scenarios

Because electricity retailers must ensure that energy supply matches end-user demand, electricity that is not traded through bilateral contracts is typically traded in power exchanges which are subject to great price volatility. In Colombia, the spot price is a reflection of climate variability because approximately 70% of the country’s electricity is generated by large hydropower stations. In this study, we forecast 2018′s prices and calculated its corresponding purchase margins using the 2015 to 2017 bilateral contract prices for electricity plus power exchange price information and climate information. Our forecasts included climate uncertainty and evaluated two multi-period portfolio methods for deciding among three purchasing strategies: bilateral contracts in the regulated market, bilateral contracts in the non-regulated markets, and purchases in the power exchange. The results indicate that retailers should follow a middle course that is neither conservative nor risky. Creation of portfolios independent of the multi-period method can balance purchases through bilateral contracts and in the power exchange in a way that considers climatic uncertainty. This type of balanced portfolio could control medium-term risks of price volatility and result in good levels of purchase margins.

Penalty Methods for Bilateral XVA Pricing in European and American Contingent Claims by a PDE Model

Taking into account default risk in the valuation of financial derivatives has become increasingly important, especially after the 2007-2008 financial crisis. Under some assumptions, the valuation of financial derivatives, including a value adjustment to account for default risk (the so-called XVA), gives rise to a nonlinear PDE. We propose numerical methods for handling the nonlinearity in this PDE, the most efficient of which are discrete penalty iteration methods. We first formulate a penalty iteration method for the case of European contingent claims, and study its convergence. We then extend the method to the case of American contingent claims, resulting in a double-penalty iteration. We also propose boundary conditions and their discretization for the XVA PDE problem in the cases of call and put options, as well as the case of a forward contract. Numerical results demonstrate the effectiveness of our methods.

Model-based long-term pricing in maritime container shipping

This article reports the development and the assessment of a freight rate optimization approach based on mathematical modeling and optimization. It exploits the functional interdependency between the price of a (service) product and the quantity of the product using this price. Solving the proposed model enables a differentiated and shipper-specific rate determination accompanied by the allocation of the transport capacity provided by the carrier to different shippers. This bilateral pricing between carrier and shippers considers market-based reference rates typically available in the maritime container shipping industry. Herewith, we integrate market-based pricing with demand-based pricing. We validate the proposed model in computational experiments for an artificial pricing scenario. An analysis of the achieved results demonstrates that missing overcapacities will lead to reduced revenues if spot market prices are too low.

Dominant Currency Paradigm

We propose a “dominant currency paradigm” with three key features: dominant currency pricing, pricing complementarities, and imported inputs in production. We test this paradigm using a new dataset of bilateral price and volume indices for more than 2,500 country pairs that covers 91 percent of world trade, as well as detailed firm-product-country data for Colombian exports and imports. In strong support of the paradigm we find that (i) noncommodities terms-of-trade are uncorrelated with exchange rates; (ii) the dollar exchange rate quantitatively dominates the bilateral exchange rate in price pass-through and trade elasticity regressions, and this effect is increasing in the share of imports invoiced in dollars; (iii) US import volumes are significantly less sensitive to bilateral exchange rates, compared to other countries’ imports; (iv) a 1 percent US dollar appreciation against all other currencies predicts a 0.6 percent decline within a year in the volume of total trade between countries in the rest of the world, controlling for the global business cycle. We characterize the transmission of, and spillovers from, monetary policy shocks in this environment. (JEL E52, F14, F31, F44)

XVA: DEFINITION, EVALUATION AND RISK MANAGEMENT

xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

A Stochastic Model of Bilateral Oligopoly and Price Control for Competition on High-Tech Product Markets

We consider the problem of strategic competition management on the markets of high-tech industry. We take into account that an aggressive pricing policy in the long run can lead to suppliers leaving the market, reducing its competitiveness and increasing purchase prices. To optimize the pricing policy of customers while accounting for this effect, we propose a model of bilateral oligopoly as a closed queuing system.

When Tariffs Disturb Global Supply Chains

We study unanticipated tariffs on imports of intermediate goods in a setting with firm-to-firm supply relationships. Firms that produce differentiated products conduct costly searches for potential input suppliers and negotiate bilateral prices with those that pass a reservation level of match productivity. Global supply chains are formed in anticipation of free trade. Once they are in place, the home government surprises with an input tariff. This can lead to renegotiation with initial suppliers or new search for replacements. We identify circumstances in which renegotiation generates improvement or deterioration in the terms of trade. The welfare implications of a tariff are ambiguous in this second-best setting, but plausible parameter values suggest a welfare loss that rises rapidly at high tariff rates.

A novel decision strategy for a bilateral energy contract

Due to the relatively high transportation cost of energy in remote regions, an effective and efficient energy trading market is required. In this paper, first, we extend the idea of a smart home community architecture comprising a small number of smart homes that suit these sorts of regions. Second, we propose an energy trading market at two levels. At the top-level, global generators and global consumers participate in energy trading. At the second level, smart homes in a smart home community participate in the energy market as local generators and consumers. Third, we develop a bilateral energy trading scheme and a novel decision strategy for choosing a bilateral price for both seller and buyer. The developed strategy and energy trading schemes are more efficient than those proposed in traditional work as they require far fewer rounds for negotiations between buyers and sellers to arrive at a mutually appropriate bilateral price. Fourth, we present two distinct cases for bilateral energy trading; single seller single buyer and single seller multiple buyers and show that the latter case has more benefits for both the seller and the buyer. Lastly, we conduct a series of experiments to illustrate the effectiveness of the proposed work.

