Martingale representations for diffusion processes and backward stochastic differential equations

In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of continuous Hunt processes under certain technical conditions. In particular we establish the martingale representation theorem for the martingale parts of (reflecting) symmetric diffusions in a bounded domain with a continuous boundary. Together with an approach put forward in Lyons et al(2009), our martingale representation theorem is then applied to the study of initial and boundary problems for quasi-linear parabolic equations by using solutions to backward stochastic differential equations over the filtered probability space determined by reflecting diffusions in a bounded domain with only continuous boundary.Comment: 28 page

Do steel prices move together? : a cointegration test

Lack of international comparability in crude steel prices presents a problem in constructing an econometric model of the global steel market. The commonly used measures of crude steel prices are the weighted average of the prices of steel products and the index of the weighted average of prices based on a certain year. But in the context of constructing an econometric model of the global steel market, these measures are not comparable internationally. If the various product prices are cointegrated, it is appropriate to use the price of the most widely produced and traded product in the model (uncoated steel sheet) as an indicator of the general movement of crude steel prices. This paper concludes that the price of uncoated steel sheet cointegrates with the prices of other steel products in France and Germany. The same is not true of the United States, which may point to quality problems with the price data. Use of the price data of uncoated steel sheet as the indicator of crude steel prices in the global steel model would thus seem appropriate for capturing long-term price movements of various steel products. Using cointegration tests, this paper also investigates the relationship between macroeconomic variables and steel product prices.Primary Metals,Environmental Economics&Policies,Markets and Market Access,Access to Markets,Economic Theory&Research

Application of flexible functional forms to substitutability among metals in U.S. industries

This report looks at the use of a new functional form - the Symmetric Generalized Mcfadden Cost Function (SGM) - to estimate substitutability among metals in five U.S. industries. The SGM specification has the advantage of imposing curvature conditions globally on the cost function, thus ensuring that the results satisfy basic, widely believed economic theory. For the first time, this study assumes separability in estimating an SGM system, and experiments with a"bootstrapping"technique to estimate the standard errors of parameters derived from flexible functional forms. The paper provides empirical evidence of structural change in U.S. industry. A jump in the own-price elasticities of energy during the sample period coincided with a sharp increase in oil prices. The SGM flexible functional form found aluminum and steel to be complementary in four out of five industries but suggests that they are substitutes in the technically compensated sense: when total metals use is constant, an increase in the price of one metal reduces consumption of that metal and increases consumption of the other. Use of the bootstrapping technique provided insights into the stability of the elasticity estimates. The results are promising at the aggregate level when the number of free parameters is not large compared to the sample size. Bootstrapping also clarifies the problem at the disaggregated level where most elasticities are not significantly different from zero.Primary Metals,Mining&Extractive Industry (Non-Energy),Montreal Protocol,Environmental Economics&Policies,Coastal and Marine Resources

Risk management in sub-Saharan Africa

This paper investigates the vulnerability of countries in sub - Saharan Africa to uncertainty about commodity prices, exchange rates, and interest rates. It discusses some of the instruments these countries can use to manage financial risk and conclude that instruments linked to commodity prices would significantly reduce their risk. To account for possible interactions between external risks, the paper estimates the optimal portfolio of financial instruments for sub - Saharan Africa. It shows that the risk-minimizing portfolio for sub - Saharan Africa comprises only about 30 percent of general-obligation loans and about 70 percent of loans for which repayment obligations are indexed to the price of sub - Saharan Africa's most important exports: cocoa, coffee, cotton, copper, and oil. This portfolio reduces by about 90 percent the uncertainty of sub - Saharan Africa's resources available for imports. The risk-reduction benefit of the optimal portfolio is fairly stable for specific commodities included and for the specific period for which it is estimated.Insurance&Risk Mitigation,Financial Intermediation,Banks&Banking Reform,Economic Theory&Research,Environmental Economics&Policies

Does exchange rate volatility hinder export growth? Additional evidence

The authors examine the impact of exchange rate volatility on trade, using and ARCH-in-mean model. The advantages of this statistical approach over earlier approaches is that it provides more efficient coefficient estimates and it prevents the problem of spurious regressions. They applied the model to six countries, estimating both bilateral and aggregate exports. The results led to the hypothesis that the impact of exchange rate volatility may be influenced by the invoicing of exports. Also, one can argue that the effect of exchange rate volatility on trade is overstated, for the following reasons: exchange rate volatility does not measure the added riskiness of a firm's portfolio;exchange rates can provide a natural hedge in a firm's portfolio; exchange rates may be negatively correlated with each other or with the firm's other assets; and finally, the use of forward markets can provide a useful short-term hedge.Economic Stabilization,Environmental Economics&Policies,Macroeconomic Management,Fiscal&Monetary Policy,Economic Theory&Research

Optimal hedging strategy revisited : acknowledging the existence of nonstationary economic timeseries

Recognizing that a country's commodity prices, foreign exchange rates, and export earnings are related, earlier studies developed an optimal portfolio model based on an integrated approach. But the estimates were inefficient because they summed that the time series data used in the model were stationary. As a result, the model produced unstable solutions that were sensitive to exogenous changes. Many economic time series - include aggregate consumption, national income, exchange rates, interest rates, commodity prices, and volume of trade - are nonstationary (drift over time). A shock to the nonstationary series has a permanent effect. Problems of nonsense regression or spurious regression can rise when performing regression with nonstationary series. To correct the problem, the authors used Engle and Granger's (1987) vector error correction (VEC) specification in the optimal portfolio estimation process. The VEC approach expands the application of the optimal portfolio model to nonstationary economic time series data. They apply the new approach to data for Papua New Guinea in an analysis of optimal hedging of commodity price and exchange rate risks using commodity-linked bonds and varying the mix of foreign-currency-dominated borrowings. They find the time series of commodity prices and foreign exchange rate to be nonstationary. When the VEC approach is applied, the results are comparable to those from the earlier study where the nonstationary was ignored. The optimal portfolio of commodity-linked bonds and foreign currency borrowings derived from the new model shows more significant risk reduction (measured by ex-ante risk reduction) and less sensitivity to changes in assumption about the real interest rate. In addition, establishing the cointegration relationships among the commodity prices and foreign exchange rates makes it easier to develop economic institutions in explaining the composition of the optimal portfolio. TheVEC's most significant advantage, however, is the stability achieved in the optimal portfolio solutions to changes in assumptions because of the superior long-run properties of the cointegration and error-correction representation.Fiscal&Monetary Policy,Insurance&Risk Mitigation,Statistical&Mathematical Sciences,Economic Theory&Research,Environmental Economics&Policies

Managing financial risks in Papua New Guinea : an optimal external debt portfolio

This report shows that Papua New Guinea's assets and liabilities may be poorly balanced for debt servicing. Thus, it could benefit substantially from active risk management, especially through better selection of the financial instruments in its debt portfolio. The authors present a model and estimate of an optiomal debt portfolio that allows for the use of commodity-linked bonds and conventional debt denominated in different currencies. They judge the hedging effectiveness of this portfolio by how much the variance of expected real import is reduced. The results indicate that commodity-linked bonds could play an important role in the country's risk management strategy. They also show that the country's external debt structure is not well balanced to hedge the foreign exchange risk from the existing composition of non-U.S. dollar-denominated liabilities. The debt portfolio contains an excess of Japanese yen - and Deutschemark - denominated liabilities, while liabilities denominated in British pounds are substantially underrepresented.Economic Theory&Research,Environmental Economics&Policies,Public Sector Economics&Finance,Settlement of Investment Disputes,Strategic Debt Management

Privatization, concentration, and pressure for protection : a steel sector study

In considering whether to privatize a large state-owned steel enterprise in Argentina, the question arose: Would its sale to a consortium of large domestic enterprises, and the resulting increase in firm concentration, inevitably lead to cries for protection? To shed light on the question, the authors examine data for steel industries in the major industrial countries. They also construct a simulation of Argentina's steel sector to study the relationships between levels of industrial concentration, substitutability between domestic and imported steels, trade policy regimes, and mark-ups of domestic prices over international prices. Their simulation results show that heavier rents and economic distortions are generated through fixed-ratio import quotas (quotas that are a fixed proportion of domestic sales) than through use of a tariff or a fixed-quantity import quota. The results show why industries seeking protection prefer a fixed-ratio import restraint - a practice being used increasingly often in industrial countries. If there is not perfect substitutability between domestic and imported steels, the incentives for the Argentine industry to seek protection - particularly as a fixed-ratio quota - are greater, the more concentrated the industry is. The lesson for policymakers - who should be trying to minimize economic distortions - is that if protection is necessary, tariffs are preferable to import quotas, perhaps even to the point of making quota-type restrictions unconstitutional. The simulation results for Argentina confirm that the less substitutable domestic and foreign goods are, the higher the rents of domestic industry can extract. So, it is important for policymakers implementing privatization schemes to ease any explicit or implicit obstacles to imports by such measures as: (a) standardizing domestic product classifications with international classifications; (b) modernizing transportation facilities to improve the speed of shipment and communication; (c) reducing bureaucratic practices related to trade in goods and services; and (d) releasing foreign exchange restrictions. The goal should be to make a foreign transaction as easy as a domestic transaction.TF054105-DONOR FUNDED OPERATION ADMINISTRATION FEE INCOME AND EXPENSE ACCOUNT,Markets and Market Access,Access to Markets,Environmental Economics&Policies,Economic Theory&Research