Multilateral Sato–Vartia index for international comparisons of prices and real expenditures

The Sato–Vartia (SV) index for bilateral price comparisons has impressive analytical properties and is used intensively in recent international trade and macroeconomic analyses. We show that the SV index is only one of many logarithmic indices that satisfy the factor reversal test discussed in index number theory. In this paper we propose several transitive multilateral versions of the SV index but note that these do not satisfy factor reversal test. We derive closed form expressions for the transitive logarithmic indices and empirically implement the new indices for cross-country price comparisons using World Bank data from the 2011 International Comparison Program.

Decomposing Multilateral Price Indexes into the Contributions of Individual Commodities

Abstract This article describes methods for decomposing price indexes into contributions from individual commodities, to help understand the influence of each commodity on aggregate price index movements. Previous authors have addressed the decomposition of bilateral price indexes, which aggregate changes in commodity prices from one time period to another. Our focus is the decomposition of multilateral price indexes, which aggregate commodity prices across more than two time periods or countries at once. Multilateral indexes have historically been used for spatial comparisons, and have recently received attention from statistical agencies looking to produce temporal price indexes from large and high frequency price data sets, such as scanner data. Methods for decomposing these indexes are of practical relevance. We present decompositions of three multilateral price indexes. We also review methods proposed by other researchers for extending multilateral indexes without revising previously published index levels, and show how to decompose the extended indexes they produce. Finally, we use a data set of seasonal prices and quantities to illustrate how these decomposition methods can be used to understand the influence of individual commodities on multilateral price index movements, and to shed light on the relationships between various multilateral and extension methods.

Dollar Invoicing and the Heterogeneity of Exchange Rate Pass-Through

We show empirically that the variation across country pairs in exchange rate pass-through and trade elasticity is meaningfully explained by the dollar's dominance as invoicing currency. We use a hierarchical Bayesian approach to directly and flexibly model pass-through heterogeneity conditional on the invoicing currency share. We estimate that the importer's country-level dollar invoicing share explains 15 percent of the overall variance across trading pairs in dollar exchange rate pass-through into bilateral prices.

Variation in nominal and real effective exchange rates: evidence across developed and developing countries

Recent episodes of excessive volatility in the foreign exchange market have brought to the fore the interest in studying the transmission mechanism of global uncertainty on the domestic economy. At the core is the degree of adjustment in the exchange rate as a shock absorber and the impacts of domestic policies in mitigating the spillover effects of global volatility. Using data for a sample of advanced and developing countries, the paper studies the responses of the nominal effective exchange rate, the real effective exchange rate, and price inflation to domestic and external sources of economic shifts. Subsequently, the analysis evaluates the degree of correlations between the responses of these variables to each economic shift. The objective is to study sources of movements in the real effective exchange rate and bilateral nominal exchange rates versus price inflation. The analysis then turns to evaluation of the determinants across countries of the time-series correlations between the change in the real effective exchange rate and its underlying components—nominal change and inflation—within countries over time. Cross-country regressions establish the relevance of the trend and variability of each of price inflation, the change in the nominal exchange rate, and the change in the real exchange rate on the degree of association between each pair. The evidence attests to a high pass-through from fluctuations in the nominal exchange rate to price inflation, which is more pronounced in developing countries, attesting to the need to target the real effective exchange rate as a framework for monetary policy.

Financial distress, short sale constraints, and mispricing

This paper specifically examine how the extent of the distress puzzle differs according to the degree of mispricing and short sale constraints. We find that the distress puzzle observed for overpriced stocks, not for underpriced stocks, becomes insignificant after adjustment for short sale constraints due to an asymmetric pricing effect of short sale constraints only on the short-leg side of distress. However, after adjustment for arbitrage risk, the distress puzzle remains unchanged. These results indicate that the distress puzzle is mainly attributable to short sale constraints, rather than other limits-to-arbitrages such as arbitrage risk, which has a bi-lateral pricing effect on both short-leg and long-leg sides of distress. To mitigate a possible endogeneity problem relation among financial distress, mispricing, and short sale constraints, we measure these variables with different timing.

Fair bilateral pricing under funding costs and exogenous collateralization

AbstractBielecki and Rutkowski introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts, and margin accounts. In this paper, we examine the pricing and hedging of contract from the perspective of both the hedger and the counterparty with arbitrary initial endowments. We derive inequalities for unilateral prices and we study the range of fair bilateral prices. We also examine the positive homogeneity and monotonicity of unilateral prices with respect to the initial endowments. Our study hinges on results from Nie and Rutkowski for backward stochastic differential equations (BSDEs) driven by continuous martingales, but we also derive the pricing partial differential equations (PDEs) for path‐independent contingent claims of a European style in a Markovian framework.

Interest rate swap pricing with default risk under variance gamma process

Under the assumption that the dynamic assets price follows the variance gamma process, we establish a new bilateral pricing model of interest rate swap by integrating the reduced form model for swap pricing and the structural model for default risk measurement. Our pricing model preserves the simplicity of the reduced form model and also considers the dynamic evolution of the counterparty assets price by incorporating with the structural model for default risk measurement. We divide the swap pricing framework into two parts, simplifying the pricing model relatively. Simulation results show that, for a one year interest rate swap, a bond spread of one hundred basis points implies a swap credit spread about 0.1054 basis point.

Resale Price Maintenance with Secret Contracts and Retail Service Externalities

We analyze a setting where a monopolist sells through retailers that set prices and provide valuable but non-contractible services to customers. We assume that contracts are private. We find that purely bilateral price restraints have no effect on the equilibrium outcome and that the standard Bertrand prices and service levels prevail. We also show that if manufacturers can commit to industry-wide resale prices, they can obtain higher prices and service levels but will generally not be able to achieve the fully integrated outcome. Using a specific linear demand system, we find that industry-wide price floors are harmful to consumers. (JEL L12, L42, L81, L60, D42, D86, D62)